Apparatus and methods employing liquid-impregnated surfaces

Abstract

In certain embodiments, the invention is directed to apparatus comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, and methods thereof. In some embodiments, one or both of the following holds: (i) 0<ϕ≤0.25, where ϕ is a representative fraction of the projected surface area of the liquid-impregnated surface corresponding to non-submerged solid at equilibrium; and (ii) Sow(a)<0, where Sow(a) is spreading coefficient, defined as γwa−γwo−γoa, where γ is the interfacial tension between the two phases designated by subscripts w, a, and o, where w is water, a is air, and o is the impregnating liquid.

Description

TECHNICAL FIELD

This invention relates generally to non-wetting and low adhesion surfaces. More particularly, in certain embodiments, the invention relates to non-wetting, liquid-impregnated surfaces that are engineered to eliminate pinning and/or to either avoid or induce cloaking.

BACKGROUND

The advent of micro/nano-engineered surfaces in the last decade has opened up new techniques for enhancing a wide variety of physical phenomena in thermofluids sciences. For example, the use of micro/nano surface textures has provided nonwetting surfaces capable of achieving less viscous drag, reduced adhesion to ice and other materials, self-cleaning, and water repellency. These improvements result generally from diminished contact (i.e., less wetting) between the solid surfaces and adjacent liquids.

One type of non-wetting surface of interest is a superhydrophobic surface. In general, a superhydrophobic surface includes micro/nano-scale roughness on an intrinsically hydrophobic surface, such as a hydrophobic coating. Superhydrophobic surfaces resist contact with water by virtue of an air-water interface within the micro/nano surface textures.

One of the drawbacks of existing non-wetting surfaces (e.g., superhydrophobic, superoleophobic, and supermetallophobic surfaces) is that they are susceptible to impalement, which destroys the non-wetting capabilities of the surface. Impalement occurs when an impinging liquid (e.g., a liquid droplet or liquid stream) displaces the air entrained within the surface textures. Previous efforts to prevent impalement have focused on reducing surface texture dimensions from micro-scale to nano-scale.

Although not well recognized in previous studies of liquid-impregnated surfaces, the impregnating liquid may spread over and “cloak” the contacting liquid (e.g., water droplets) on the surface. For example, cloaking can cause the progressive loss of impregnating liquid through entrainment in the water droplets as they are shed from the surface.

Frost formation is another problem affecting a large variety of industries, including transportation, power generation, construction, and agriculture. The effects of frosting may lead to downed power lines, damaged crops, and stalled aircrafts. Moreover, frost and ice accumulation significantly decreases the performance of ships, wind turbines, and HVAC systems. Currently used active chemical, thermal, and mechanical techniques of ice removal are time consuming and costly in operation. Development of passive methods preventing frost and ice accretion is highly desirable. Hydrophobic surfaces have a high energy barrier for ice nucleation and low ice adhesion strength and, if properly roughened on the nano- and/or micro-scales, can repel impact of supercooled water droplets. However, the anti-icing properties of hydrophobic as well as superhydrophobic surfaces are negated once the surfaces are frosted. Frost formation and ice adhesion can also be reduced by addition of a liquid or grease onto the working surface. For example, ice adhesion to aircraft surfaces is significantly reduced through application of silicone grease, and frost formation can be prevented on exterior of freezers and heat exchangers coated with a 100 μm porous layer infused with propylene glycol antifreeze. However, in both of these cases the non-solid phases are sacrificial and can leak into the surroundings causing significant environmental problems.

There is a need for non-wetting surfaces that are robust and/or deliver optimal non-wetting properties and resist frost formation.

SUMMARY OF THE INVENTION

Described herein are non-wetting surfaces that include a liquid impregnated within a matrix of micro/nano-engineered features on the surface, or a liquid filling pores or other tiny wells on the surface. In certain embodiments, compared to previous non-wetting surfaces, which include a gas (e.g., air) entrained within the surface textures, these liquid-impregnated surfaces are resistant to impalement and frost formation, and are therefore more robust.

Impregnating fluids that cover the tops of the matrix of solid features offer a non-wetting benefit. However, at equilibrium, the impregnating liquid may not cover the tops of solid features (e.g., microposts or nanograss) of the surface without being continually replenished. Furthermore, while certain impregnating fluids do cover the tops of solid features, offering a non-wetting benefit, they often exhibit cloaking, and the impregnating fluid is depleted unless replenished.

It is discovered that liquid-impregnated surfaces can be engineered to provide resistance to impalement and to provide non-wettability, without requiring replenishment of impregnating fluid to make up for liquid lost to cloaking, and without requiring replenishment of impregnating liquid to maintain coverage over the tops of the solid features.

In one aspect, the invention is directed to an article comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) 0<ϕ≤0.25, where ϕ is a representative fraction of the projected surface area of the liquid-impregnated surface corresponding to non-submerged solid (i.e., non-submerged by the impregnating liquid, e.g., can be “non-submerged” and still in contact with water) at equilibrium (e.g., where equilibrium can encompass pseudo-equilibrium); and (ii) S_ow(v)<0, where S_ow(v) is spreading coefficient, defined as γ_wv−γ_wo−γ_ov, where γ is the interfacial tension between the two phases designated by subscripts, said subscripts selected from w, v, and o, where w is water, v is vapor phase in contact with the surface (e.g., air), and o is the impregnating liquid.

In some embodiments, 0<ϕ≤0.25, or 0.01<ϕ≤0.25, or 0.05<ϕ≤0.25. In some embodiments, S_ow(v)<0.

In some embodiments, the impregnating liquid comprises at least one member selected from the group consisting of silicone oil, propylene glycol dicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin (PAO), synthetic hydrocarbon cooligomer, fluorinated polysiloxane, propylene glycol, tetrachloroethylene (perchloroethylene), phenyl isothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene, o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene, acetylene tetrabromide, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm), tribromohydrin (1,2,3-tribromopropane), ethylene dibromide, carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbon disulfide, phenyl mustard oil, monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleic acid, and amyl phthalate.

In some embodiments, the solid features comprise at least one member selected from the group consisting of a polymeric solid, a ceramic solid, a fluorinated solid, an intermetallic solid, and a composite solid. In some embodiments, the solid features comprise a chemically modified surface, coated surface, surface with a bonded monolayer. In some embodiments, the solid features define at least one member selected from the group consisting of pores, cavities, wells, interconnected pores, and interconnected cavities. In some embodiments, the solid features comprise at least one member selected from the group consisting of posts, nanoneedles, nanograss, substantially spherical particles, and amorphous particles. In some embodiments, the solid features have a rough surface (e.g., the solid features have a surface roughness>50 nm, >100 nm, e.g., and also <1 μm). In some embodiments, the rough surface provides stable impregnation of liquid therebetween or therewithin, such that θ_{os(v),receding}<θ_c, where θ_c is critical contact angle.

In some embodiments, the liquid-impregnated surface is configured such that water droplets contacting the surface are not pinned or impaled on the surface and have a roll-off angle α of less than 40°. In some embodiments, the water droplets have a roll-off angle α of less than 35°, less than 30°, less than 25°, or less than 20°.

In another aspect, the invention is directed to an article comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) θ_{os(w),receding}=0; and (ii) θ_{os(v),receding}=0 and θ_{os(w),receding}=0, where θ_{os(w),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of water (subscript ‘w’), and where θ_{os(v),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g., air).

In another aspect, the invention is directed to a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) θ_{os(v),receding}>0; and (ii) θ_{os(w),receding}>0, where θ_{os(v),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g., air), and where θ_{os(w),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of water (subscript ‘w’).

In some embodiments, both θ_{os(v),receding}>0 and θ_{os(w),receding}>0. In some embodiments, one or both of the following holds: (i) θ_{os(v),receding}<θ_c; and (ii) θ_{os(w),receding}<θ_c, where θ_c is critical contact angle. In some embodiments, one or both of the following holds: (i) θ_{os(v),receding}<θ*_c; and (ii) θ_{os(w),receding}<θ*_c, where θ*_c=cos⁻¹(1/r), and where r is roughness of the solid portion of the surface.

In some embodiments, the article is a member selected from the group consisting of a pipeline, a steam turbine part, a gas turbine part, an aircraft part, a wind turbine part, eyeglasses, a mirror, a power transmission line, a container, a windshield, an engine part, a nozzle, a tube, or a portion or coating thereof.

In another aspect, the invention is directed to an article comprising an interior surface, said article being at least partially enclosed (e.g., the article is an oil pipeline, other pipeline, consumer product container, other container) and adapted for containing or transferring a fluid of viscosity μ₁, wherein the interior surface comprises a liquid-impregnated surface, said liquid-impregnated surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein the impregnating liquid comprises water (having viscosity μ₂).

In some embodiments, μ₁/μ₂>1. In some embodiments, μ₁/μ₂>0.1. In some embodiments, (h/R)(μ₁/μ₂)>0.1 (where h is average height of the solid features and R is the radius of the pipe or the average fluid depth in an open system). In some embodiments, (h/R)(μ₁/μ₂)>0.5. In some embodiments, R<1 mm.

In some embodiments, the impregnating liquid comprises an additive (e.g., a surfactant) to prevent or reduce evaporation of the impregnating liquid. In some embodiments, said surface comprises a pulled-up region of excess impregnating liquid (e.g., oil) extending above said solid features.

In another aspect, the invention is directed to an article comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) 0<ϕ≤0.25, where ϕ is a representative fraction of the projected surface area of the liquid-impregnated surface corresponding to non-submerged solid (i.e., non-submerged by the impregnating liquid—can be “non-submerged” and still in contact with the non-vapor phase external to the surface) at equilibrium (e.g., where equilibrium can encompass pseudo-equilibrium); and (ii) S_oe(v)<0, where S_oe(v) is spreading coefficient, defined as γ_ev−γ_eo−γ_ov, where γ is the interfacial tension between the two phases designated by subscripts, said subscripts selected from e, v, and o, where e is a non-vapor phase (e.g., liquid or semi-solid) external to the surface and different from the impregnating liquid, v is vapor phase external to the surface (e.g., air), and o is the impregnating liquid.

In some embodiments, 0<ϕ≤0.25. In some embodiments, 0.01<ϕ≤0.25. In some embodiments, 0.05<ϕ≤0.25. In some embodiments, S_oe(v)<0.

In some embodiments, the impregnating liquid comprises at least one member selected from the group consisting of silicone oil, propylene glycol dicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin (PAO), synthetic hydrocarbon cooligomer, fluorinated polysiloxane, propylene glycol, tetrachloroethylene (perchloroethylene), phenyl isothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene, o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene, acetylene tetrabromide, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm), tribromohydrin (1,2,3-tribromopropane), ethylene dibromide, carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbon disulfide, phenyl mustard oil, monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleic acid, and amyl phthalate.

In some embodiments, the solid features comprise at least one member selected from the group consisting of a polymeric solid, a ceramic solid, a fluorinated solid, an intermetallic solid, and a composite solid. In some embodiments, the solid features comprise a chemically modified surface, coated surface, surface with a bonded monolayer. In some embodiments, the solid features define at least one member selected from the group consisting of pores, cavities, wells, interconnected pores, and interconnected cavities. In some embodiments, the solid features comprise at least one member selected from the group consisting of posts, nanoneedles, nanograss, substantially spherical particles, and amorphous particles. In some embodiments, the solid features have a rough surface (e.g., the solid features have a surface roughness<1 μm). In some embodiments, the rough surface provides stable impregnation of liquid therebetween or therewithin, such that θ_{os(v),receding}<θ_c, where θ_c is critical contact angle. In some embodiments, the liquid-impregnated surface is configured such that water droplets contacting the surface are not pinned or impaled on the surface and have a roll-off angle α of less than 40°. In some embodiments, the water droplets have a roll-off angle α of less than 35°, less than 30°, less than 25°, or less than 20°.

In another aspect, the invention is directed to an article comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) θ_{os(e),receding}=0; and (ii) θ_{os(v),receding}=0 and θ_{os(e),receding}=0, where θ_{os(e),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of a non-vapor (e.g., liquid, solid, semi-solid, gel) phase external to the surface that is different from the impregnating liquid (subscript ‘e’), and where θ_{os(v),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g., air).

In another aspect, the invention is directed to an comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) θ_{os(v),receding}>0; and (ii) θ_{os(e),receding}>0, where θ_{os(v),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of vapor phase (subscript ‘v’, e.g., air), and where θ_{os(e),receding} is receding contact angle of the impregnating liquid (e.g., oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of a non-vapor (e.g., liquid, solid, semi-solid, gel) phase external to the surface that is different from the impregnating liquid (subscript ‘e’).

In some embodiments, both θ_{os(v),receding}>0 and θ_{os(e),receding}>0. In some embodiments, one or both of the following holds: (i) θ_{os(v),receding}<θ_c; and (ii) θ_{os(e),receding}<θ_c, where θ_c is critical contact angle. In some embodiments, one or both of the following holds: (i) θ_{os(v),receding}<θ*_c; and (ii) θ_{os(e),receding}<θ_c, where θ*_c=cos₋₁(1/r), and where r is roughness of the solid portion of the surface.

In some embodiments, the article is a member selected from the group consisting of a pipeline, a steam turbine part, a gas turbine part, an aircraft part, a wind turbine part, eyeglasses, a mirror, a power transmission line, a container, a windshield, an engine part, tube, nozzle, or a portion or coating thereof. In some embodiments, said surface comprises a pulled-up region of excess impregnating liquid (e.g., oil) extending above said solid features.

In some embodiments of any of the aspects described herein (e.g., herein above), the article further comprises material of said non-vapor phase external to said surface (and in contact with said surface), said article containing said non-vapor phase material [e.g. wherein the article is a container, a pipeline, nozzle, valve, a conduit, a vessel, a bottle, a mold, a die, a chute, a bowl, a tub, a bin, a cap (e.g., laundry detergent cap), and/or a tube]. In some embodiments, said material of said non-vapor phase external to said surface comprises one or more of the following: food, cosmetic, cement, asphalt, tar, ice cream, egg yolk, water, alcohol, mercury, gallium, refrigerant, toothpaste, paint, peanut butter, jelly, jam, mayonnaise, ketchup, mustard, condiment, laundry detergent, consumer product, gasoline, petroleum product, oil, biological fluid, blood, plasma.

In another aspect, the invention is directed to a method of using any article described herein (e.g., herein above), the method comprising the step of exposing said surface to water.

In another aspect, the invention is directed to a method of using the article of any one of claims 1 to 10, the method comprising the step of exposing said surface to said non-vapor phase (e.g., liquid or semi-solid) external to the surface and different from the impregnating liquid. In some embodiments, the non-vapor phase comprises one or more of the following: food, cosmetic, cement, asphalt, tar, ice cream, egg yolk, water, alcohol, mercury, gallium, refrigerant, toothpaste, paint, peanut butter, jelly, jam, mayonnaise, ketchup, mustard, condiment, laundry detergent, consumer product, gasoline, petroleum product, oil, biological fluid, blood, plasma.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the invention can be better understood with reference to the drawing described below, and the claims.

FIG. 1 illustrates a schematic cross-sectional and corresponding top view of a liquid-impregnated surface that are partially submerged.

FIG. 1(a) illustrates a schematic diagram of a liquid droplet placed on a textured surface impregnated with a lubricant that wets the solid completely.

FIG. 1(b) illustrates a schematic diagram of a liquid droplet placed on a textured surface impregnated with a lubricant that wets the solid with a non-zero contact angle in the presence of air and the droplet liquid.

FIG. 1(c) illustrates a water droplet on a silicon micro post surface (post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS (octadecyltrichlorosilane) and impregnated with silicone oil.

FIG. 1(d) illustrates a water droplet on a silicon micro post surface (post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS (octadecyltrichlorosilane) and impregnated with 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide (BMIm).

FIGS. 1(e) and 1(f) illustrate a water droplet under UV illumination when a fluorescent dye was dissolved in silicone oil and BMIm. The bottom regions show that the lubricating oils are pulled up above the texture surface (b=50 μm).

FIGS. 1(g) and 1(h) show laser confocal fluorescence microscopy (LCFM) images of the impregnated texture showing that post tops were bright in the case of silicone oil (FIG. 1(g)), suggesting that they were covered with oil, and were dark in the case of BMIm (FIG. 1(h)), suggesting that they were dry.

FIG. 1(i) illustrates an ESEM image of the impregnated texture showing the silicone oil trapped in the texture and suggesting that the film that wets the post tops is thin.

FIG. 1(j) illustrates a SEM image of the texture impregnated with BMIm showing discrete droplets on post tops indicating that a film was not stable in this case.

FIG. 1(k) illustrates schematics of wetting configurations outside and underneath a drop. The total interface energies per unit area are calculated for each configuration by summing the individual interfacial energy contributions. Equivalent requirements for stability of each configuration are also shown in FIG. 1(a).

FIG. 2 illustrates a schematic diagram of possible thermodynamic states of a water droplet placed on a lubricant-encapsulated surface. The top two schematics illustrate whether or not the droplet becomes cloaked by the lubricant. For each case, there are six possible states, as illustrated, depending on how the lubricant wets the texture in the presence of air (the vertical axis) and water (horizontal axis).

FIG. 3(a) illustrates measured velocities of water droplets as a function of substrate tilt angle for various lubricant viscosities, post spacings, and droplet sizes.

FIG. 3(b) is a schematic of a water droplet moving on a lubricant-impregnated surface showing the various parameters considered in the scaling model.

FIG. 3(c) illustrates trajectories of a number of coffee particles measured relative to the water droplet revealing that the drop rolls rather than slips across the surface.

FIG. 3(d) is a non-dimensional plot that collapses the data points shown in FIG. 3(a) onto a single curve.

FIG. 4 is a schematic describing six liquid-impregnated surface wetting states, in accordance with certain embodiments of the invention.

FIG. 5 is a schematic showing conditions for the six liquid-impregnated surface wetting states shown in FIG. 4 in accordance with certain embodiments of the invention.

FIG. 6 includes a plot of roll-off angle versus emerged area fraction ϕ and two SEM images of BMIm impregnated texture, in accordance with certain embodiments of the invention.

FIGS. 7 and 8 demonstrate condensation inhibition by preventing coalescence due to liquid cloaking, in accordance with certain embodiments of the invention.

FIG. 9 demonstrates condensation inhibition by the decreased drainage rate of oil between neighboring water droplets, particularly where the oil has high viscosity, in accordance with certain embodiments of the invention.

FIG. 10 demonstrates frost inhibition because of decreased drainage rate of oil between neighboring water droplets, particularly where the oil has high viscosity, in accordance with certain embodiments of the invention.

FIG. 11(a) shows measured roll-off angles for different encapsulating liquids as a function of post spacing b, according to some embodiments described herein. Extremely low roll-off angles were observed in some embodiments in the case of silicone oil impregnated surfaces, consistent with the post tops being encapsulated both outside and underneath the droplet (state A3-W3, θ_os(a), θ_os,w=0). The high roll-off angles seen in the case of BMIm impregnated surfaces are consistent with the post tops being emergent outside and underneath the droplet (state A2-W2, θ_c>θ_os(a), θ_os(w)>0).

FIG. 11(b) shows an SEM image of the BMIm impregnated texture and reveals that the post tops are dry, in accordance with certain embodiments of the invention.

FIG. 11(c) shows an SEM image of the posts that are further roughened by adding nanograss, the posts are covered with BMIm and consequently, the roll-off angle decreases, in accordance with certain embodiments of the invention.

FIG. 11(d) shows a non-dimensional plot of scaled gravitational force (left side of Eq. (11) discussed below) at the instant of roll-off as a function of the relevant pinning force (right side of Eq. (11) discussed below), demonstrating that the roll-off data is in general agreement with the scaling, in accordance with certain embodiments of the invention.

FIG. 12(a) is a SEM image of a silicon micropost array, in accordance with certain embodiments of the invention.

FIG. 12(b) is a SEM image of silicon microposts etched with nanograss, in accordance with certain embodiments of the invention.

FIG. 13 shows SEM images of nanograss-covered silicon micropillars impregnated with an ionic liquid (BMIm), in accordance with certain embodiments of the invention. In some embodiments, BMIm completely fills the voids between the nano-ridges, as shown on the right, resulting in almost no exposure of the solid surface to air after dip-coating (ϕ≅0).

DESCRIPTION

It is contemplated that compositions, mixtures, systems, devices, methods, and processes of the claimed invention encompass variations and adaptations developed using information from the embodiments described herein. Adaptation and/or modification of the compositions, mixtures, systems, devices, methods, and processes described herein may be performed by those of ordinary skill in the relevant art.

Throughout the description, where articles, devices, apparatus and systems are described as having, including, or comprising specific components, or where processes and methods are described as having, including, or comprising specific steps, it is contemplated that, additionally, there are articles, devices, apparatus and systems of the present invention that consist essentially of, or consist of, the recited components, and that there are processes and methods according to the present invention that consist essentially of, or consist of, the recited processing steps.

Similarly, where articles, devices, mixtures, apparatus and compositions are described as having, including, or comprising specific compounds and/or materials, it is contemplated that, additionally, there are articles, devices, mixtures, apparatus and compositions of the present invention that consist essentially of, or consist of, the recited compounds and/or materials.

It should be understood that the order of steps or order for performing certain actions is immaterial so long as the invention remains operable. Moreover, two or more steps or actions may be conducted simultaneously.

The mention herein of any publication, for example, in the Background section, is not an admission that the publication serves as prior art with respect to any of the claims presented herein. The Background section is presented for purposes of clarity and is not meant as a description of prior art with respect to any claim.

Surfaces with designed chemistry and roughness possess remarkable non-wetting properties, which can be very useful in a wide variety of commercial and technological applications, as will be described in further detail below.

In some embodiments, where “a” is used as a subscript of a variable to denote air, “v” is also appropriate (where v indicates a vapor phase). Also, where “w” as a subscript of a variable to denote water, “e” is also appropriate (where e indicates a non-vapor (e.g., liquid, solid, semi-solid, gel) phase external to the surface that is different from the impregnating liquid.

In some embodiments, a non-wetting, liquid-impregnated surface is provided that includes a solid having textures (e.g., posts) that are impregnated with an impregnating liquid. In some embodiments, the lubricant is stabilized by the capillary forces arising from the microscopic texture, and provided that the lubricant wets the solid preferentially, this allows the droplet to move (e.g., slide, roll, slip, etc.) above the liquid-impregnated surface with remarkable ease, as evidenced by the extremely low contact angle hysteresis (˜1°) of the droplet. In some embodiments, in addition to low hysteresis, these non-wetting surfaces can provide self-cleaning properties, withstand high drop impact pressures, self-heal by capillary wicking upon damage, repel a variety of liquids, and reduce ice adhesion. Contact line morphology governs droplet pinning and hence its mobility on the surface.

In general, solid features can be made from or can comprise any material suitable for use in accordance with the present invention. In accordance with various embodiments of the present invention, micro-scale solid features are used (e.g., from about 1 micron to about 100 microns in characteristic dimension, e.g., from about 1-10 microns, 10-20 microns, 20-30 microns, 30-50 microns, 50-70 microns, 70-100 microns). In certain embodiments, nano-scale solid features are used (e.g., less than about 1 micron, e.g., about 1 nm to about 1 micron e.g., about 1-10 nm, 10-50 nm, 50-100 nm, 100-200 nm, 200-300 nm, 300-500 nm, 500-700 nm, 700 nm-1 micron).

In some embodiments, micro-scale features are used. In some embodiments, a micro-scale feature is a particle. Particles can be randomly or uniformly dispersed on a surface. Characteristic spacing between particles can be about 200 μm, about 100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm or 1 μm. In some embodiments, characteristic spacing between particles is in a range of 100 μm-1 μm, 50 μm-20 μm, or 40 μm-30 μm. In some embodiments, characteristic spacing between particles is in a range of 100 μm-80 μm, 80 μm-50 μm, 50 μm-30 μm or 30 μm-10 μm. In some embodiments, characteristic spacing between particles is in a range of any two values above.

Particles can have an average dimension of about 200 μm, about 100 μm, about 90 μm, about 80, about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm or 1 μm. In some embodiments, an average dimension of particles is in a range of 100 μm-1 μm, 50 μm-10 μm, or 30 μm-20 μm. In some embodiments, an average dimension of particles is in a range of 100 μm-80 μm, 80 μm-50 μm, 50 μm-30 μm or 30 μm-10 μm. In some embodiments, an average dimension of particles is in a range of any two values above.

In some embodiments, particles are porous. Characteristic pore size (e.g., pore widths or lengths) of particles can be about 5000 nm, about 3000 nm, about 2000 nm, about 1000 nm, about 500 nm, about 400 nm, about 300 nm, about 200 nm, about 100 nm, about 80 nm, about 50, about 10 nm. In some embodiments, characteristic pore size is in a range of 200 nm-2 μm or 100 nm-1 μm. In some embodiments, characteristic pore size is in a range of any two values above.

In some embodiments, the liquid-impregnated surface is configured such that water droplets contacting the surface are not pinned or impaled on the surface.

As used herein, emerged area fraction ϕ is defined as a representative fraction of the projected surface area of the liquid-impregnated surface corresponding to non-submerged solid at equilibrium. The term “equilibrium” as used herein refers to the condition in which the average thickness of the impregnating film does not change over time due to drainage by gravity when the substrate is held away from horizontal, and where evaporation is negligible (e.g., if the liquid impregnated liquid were to be placed in an environment saturated with the vapor of that impregnated liquid). Similarly, the term “pseudo-equilibrium” as used herein refers to equilibrium with the condition that evaporation may occur or gradual dissolving may occur. Note that the average thickness of a film at equilibrium may be less on parts of the substrate that are at a higher elevation, due to the decreased hydrostatic pressure within the film at increasing elevation. However, it will eventually reach an equilibrium (or pseudo-equilibrium), in which the average thickness of any part of the surfaces is unchanging with time.

In general, a “representative fraction” of a surface refers to a portion of the surface with a sufficient number of solid features thereupon such that the portion is reasonably representative of the whole surface. In certain embodiments, a “representative fraction” is at least a tenth of the whole surface.

Referring to FIG. 1, a schematic cross-sectional view and the corresponding top view of a liquid-impregnated surface that is partially submerged is shown. The upper left drawing of FIG. 1 shows a cross-sectional view of a row of cone-shaped solid features. The projected surface area of the non-submerged solid 102 is illustrated as shaded areas of the overhead view, while the remaining non-shaded area represents the projected surface area of the submerged liquid-impregnated surface 100. In addition to the projection surface area of this row of solid features, other solid features placed in a semi-random pattern are shown in shade in the overhead view. Similarly, the cross-section view of a row of evenly spaced posts is shown on the right of FIG. 1. Additional rows of well-patterned posts are shown in shade in the overhead view. As demonstrated, in some embodiments of the present invention, a liquid-impregnated surface includes randomly and/or non-randomly patterned solid features.

In certain embodiments of the present invention, ϕ is less than 0.30, 0.25, 0.20, 0.15, 0.10, 0.05, 0.01, or 0.005. In certain embodiments, ϕ is greater than 0.001, 0.005, 0.01, 0.05, 0.10, 0.15, or 0.20. In certain embodiments, ϕ is in a range of about 0 and about 0.25. In certain embodiments, ϕ is in a range of about 0 and about 0.01. In certain embodiments, ϕ is in a range of about 0.001 and about 0.25. In certain embodiments, ϕ is in a range of about 0.001 and about 0.10.

In some embodiments, the liquid-impregnated surface is configured such that cloaking by the impregnating liquid can be either eliminated or induced, according to different embodiments described herein.

As used herein, the spreading coefficient, S_ow(a), is defined as γ_wa−γ_wo−γ_oa, where γ is the interfacial tension between the two phases designated by subscripts w, a, and o, where w is water, a is air, and o is the impregnating liquid. Interfacial tension can be measured using a pendant drop method as described in Stauffer, C. E., “The measurement of surface tension by the pendant drop technique,” J. Phys. Chem. 1965, 69, 1933-1938, the text of which is incorporated by reference herein. Exemplary surfaces and its interfacial tension measurements (at approximately 25° C.) are Table 3 below.

Without wishing to be bound to any particular theory, impregnating liquids that have S_ow(a), less than 0 will not cloak matter as seen in FIG. 1(c), resulting in no loss of impregnating liquids, whereas impregnating liquids that have S_ow(a) greater than 0 will cloak matter (condensed water droplets, bacterial colonies, solid surface) as seen in FIG. 1(b) and this may be exploited to prevent corrosion, fouling, etc. In certain embodiments, cloaking is used for preventing vapor-liquid transformation (e.g., water vapor, metallic vapor, etc.). In certain embodiments, cloaking is used for inhibiting liquid-solid formation (e.g., ice, metal, etc.). In certain embodiments, cloaking is used to make reservoirs for carrying the materials, such that independent cloaked materials can be controlled and directed by external means (like electric or magnetic fields).

FIG. 1(c) illustrates a water droplet on a silicon micro post surface (post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS (octadecyltrichlorosilane) and impregnated with silicone oil. FIG. 1(d) illustrates a water droplet on a silicon micro post surface (post side a=10 μm, height=10 μm, and spacing b=10 μm) coated with OTS (octadecyltrichlorosilane) and impregnated with 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm). FIGS. 1(e) and 1(f) illustrate a water droplet under UV illumination when a fluorescent dye was dissolved in silicone oil and BMIm. The bottom regions show that the lubricating oils are pulled up above the texture surface (b=50 μm).

FIG. 1(c) shows an 8 μl water droplet placed on the silicone oil impregnated texture. The droplet forms a large apparent contact angle (˜100°) but very close to the solid surface (shown by arrows in FIG. 1(c)), its profile changes from convex to concave.

When a fluorescent dye was added to the silicone oil and imaged under UV light, the point of inflection corresponded to the height to which an annular ridge of oil was pulled up in order to satisfy a vertical force balance of the interfacial tensions at the inflection point (FIG. 1(e)). Although the oil should spread over the entire droplet (FIG. 1(c)), the cloaking film was too thin to be captured in these images. The “wetting ridge” was also observed in the case of ionic liquid (FIGS. 1(d), 1(f)). The importance of the wetting ridge to droplet mobility will be discussed below. Such wetting ridges are reminiscent of those observed around droplets on soft substrates.

The texture can be completely submerged in the oil if θ_os(a)=0°. This condition was found to be true for silicone oil, implying that the tops of the posts should be covered by a stable thin oil film. This film was observed experimentally using laser confocal fluorescence microscopy (LCFM); the post tops appear bright due to the presence of a fluorescent dye that was dissolved in the oil (FIG. 1(g)). Environmental SEM images of the surface (FIG. 1(i)) show the oil-filled texture and confirm that this film is less than a few microns thick, consistent with prior estimates of completely-wetting films. On the other hand, BMIm has a non-zero contact angle on a smooth OTS-coated silicon surface (θ_os(a)=65±5°) indicating that with this lubricant the post tops should remain dry. Indeed, LCFM images confirmed this (FIG. 1 (h))—the post tops appear dark as there is no dye present to fluoresce. Since BMIm is conductive and has an extremely low vapor pressure, it could be imaged in a SEM. As shown in FIG. 1(j), discrete droplets resting on post tops are seen, confirming that a thin film was not stable on the post tops in this case.

The stable wetting configuration affects the mobility of droplets. As shown in FIG. 1(b), in the case of BMIm, there are three distinct phase contact lines at the perimeter of the drop that confine the wetting ridge: the oil-water-air contact line, the oil-solid-air contact line outside the drop, and the oil-solid-water contact line underneath the drop. These contact lines exist because θ*_os(a)>θ, _θos(w)>0, and S_ow(a)<0. In contrast, in the case of silicone oil (FIG. 1(a)), none of these contact lines exist because θ_os(a)=0, θ_os(w)=0, and S_ow(a)>0. These configurations are just two of the 12 different configurations in such a four-phase system where oil impregnation is possible. These configurations are discussed below.

A thermodynamic framework that allows one to predict which of these 12 states will be stable for a given droplet, oil, and substrate material will be discussed in the paragraphs below. There are three possible configurations to consider for the interface outside of the droplet (in an air environment), and three possible configurations to consider for the interface underneath the droplet (in a water environment). These configurations are shown in FIG. 1(k) along with the total interface energy of each configuration. The configurations possible outside the droplet are A1 (not impregnated, i.e., dry), A2 (impregnated with emergent features), and A3 (impregnated with submerged features—i.e., encapsulated). On the other hand, underneath the droplet, the possible configurations are W1 (impaled), W2 (impregnated with emergent features), and W3 (impregnated with submerged features—i.e., encapsulated). The stable configuration will be the one that has the lowest total interface energy. Referring now to configurations outside the droplet, the textured surface as it is slowly withdrawn from a reservoir of oil could be in any of states A1, A2, and A3 depending on which has the lowest energy. For example, state A2 would be stable if it has the lowest total interface energy, i.e. E_A2<E_A1, E_A3. From FIG. 1(k), this results in:E_A2<E_A1(γ_sa−γ_os)/γ_oa>(1−ϕ)/(r−ϕ)  (1)E_A2<E_A3γ_sa−γ_os−γ_oa<0  (2)

where ϕ is the fraction of the projected area of the surface that is occupied by the solid and r is the ratio of total surface area to the projected area of the solid. In the case of square posts with width “a”, edge-to-edge spacing “b”, and height “h”, ϕ=a²/(a+b)² and r=1+4ah/(a+b)². Applying Young's equation, cos(θos(a))=(γ_sa−γ_os)/γ_oa, Eq. (1) reduces to the hemi-wicking criterion for the propagation of oil through a textured surface: cos(θ_os(a))>(1−ϕ)/(r−ϕ)=cos(θ_c). This requirement can be conveniently expressed as θ_os(a)<θ_c. In Eq. (2), γ_sa−γ_os−γ_oa, is simply the spreading coefficient S_os(a) of oil on the textured surface in the presence of air. This may be reorganized as (γ_sa−γ_os)/γ_oa<1, and applying Young's equation again, Eq. (2) can be written as θ_os(a)>0. Expressing Eq. (1) in terms of the spreading coefficient S_os(a), yields: −γ_oa(r−1)/(r−ϕ)<S_os(a). The above simplifications then lead to the following equivalent criteria for the surface to be in state A2:E_A2<E_A1,E_A3θ_c>θ_os(a)>0γ_oa(r−1)/(r−ϕ)<S_os(a)<0  (3)

Similarly, state A3 would be stable if E_A3<E_A2, E_A1. From FIG. 1(k), this gives:E_A3<E_A2θ_os(a)=0γ_sa−γ_oa≡S_os(a)≥0  (4)E_A3<E_A1θ_os(a)<cos⁻¹(1/r)S_os(a)>−γ_oa(1/1/r)  (5)

Note that Eq. (5) is automatically satisfied by Eq. (4), thus the criterion for state A3 to be stable (i.e., encapsulation) is given by Eq. (4). Following a similar procedure, the condition for state A1 to be stable can be derived asE_A1<E_A2,E_A3θ_os(a)>θ_cS_os(a)<−γ_oa(r−1)/(r−ϕ)  (6)

The rightmost expression of Eq. (4) can be rewritten as (γ_sa−γ_os)/γ_oa≥1. This raises an important point: Young's equation would suggest that if θ_os(a)=0, then (γ_sa−γ_os)/γ_oa=1 (i.e., S_os(a)=0). However, θ_os(a)=0 is true also for the case that (γ_sa−γ_os)/γ_oa>1 (i.e. S_os(a)>0). It is important to realize that Young's equation predicts the contact angle based on balancing the surface tension forces on a contact line—the equality only exists for a contact line at static equilibrium. For a spreading film (S_os(a)>0) a static contact line doesn't exist, hence precluding the applicability of Young's equation.

The configurations possible underneath the droplet are discussed in the paragraphs below. Upon contact with water, the interface beneath the droplet will attain one of the three different states—W1, W2, or W3 (FIG. 1(k))—depending on which has the lowest energy. Applying the same method to determine the stable configurations of the interface beneath the droplet, and using the total interface energies provided in Table 1, the stability requirements take a form similar to Eqs. (3), (4), and (6), with γ_oa, γ_sa, θ_os(a), S_os(a), replaced with γ_ow, γ_sw, θ_os(w), S_os(w) respectively. Notice also that θ_c is not affected by the surrounding environment as it is only a function of the texture parameters, ϕ and r. Thus, the texture will remain impregnated with oil beneath the droplet with emergent post tops (i.e., state W2) when:E_W2<E_W1,E_W3θ_c>θ_os(w)>0−γ_ow(r−1)/(r−ϕ)<S_os(w)<0  (7)State W3 will be stable (i.e., the oil will encapsulate the texture) when:E_W3<E_W1,E_W2θ_os(w)=0γ_sw−γ_os−γ_ow−S_os(w)≥0  (8)and the droplet will displace the oil and be impaled by the textures (state W1) when:E_W1<E_W2,E_W3θ_os(w)>θ_cS_os(w)<−γ_ow(r−1)/(r−ϕ)  (9)

Combining the above criteria along with the criterion for cloaking of the water droplet by the oil film described earlier, the various possible states can be organized in a regime map, which is shown FIG. 3. The cloaking criterion is represented by the upper two schematic drawings. For each of these cases, there are six different configurations possible depending on how the oil interacts with the surface texture in the presence of air (vertical axis in FIG. 3) and water (horizontal axis in FIG. 3). The vertical and horizontal axes are the normalized spreading coefficients S_os(a)/γ_oa and S_os(w)/γ_ow respectively. Considering first the vertical axis of FIG. 3, when S_os(a)/γ_oa<−(r−1)/(r−ϕ), i.e., when Eq. (6) holds, oil does not even impregnate the texture. As S_os(a)/γ_oa increases above this important value, impregnation becomes feasible but the post tops are still left emerged. Once S_os(a)/γ_oa>0, the post tops are also submerged in the oil leading to complete encapsulation of the texture. Similarly, on the x-axis of FIG. 3 moving from left to right, as S_os(w)/γ_ow increases, the droplet transitions from an impaled state to an impregnated state to a fully-encapsulated state. Although prior studies have proposed simple criteria for whether a deposited drop would float or sink, additional states, as shown in FIG. 3, were not recognized.

FIG. 3 shows that there can be up to three different contact lines, two of which can get pinned on the texture. The degree of pinning determines the roll-off angle α*, the angle of inclination at which a droplet placed on the textured solid begins to move. Droplets that completely displace the oil (states A3-W1, A2-W1 in FIG. 3) are not expected to roll off the surface. These states are achieved when θ_ow>θ_c, as is the case for both BMIm and silicone oil impregnated surfaces when the silicon substrates are not treated with OTS. As expected, droplets did not roll off of these surfaces. Droplets in states with emergent post tops (A3-W2, A2-W2, A2-W3) are expected to have reduced mobility that is strongly texture dependent, whereas those in states with encapsulated posts outside and beneath the droplet (the A3-W3 states in FIG. 3) are expected to exhibit no pinning and consequently infinitesimally small roll-off angles.

Roll-off angles of 5 μl droplets on silicone oil and BMIm impregnated textures while varying the post spacing b were measured experimentally. For comparison, the same textures without a lubricant (i.e., the conventional superhydrophobic case) were also evaluated. The results of these experiments are shown in FIG. 11(a). The silicone oil encapsulated surfaces have extremely low roll-off angles regardless of the post spacing and oil viscosity, showing that contact line pinning was negligible, as predicted for a liquid droplet in an A3-W3 state with no contact lines on the textured substrate. On the other hand, BMIm impregnated textures showed much higher roll-off angles, which increased as the spacing decreased—a trend that is similar to Cassie droplets on superhydrophobic surfaces. This observation illustrates that pinning was significant in this case, and occurs on the emergent post tops, illustrated in FIG. 11(b). However, the pinning was significantly reduced by adding a second smaller length scale texture (i.e., nanograss on the posts), so that BMIm impregnated the texture even on the post tops, thereby substantially reducing ϕ (as illustrated by FIG. 1 (c) as well as FIGS. 12-13). The roll-off angle decreased from over 30° to only about 2°. The reduction in the emergent area fraction ϕ was not due to the absolute size of the texture features; since the oil-water and oil-air interfaces must intersect surface features at contact angles θ_os(w) and θ_ow(a), ϕ rather depends on these contact angles and feature geometry.

The effect of texture on the roll-off angle can be modelled by balancing gravitational forces with pinning forces. A force balance of a water droplet on a smooth solid surface at incipient motion gives ρ_wΩg sin α*≈2R_bγ_wa (cos θ_rec,ws(a)−cos θ_adv,ws(a)), where ρ_w is the density of the liquid droplet of volume Ω, g is the gravitational acceleration, R_b is the droplet base radius, and θ_adv,ws(a) and θ_rec,ws(a) are the advancing and receding contact angles of droplet in air on the smooth solid surface. To extend this treatment to our system, we recognize that pinning results from contact angle hysteresis of up to two contact lines: an oil-air-solid contact line with a pinning force per unit length given by γ_oa(cos θ_rec,os(a)−cos θ_adv,os(a)) and an oil-water-solid contact line with a pinning force per unit length given by γ_ow(cos θ_rec,os(w)−cos θ_adv,os(w)). In some embodiments, the length of the contact line over which pinning occurs is expected to scale as R_bϕ^1/2, where ϕ^1/2 is the fraction of the droplet perimeter (˜R_b) making contact with the emergent features of the textured substrate. Thus, a force balance tangential to the surface gives:ρ_wΩg sin α*˜R_bϕ^1/2[γ_ow(cos θ_rec,os(w)−cos θ_adv,os(w))+γ_oa cos θ_rec,os(a)−cos θ_adv,os(a))]   (10)Dividing Eq. (10) by R_bγ_wa, we obtain a non-dimensional expression:Bo sin α*f(θ)˜ϕ_1/2[γ_ow(cos θ_rec,os(w)−cos θ_adv,os(w))+γ_oa(cos θ_rec,os(a)−cos θ_adv,os(a))]/γ_wa  (11)where

${f\left(\theta \right)=\frac{{\Omega }^{\frac{1}{3}}}{R_b}=\left[\left(\frac{\pi }{3}\right)\left(2+\cos \theta \right){\left(1-\cos \theta \right)}^2/{\sin }^3\theta \right)]}^{1/3}$ by assuming the droplet to be a spherical cap making an apparent contact angle θ with the surface.

$\mathrm{Bo}={\Omega }^{\frac{2}{3}}{\rho }_{w}g/{\gamma }_{\mathrm{wa}}$ is the Bond number, which compares the relative magnitude of gravitational forces to surface tension forces. Values for θ_rec,os(w), θ_adv,os(w), θ_rec,os(a), θ_adv,os(a), γ_ow, γ_oa, and γ_wa are provided in Tables 2 and 3 below. FIG. 11(d) shows that the measured data is in agreement with the scaling of Eq. (11). The data for the silicone oil encapsulated surface and for the BMIm impregnated, nanograss-covered posts lie close to the origin as both ϕ and α* are very small in these cases.

Described in the following paragraphs are embodiments that illustrate dynamics of droplet shedding. Once the gravitational forces on a droplet overcome the pinning forces, the velocity attained by the droplet determines how quickly it can be shed, which reflects the non-wetting performance of the surface. For a droplet of volume Ω this velocity may depend on both the contact line pinning and viscosity of the lubricant. In some embodiments, the steady-state shedding velocity V of water droplets may be measured using a high-speed camera while systematically varying lubricant dynamic viscosity μ_o, post spacing b, substrate tilt angle α, and droplet volume, Ω. These measurements are illustrated in FIG. 3(a) where V is plotted as a function of a for different μ_o, b, and Ω; the velocity V, increases with α and Ω as both increase the gravitational force acting on the droplet. However, V decreases with μ_o and ϕ as both increase the resistance to droplet motion.

To explain these trends, it must first be determined whether the droplet is rolling or sliding. Referring now to the oil-water interface beneath the droplet as shown in FIG. 3(b), the shear stress at this interface, on the water side, scales as τ_w˜μ_w(V−V_i)/h_cm, and on the oil side scales as τ_o˜μ_oV_i/t, where V_i is the velocity of the oil-water interface and h_cm is the height of the centre of mass of the droplet above the solid surface, and t is the thickness of the oil film. Since τ_w must be equal to τ_o at the oil-water interface, μ_w(V−V_i)/h_cm˜μ_oV_i/t. Rearranging this yields:V_i/V˜(1+(μ_oh_cm)/(μ_wt))⁻¹  (12)

Since (μ_o/μ_w)(h_cm/t)>>1 in some of the conducted experiments, V_i/V<<1, i.e., the oil-water interface moves at a negligibly small velocity relative to that of the droplet's center of mass. Thus, in some embodiments, the droplets being shed were rolling off the surface. The experiment was repeated with ground coffee particles being added to the water droplets, and the motion of the ground coffee particles was tracked with a high speed camera as the droplet moved across the surface. Particle trajectories, shown in FIG. 3(c), clearly show that the droplets roll across the liquid-impregnated surface as they are shed (μ_o=96.4 cP).

To determine the magnitude of V, the rate of change of gravitational potential energy as the droplet rolls down the incline with the total rate of energy dissipation due to contact line pining and viscous effects were balanced. The resulting energy balance gives:V(F_g−F_p)˜μ_w∫_Ωdrop(Vū)_drop²dΩ+μ_o∫_Ωfilm(Vū)_film²dΩ+μoμw∫_Ωridge(Vū)_ridge²dΩ.   (13)where F_g and F_p represent the net gravitational and pinning forces acting on the droplet, the Ω terms are the volume over which viscous dissipation occurs, and the Vū terms are the corresponding velocity gradients. The form of Eq. (13) is similar to that for viscous droplets rolling on completely non-wetting surfaces, though additional terms are present due to the presence of impregnated oil. The three terms on the right side of Eq.(13) represent the rate of viscous dissipation within the droplet (I), in the oil film beneath the droplet (II), and in the wetting ridge near the three-phase contact line (III).

The rate of viscous dissipation within the droplet (I) is primarily confined to the volume beneath its centre of mass and can be approximated as I˜μ_w(V/h_cm)²R_b²h_cm, where R_b is the base radius of the droplet. Applying geometrical relations for a spherical cap, R_b/h_cm=g(θ)=4/3(sin θ)(2+cos θ)/(1+cos θ)², yields: I˜μ_WV²R_bg(θ)

In some embodiments, the rate of viscous dissipation within the film (II) can be approximated as II˜μ₀(V_i/t)²R_b²t. Since (μ_w/μ₀)(t/h_cm)<<1, from Eq.(12), Vū_film˜V_i/t˜(μ_w/μ₀)(V/h_cm). Using

$h_{\mathrm{cm}}=R_b/g\left(\theta \right),\mathrm{yields}\text{:}\mathrm{II}\sim \frac{{\mu }_w^2}{{\mu }_0}{V^2\left[g\left(\theta \right)\right]}^{2}t$

In some embodiments, the rate of viscous dissipation in the wetting ridge (III) can be approximated as III˜μ₀(V/h_ridge)²R_bh_ridge² since fluid velocities within the wetting ridge must scale as the velocities within the wetting ridge must scale as the velocity of the centre of mass and vanish at the solid surface, giving velocity gradients that scale as Vū_ridge˜V/h_ridge, where h_ridge is the height of the wetting ridge. Thus, III˜μ₀V²R_b.

Noting that F_g=μ_wΩg sin α and F_p=μ_wΩg sin α* and dividing both sides of Eq.(13) by R_bVγ_wa yields.

$\begin{array}{cc}\mathrm{Bo}\left(\sin \alpha -\sin {\alpha }^{*}\right)f\left(\theta \right)\sim \mathrm{Ca}\left\{g\left(\theta \right)+{\left[g\left(\theta \right)\right]}^2\frac{{\mu }_w}{{\mu }_0}\frac{t}{R_b}+\frac{{\mu }_0}{{\mu }_w}\right\}& \left(14\right)\end{array}$ where Ca=μ_wV/γ_wa, is the capillary number, Bo=Ω^2/3μ_w g/γ_wa is the Bond number, and f(θ)=Ω^1/3/R_b. Since (μ_w/μ₀)(t/R_b)<<1, and μ₀/μ_w>>g(θ) in some embodiments and experiments, Eq. (14) can be simplified to:

$\begin{array}{cc}\mathrm{Bo}\left(\sin \alpha -\sin {\alpha }^{*}\right)f\left(\theta \right)\sim \mathrm{Ca}\frac{{\mu }_0}{{\mu }_w}& \left(15\right)\end{array}$

The datasets shown in FIG. 3(a) were organized according to Eq.(15) above and were found to collapse onto a single curve (FIG. 3(d)), demonstrating that the above scaling model captures the essential physics of the phenomenon: the gravitational potential energy of the rolling droplet is primarily consumed in viscous dissipation in the wetting ridge around the base of the rolling droplet. Furthermore, Eq.(14) and Eq.(15) apply for cloaked and uncloaked droplets, because inertial and gravitational forces in the cloaking films are very small. Consequently, the velocity is uniform across the film and viscous dissipation is negligible.

Droplets placed on lubricant-impregnated surfaces exhibit fundamentally different behavior compared to typical superhydrophobic surfaces. In some embodiments, these four-phase systems can have up to three different three-phase contact lines, giving up to twelve different thermodynamic configurations. In some embodiments, the lubricant film encapsulating the texture is stable only if it wets the texture completely (θ=0), otherwise portions of the textures dewet and emerge from the lubricant film. In some embodiments, complete encapsulation of the texture is desirable in order to eliminate pinning. In some embodiments, texture geometry and hierarchical features can be exploited to reduce the emergent areas and achieve roll-off angles close to those obtained with fully wetting lubricants. In some embodiments, droplets of low-viscosity liquids, such as water placed on these impregnated surfaces, roll rather than slip with velocities that vary inversely with lubricant viscosity. In some embodiments, additional parameters, such as droplet and texture size, as well as the substrate tilt angle, may be modeled to achieve desired droplet (and/or other substance) movement (e.g., rolling) properties and/or to deliver optimal non-wetting properties.

FIG. 4 is a schematic describing six liquid-impregnated surface wetting states, in accordance with certain embodiments described herein. The six surface wetting states (state 1 through state 6) depend on the four wetting conditions shown at the bottom of FIG. 4 (conditions 1 to 4). In some embodiments, the non-wetted states are preferred (states 1 to 4). Additionally, where a thin film stably forms on the tops of the posts (or other features on the surface), as in non-wetted states 1 and 3, even more preferable non-wetting properties (and other related properties described herein) may be observed.

In order to achieve non-wetted states, it is often preferable to have low solid surface energy and low surface energy of the impregnated liquid compared to the nonwetted liquid. For example, surface energies below about 25 mJ/m² are desired in some embodiments. Low surface energy liquids include certain hydrocarbon and fluorocarbon-based liquids, for example, silicone oil, perfluorocarbon liquids, perfluorinated vacuum oils (e.g., Krytox 1506 or Fromblin 06/6), fluorinated coolants such as perfluoro-tripentylamine (e.g., FC-70, sold by 3M, or FC-43), fluorinated ionic liquids that are immiscible with water, silicone oils comprising PDMS, and fluorinated silicone oils.

Examples of low surface energy solids include the following: silanes terminating in a hydrocarbon chain (such as octadecyltrichlorosilane), silanes terminating in a fluorocarbon chain (e.g., fluorosilane), thiols terminating in a hydrocarbon chain (such butanethiol), and thiols terminating in a fluorocarbon chain (e.g. perfluorodecane thiol). In certain embodiments, the surface comprises a low surface energy solid such as a fluoropolymer, for example, a silsesquioxane such as fluorodecyl polyhedral oligomeric silsesquioxane. In certain embodiments, the fluoropolymer is (or comprises) tetrafluoroethylene (ETFE), fluorinated ethylenepropylene copolymer (FEP), polyvinylidene fluoride (PVDF), perfluoroalkoxytetrafluoroethylene copolymer (PFA), polytetrafluoroethylene (PTFE), tetrafluoroethylene, perfluoromethylvinylether copolymer (MFA), ethylenechlorotrifluoroethylene copolymer (ECTFE), ethylene-tetrafluoroethylene copolymer (ETFE), perfluoropolyether, or Tecnoflon.

In FIG. 4, γ_wv is the surface energy of the non-wetted phase in equilibrium with vapor; γ_ow is the interfacial energy between the non-wetted phase and the impregnated liquid; γ_ov is the surface energy of the impregnated liquid phase in equilibrium with vapor, γ_sv is the surface energy of the solid in equilibrium with vapor, γ_so is the interfacial energy between the impregnated phase and the solid; γ_sw is the interfacial energy between the solid and the non-wetted phase; r=total surface area divided by projected surface area; Θ_c1, Θ_c2, Θ_c3, Θ_c4, Θ_w1, Θ_w2, are the macroscopic contact angles made by the non-wetted phase in each wetting state; Θ*_os(v) is the macroscopic contact angle of oil on the textured substrate when the phase surrounding the textured substrate is vapor; Θ_os(v) is the contact angle of oil on a smooth solid substrate of the same chemistry when the phase surrounding the oil droplet is vapor; Θ*_os(w) is the macroscopic contact angle of oil on the textured substrate when the phase surrounding the oil droplet is water; and Θ_os(w) is the contact angle of oil on a smooth substrate of the same chemistry as the textured surface when the phase surrounding the oil droplet is water.

FIG. 5 is a schematic showing conditions for the six liquid-impregnated surface wetting states shown in FIG. 4, in accordance with certain embodiments of the invention.

In certain embodiments, lubricant cloaking is desirable and is used a means for preventing environmental contamination, like a time capsule preserving the contents of the cloaked material. Cloaking can result in encasing of the material thereby cutting its access from the environment. This can be used for transporting materials (such as bioassays) across a length in a way that the material is not contaminated by the environment.

In certain embodiments, the amount of cloaking can be controlled by various lubricant properties such as viscosity, surface tension. Additionally or alternatively, the de-wetting of the cloaked material to release the material may be controlled. Thus, it is contemplated that a system in which a liquid is dispensed in the lubricating medium at one end, and upon reaching the other end is exposed to environment that causes the lubricant to uncloak.

In certain embodiments, an impregnating liquid is or comprises an ionic liquid. Ionic liquids have extremely low vapor pressures ˜(10⁻¹² mmHg), and therefore they mitigate the concern of the lubricant loss through evaporation. In some embodiments, an impregnating liquid can be selected to have a S_ow(a) less than 0. Exemplary impregnating liquids include, but are not limited to, tetrachloroethylene (perchloroethylene), phenyl isothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene, o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene, acetylene tetrabromide, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm), tribromohydrin (1,2,3-tribromopropane), tetradecane, cyclohexane, ethylene dibromide, carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbon disulfide, phenyl mustard oil, monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleic acid, amyl phthalate and any combination thereof.

In accordance with the present invention, exemplary solid features include, but are not limited to, polymeric solid, a ceramic solid, a fluorinated solid, an intermetallic solid, and a composite solid and any combination thereof. As demonstrated in FIG. 1, solid features can comprise any suitable shapes and/or define any suitable structures. Exemplary solid features include, but are not limited to, pores, cavities, wells, interconnected pores, and interconnected cavities and any combination thereof.

In some embodiments, solid features have a roughened surface. As used herein, θ_os(a)(is defined as the contact angle of oil (subscript ‘o’) on the textured solid (subscript ‘s’) in the presence of air (subscript ‘a’). In certain embodiments, the roughened surface of solid features provides stable impregnation of liquid therebetween or therewithin, when θ_os(v)>θ_c.

In certain embodiments, liquid-impregnated surfaces described herein have advantageous droplet roll-off properties that minimize the accumulation of the contacting liquid on the surfaces. Without being bound to any particular theory, a roll-off angle α of the liquid-impregnated surface in certain embodiments is less than 50°, less than 40°, less than 30°, less than 25°, or less than 20°.

Typically, flow through a pipe or channel, having an liquid-impregnate surface on its interior may be modeled according to Eq. (14):

$\begin{array}{cc}\frac{Q}{\Delta p/L}\sim \left(\frac{R^4}{{\mu }_1}\right)\left[1+\left(\frac{h}{R}\right)\left(\frac{{\mu }_1}{{\mu }_2}\right)\right]& \left(14\right)\end{array}$ where Q is the volumetric flow rate, R is pipe radius, h is the height of the texture, μ₂ is the viscosity of lubricant and μ₁ is the viscosity of the fluid flowing through the pipe. Δp/L is the pressure drop per L. Without being bound to any particular theory, it is believed that (h/R)(μ₁/μ₂) is greater than 1 for this to have a significant effect and this sets the height of the texture in relation to the viscosity ratio.

Although modeled for pipe flow, the general principals also apply to open systems, where R is replaced with the characteristic depth of the flowing material. The average velocity of the flow ˜Q/A, where A is the cross-sectional area of the flowing fluid.

For example, mayonnaise has a viscosity that approaches infinity at low shear rates (it is a Bingham plastic (a type of non-Newtonian material)), and therefore behaves like a solid as long as shear stress within it remains below a critical value. Whereas, for honey, which is Newtonian, the flow is much slower. For both systems, h and R are of the same order of magnitude, and μ₂ is the same. However, since μ_honey<<μ_mayonnaise, then

$\begin{array}{cc}\left(\frac{h}{R}\right)\left(\frac{{\mu }_{\mathrm{honey}}}{{\mu }_2}\right)⪡\left(\frac{h}{R}\right)\left(\frac{{\mu }_{\mathrm{mayonnaise}}}{{\mu }_2}\right)& \left(15\right)\end{array}$

thus mayonnaise flows much more quickly out of the bottle than honey.

According to some embodiments of the present invention, an article includes an interior surface, which is at least partially enclosed (e.g., the article is an oil pipeline, other pipeline, consumer product container, other container) and adapted for containing or transferring a fluid of viscosity μ₁, wherein the interior surface comprises a liquid-impregnated surface, said liquid-impregnated surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein the impregnating liquid comprises water (having viscosity μ₂). In certain embodiments, μ1/μ2 is greater than about 1, about 0.5, or about 0.1.

In certain embodiments, the impregnating liquid comprises an additive to prevent or reduce evaporation of the impregnating liquid. The additive can be a surfactant. Exemplary surfactants include, but are not limited to, docosanoic acid, trans-13-docosenoic acid, cis-13-docosenoic acid, nonylphenoxy tri(ethyleneoxy) ethanol, methyl 12-hydroxyoctadecanate, 1-Tetracosanol, fluorochemical “L-1006”, and combination thereof. More details can be found in White, Ian. “Effect of Surfactants on the Evaporation of Water Close to 100 C.” Industrial & Engineering Chemistry Fundamentals 15.1 (1976): 53-59, the contents of which are incorporated herein by references. In addition or alternative, exemplary additives can be C₁₆H₃₃COOH, C₁₇H₃₃COOH, C₁₈H₃₃COOH, C₁₉H₃₃COOH, C₁₄H₂₉OH, C₁₆H₃₃OH, C₁₈H₃₇OH, C₂₀H₄₁OH, C₂₂H₄₅OH, C₁₇H₃₅COOCH₃, C₁₅H₃₁COOC₂H₅, C₁₆H₃₃OC₂H₄OH, C₁₈H₃₇OC₂H₄OH, C₂₀H₄₁OC₂H₄OH, C₂₂H₄₅OC₂H₄OH, Sodium docosyl sulfate, poly(vinyl stearate), Poly(octadecyl acrylate), Poly(octadecyl methacrylate) and combination thereof. More details can be found in Barnes, Geoff T. “The potential for monolayers to reduce the evaporation of water from large water storages.” Agricultural Water Management 95.4 (2008): 339-353, the contents of which are incorporated herein by references.

EXPERIMENTAL EXAMPLES

Example 1

FIG. 6 shows experimental measurements of water droplet mobility on liquid impregnating surfaces. FIG. 6a is a plot of roll-off angle α as a function of emerged area fraction ϕ, for different surfaces (feature spacing b varies). An ionic liquid (1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm) was used as a impregnating liquid in this work. The top inset (FIG. 6b) shows an SEM image of the BMIm impregnated texture and shows that the post tops are dry. In FIG. 6c, when the posts are further roughened by adding nanograss, they are covered with BMIm (bottom inset) and consequently, the roll-off angle decreases.

The experiments of FIG. 6 demonstrate that liquid-impregnated surfaces can be engineered to provide resistance to impalement and to provide non-wettability, without requiring replenishment of impregnating fluid to make up for liquid lost to cloaking (BMIm is an example liquid that does not cloak in the presence of air and water), and without requiring replenishment of impregnating liquid to maintain coverage over the tops of the solid features.

BMIm impregnated textures showed roll-off angles that increase as the spacing decreases. This observation shows that pinning is non-negligible in this case, and occurs on the emergent post tops (FIG. 6b). However, this pinning was significantly reduced by adding a second smaller length scale texture (i.e. nanograss on the posts), so that BMIm impregnated the texture even on the post tops, thereby substantially reducing ϕ (though still non-zero) (see FIG. 6c). It is important to note that the reduction in the emergent area fraction ϕ is not due to the absolute size of the texture features; since the oil-water and oil-air interfaces typically intersect surface features at contact angles θ_os(w) and θ_ow(a), ϕ rather depends on these contact angles and feature geometry.

Example 2

This Example demonstrates that condensation can be inhibited by preventing coalescence due to liquid cloaking.

FIG. 7(a) shows an ESEM image sequence of condensation on a micropost surface impregnated with Krytox that has positive spreading coefficient on water (S_ow>0). Condensation is inhibited as Krytox cloaks the condensed droplets. FIG. 7(b) illustrates cloaked condensate droplet depicting the thin film of condensate that spreads on the droplet. FIG. 7(c) shows an ESEM image sequence of condensation on micropost surface impregnated with BMIm that has negative spreading coefficient with water (S_ow<0). FIG. 7(b) illustrates uncloaked condensate droplet depicting the three phase contact line of the water-vapor, water-lubricant, and lubricant-vapor interfaces on one end and pinning of the droplet at the dry post tops at the other end. FIG. 7(e) is a plot comparing variation of surface area fraction covered by condensed water droplets versus time on surfaces impregnated with Krytox (S_ow>0, solid squares) and BMIm (S_ow<0, open diamonds). FIG. 7(f) is a plot comparing number of water droplets per unit area versus time on surfaces impregnated with Krytox (solid squares) and BMIm (open diamonds). The ESEM experiments were conducted under identical conditions (pressure=800 Pa, substrate temperature ˜3.6° C., beam voltage=25 kV and beam current=1.7 nA). In the analysis, t=0 s is defined as the first frame in which water drops can be identified.

Referring to FIG. 8, the very high subcooling is sufficient for condensation rate to overcome the cloaking phenomenon for 10 cSt oil. The temperature of the peltier cooler was set at −5° C. The room temperature was 20° C., and the dew point in the conditions was 12° C. However, the barrier for coalescence is significantly higher on more viscous lubricant even at this high degree of subcooling. As a result, the droplets appear on 10 cSt oil as hemispherical shapes, whereas on more viscous lubricant their sphericity is significantly lower.

Example 3

This Example demonstrates that condensation is inhibited by the decreased drainage rate of oil between neighboring water droplets, particularly where the oil has high viscosity.

Similar to the conditions described in Example 2, the temperature of the peltier cooler was set at −5° C. The room temperature was 20° C., and the dew point in the conditions was 12° C. As can be seen in FIG. 9, the condensation growth rate is significantly decreased as viscosity of the oil increases. Upon condensation on liquid-impregnated surfaces with S_ow>0, coalescence is significantly inhibited because of the presence of the cloaking oil film between droplets. As viscosity of the oil increases, the force required to drain the oil film between two neighboring droplets also increases and hence condensation/frost growth is inhibited. Further, the more viscous an oil, the less rapid the deformation of its surface upon adsorption of vapor molecules, and this may reduce the rate of formation of condensed droplets, as well.

Example 4

This Example demonstrates that frost can be inhibited by decreasing the drainage rate of oil from condensed structures, particularly where the oil has high viscosity.

Similar to the conditions described above, the temperature of the peltier cooler was set at −15° C. The experiments were conducted in low relative humidity environment such that the dew point in these conditions was −10° C. In these conditions, water vapor forms directly as frost on the peltier plate. However, on the impregnated surface, water vapor still forms as droplets, and frost. As can be seen in FIG. 10, the frost formation rate is significantly decreased as viscosity of the oil increases. On low viscosity liquid, the water phase shows mobility signifying that water exists as supercooled droplets.

Example 5

This example demonstrates results of a series of experiments that included flowing a number of different external phases on a number of different solid surfaces impregnated with different impregnating liquids. The results of the conducted experiments are shown in Table 1 below. In Table 1 below, θ_{os(a),receding} is the receding contact angle of the impregnating liquid (e.g., silicone oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of air (subscript ‘a’), and where θ_{os(e),receding} is the receding contact angle of the impregnating liquid (e.g., silicone oil, subscript ‘o’) on the surface (subscript ‘s’) in the presence of the external phase (subscript ‘e’). θ*_c=Cos⁻¹(1/r) is the critical contact angle on the textured substrate and α* is the roll-off angle.

TABLE 1
Experimental determination of roll-off angles.
					Cos−1(1/r) =	θos(a),receding ,
External		Impregnating	Θos(a),receding	θos(e),receding	θc*	θos(e),receding <	α*
phase (e)	Solid (s)	liquid (o)	( ° )	( ° )	( ° )	θ* c	( ° )
Mayonnaise	CW	PDC	0	37	47	Yes	5
Toothpaste	CW	PDC	0	25	47	Yes	3
Toothpaste	WPTFE	PDC	20	67	50	No	45
WB Paint	WPTFE	PDC	20	67	50	No	65
WB Paint	WPTFE	Krytox 1506	2	35	50	Yes	15
Peanut	WPTFE	PDC	20	90	50	No	70
Butter
Peanut	WPTFE	CL	5	35	50	Yes	20
Butter
DI Water	OTS-	Silicone oil	0	0	60	Yes	~1
	treated
	silicon
DI Water	Silicon	Silicone oil	0	122	60	No	Did not
							roll off,
							even at
							90°

Slide off angles were measured using 500 μL volumes of the external fluid, except for water, for which 5 μL droplets were used. It was observed that in experiments where θ_os(e),rec<θ*_c, the roll-off angles, α*, were low (e.g., less than or equal to 20°), whereas in cases where θ_rec,os(e)>θ*_c, the roll-off angles, α*, were high (e.g., greater than or equal to 40°).

The silicon surfaces used in the experimental data shown in Table 1 above were 10 m square silicon posts (10×10×10 μm) with 10 m interpillar spacing. The 10 m square silicon microposts were patterned using photolithographic and etched using deep reactive ion etching (DRIE). The textured substrates were cleaned using piranha solution and were coated with octadecyltrichlorosilane (OTS from Sigma-Aldrich) using a solution deposition method.

The “WPTFE” surfaces shown in Table 1 above were composed of a 7:1 spray-coated mixture of a mixture of Teflon particles and Toko LF Dibloc Wax, sprayed onto a PET substrate. The carnauba wax (CW) surfaces were composed of PPE CW spray-coated onto a PET substrate. The impregnating liquids were propylene di(caprylate/caprate) (“PDC”), Krytox 1506, DOW PMX 200 silicone, oil, 10 cSt (“Silicone oil”) and Christo-lube EXP 101413-1 (“CL”). The external phases used were mayonnaise, toothpaste (e.g., Crest extra whitening), and red water based paint. Wenzel roughness, r, was measured using a Taylor hobson inferometer. Although precise estimates of ϕ could not be easily obtained, it was observed in the inferometer that ϕ was much less than 0.25 for all the impregnated surfaces described in the table, and tested, and using 0.25 as an upper bound on ϕ for our surfaces we determine that cos⁻¹(1−ϕ)/(r−ϕ)=θ_c is no more than 5° greater than the values for θ*_c.

Materials and Methods—Lubricant-Impregnated Surfaces

The textured substrates used in the examples discussed below were square microposts etched in silicon using standard photolithography process; these square microposts are shown in FIG. 12(a). A photomask with square windows was used and the pattern was transferred to photoresist using UV light exposure. Next, reactive ion etching in inductively-coupled plasma was used to etch the exposed areas to form microposts. Each micropost had a square geometry with width a=10 μm, height h=10 μm, and varying edge-to-edge spacing b=5, 10, 25, and 50 μm.

A second level of roughness was produced on microposts in some embodiments by creating nanograss, as shown in the SEM image of FIG. 12(b). For this purpose, Piranha-cleaned micropost surfaces were etched in alternating flow of SF₆ and O₂ gases for 10 minutes in inductively-coupled plasma.

The samples were then cleaned in a Piranha solution and treated with a low-energy silane (octadecyltrichlorosilane—OTS) by solution deposition. The samples were impregnated with lubricant by slowly dipping them into a reservoir of the lubricant. They were then withdrawn at speed S slow enough that capillary numbers Ca=μ_oS/γ_oa<10⁻⁵ to ensure that no excess fluid remained on the micropost tops where μ_o is the dynamic viscosity and γ_oa is the surface tension of the lubricant. In some embodiments, when the advancing angle θ_adv,os(a) is less than θ_c (see Table 4 below) the lubricant film will not spontaneously spread into the textured surface, as can be seen for BMIm (1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) in FIG. 13. However, by withdrawing the textured surfaces from a reservoir of BMIm, the impregnating film remains stable, since θ_rec,os(a)<θ_c for the microposts with b=5 μm and 10 μm.

Laser Confocal Fluorescence Microscope (LCFM) Imaging

In order to determine whether or not the micropost tops were covered with lubricant after dipping, a LCFM (Olympus FV 300) was used. A florescent dye (DFSB-175, Risk Reactor, CA) was dissolved in the lubricant, and the textured substrate was impregnated with the dyed lubricant using dip coating, as explained above. The dye gets excited at wavelengths of ˜400 nm, and the resulting emittance was captured by the microscope. In some embodiments, as the focused laser beam scanned through the sample, areas containing dye appeared bright, indicating the presence of lubricant. This is shown, for example, in FIG. 1(g) on substrates impregnated with silicone oil. In contrast, in some embodiments, BMIm does not wet post tops, which therefore appear dark, as shown, for example, in (FIG. 1(h)). Contact angle measurements

Contact angles of silicone oil and BMIm were measured on the OTS-coated silicon surfaces in the presence of air and DI water using a Ramé-Hart Model 500 Advanced Goniometer/Tensiometer. The advancing (θ_adv,os(a), θ_adv,os(w)) and receding (θ_rec,os(a), θ_rec,os(w)) angles were taken as an average of at least 8 measurements. 5 μl droplets were deposited at a volume addition/subtraction rate of 0.2 μl s⁻¹, yielding, in some embodiments, contact line velocities V_c less than 1 mm min⁻¹. The resulting capillary numbers were Ca=μ_oV_c/γ_o(i)<10⁻⁵ ensuring that the measured dynamic contact angles were essentially the same as contact angles obtained immediately after the contact line comes to rest. The measured contact angles are shown in Table 2 below.

Table 2 shows contact angle measurements on smooth OTS-treated silicon surfaces. In some embodiments, a surface that has been dipped in silicone oil maintains an oil film on the surface after a water droplet is deposited because the film cannot dewet the surface since θ_rec,os(w)=0°. Therefore, an oil-water-solid contact line cannot exist and pinning forces must be zero. Accordingly, the oil-solid-water pinning term in Eq.'s (10) and (11) above should be neglected if θ_rec,os(w)=0°. Similarly oil-solid-air pinning term should be neglected if θ_rec,os(a)=0°. For this reason, pinning forces are taken to be zero in FIG. 11(a)-(d) for silicone oil, even though cos θ_rec,os(w)−cos θ_adv,os(w)>0.

TABLE 2
Contact Angle Measurements on Smooth OTS-Treated Silicon Surfaces.
Liquid	Substrate	θadv,os(a) (°)	θrec,os(a) (°)	θadv,os(w) (°)	θrec,os(w) (°)
Silicone oil	OTS-treated	0	0	20 ± 5	0
	silicon
BMIm	OTS treated	67.8 ± 0.3	60.8 ± 1.0	61.3 ± 3.6	12.5 ± 4.5
	silicon
DI water	OTS-treated	112.5 ± 0.6	95.8 ± 0.5	NA	NA
	silicon
Silicone oil	Silicon	0	0	153.8 ± 1.0	122 ± 0.8
BMIm	Silicon	23.5 ± 1.8	9.8 ± 0.9	143.4 ± 1.8	133.1 ± 0.9
DI water	Silicon	20 ± 5°	0	NA	NA

Table 3 shows surface and interfacial tension measurements and resulting spreading coefficients, S_ow(a)=γ_wa−γ_ow−γ_oa, of 9.34, 96.4, and 970 cP Dow Corning PMX 200 Silicone oils on water in air. Values of γ_ow for silicone oil were taken from C. Y. Wang, R. V. Calabrese, AIChE J. 1986, 32, 667, in which the authors made measurements using the du Noüy ring method (described in du Noüy, P. Lecomte. “An interfacial tensiometer for universal use.” The Journal of general physiology 7.5 (1925): 625-631), and values of γ_oa were provided by Dow Corning. The surface and interfacial tensions for BMIm and Krytox were measured using the pendant drop method (described in Stauffer, C. E., The measurement of surface tension by the pendant drop technique. J. Phys. Chem. 1965, 69, 1933-1938). Here, γ_wa, γ_ow, and γ_oa are the surface and interfacial tensions between phases at equilibrium, that is, after water and the lubricant become mutually saturated.

TABLE 3
Surface and Interfacial Tension Measurements and
Resulting Spreading Coefficients
Liquid	γow(mN/m)	γoa (mN/m)	γwa (mN/M)	Sow(a) (mN/m)
Silicone oil	46.7	20.1	72.2	5.4
(9.34 cP, 96.4 cP)
Silicone oil	45.1	21.2	72.2	5.9
(970 cP)
Krytox	49	17	72.2	6
Ionic liquid	13	34	42	−5

Table 4 shows texture parameters b, r, ϕ, and critical contact angles θ_c defined by θ_c=cos⁻¹((1−ϕ)/(r−ϕ)), and θ*_c=cos⁻¹(1/r); h, a=10 μm for all substrates tested. The approximation θ_c≈θ*_c, becomes more accurate as ϕ approaches zero. If the silicon substrate is not coated with OTS, θ_os(w)>θ_c, θ*_c for both lubricants and all b values. Thus, water droplets should displace the lubricant and get impaled by the microposts leading to significant pinning, which was confirmed experimentally, as it was observed that such droplets did not roll-off of these surfaces.

TABLE 4
Texture Parameters and Critical Angles.
Post spacing, b
(μm)	r	ϕ	θc (°)	θ*c (°)
5	2.8	0.44	76	69
7.5	2.3	0.33	70	64
10	2.0	0.25	65	60
25	1.3	0.08	42	41
50	1.1	.093	26	26

EQUIVALENTS

While the invention has been particularly shown and described with reference to specific preferred embodiments, it should be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims

1. An article comprising a liquid-impregnated surface, said surface comprising an impregnating liquid and a matrix of solid features spaced sufficiently close to stably contain the impregnating liquid therebetween or therewithin, wherein one or both of the following holds: (i) θos(e),receding =0; and(ii) θos(v),receding =0 and θos(e),receding =0,

2. The article of claim 1, further comprising material of said non-vapor phase external to said surface (and in contact with said surface), said article containing said non-vapor phase material.

3. The article of claim 2, wherein said material of said non-vapor phase external to said surface comprises one or more of the following: food, cosmetic, cement, asphalt, tar, ice cream, egg yolk, water, alcohol, mercury, gallium, refrigerant, toothpaste, paint, peanut butter, jelly, jam, mayonnaise, ketchup, mustard, condiment, laundry detergent, consumer product, gasoline, petroleum product, oil, biological fluid, blood, plasma.

4. The article of claim 1, wherein the article is a container, a pipeline, a nozzle, a valve, a conduit, a vessel, a bottle, a mold, a die, a chute, a bowl, a tub, a bin, a cap, and/or a tube.

5. The article of claim 1, wherein θos(e),receding=0.

6. The article of claim 1, wherein the article comprises an interior surface that is at least partially enclosed, the interior surface containing or transferring the phase external to the surface and having a viscosity μ1, wherein the interior surface comprises the liquid-impregnated surface, wherein the impregnating liquid is aqueous (having viscosity μ2).

7. The article of claim 6, wherein the article is a member selected from the group consisting of a pipeline, a steam turbine part, a gas turbine part, an aircraft part, a wind turbine part, eyeglasses, a mirror, a power transmission line, a container, a windshield, an engine part, tube, nozzle, or a portion or coating thereof.

8. The article of claim 6, wherein μ1 / μ2>0.1.

9. The article of claim 6, wherein the impregnating liquid comprises an additive (e.g., a surfactant) to prevent or reduce evaporation of the impregnating liquid.

10. The article of claim 1, wherein the impregnating liquid comprises at least one member selected from the group consisting of silicone oil, propylene glycol dicaprylate/dicaprate, perfluoropolyether (PFPE), polyalphaolefin (PAO), synthetic hydrocarbon cooligomer, fluorinated polysiloxane, propylene glycol, tetrachloroethylene (perchloroethylene), phenyl isothiocyanate (phenyl mustard oil), bromobenzene, iodobenzene, o-bromotoluene, alpha-chloronaphthalene, alpha-bromonaphthalene, acetylene tetrabromide, 1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl) imide (BMIm), tribromohydrin (1,2,3-tribromopropane), ethylene dibromide, carbon disulfide, bromoform, methylene iodide (diiodomethane), stanolax, Squibb's liquid petrolatum, p-bromotoluene, monobromobenzene, perchloroethylene, carbon disulfide, phenyl mustard oil, monoiodobenzene, alpha-monochloro-naphthalene, acetylene tetrabromide, aniline, butyl alcohol, isoamyl alcohol, n-heptyl alcohol, cresol, oleic acid, linoleic acid, and amyl phthalate.