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Viscometers based on flow of fluid through a microfluidic channel offer the advantages of speed, precision, and minimal sample consumption. By applying a pressure drop across a microfluidic channel and measuring the flow rate, the viscosity is determined from the linear relationship between flow rate and pressure drop that is exhibited by Newtonian fluids at low Reynolds numbers. However, a direct measurement of flow rate in microchannels is challenging because it is typically below the range of conventional flow meters, making microchannel viscometers difficult to implement. To date few are in use.
This specification teaches a method for measuring flow rate and, thereby, viscosity which may in one embodiment include a mechanically resonant microfluidic channel. In some embodiments the particles may be suspended in the fluid to be measured, and the presence and motion of the particles detected by the effect their mass has on the microchannel's resonant frequency. Methods of measuring particle characteristics such as mass and size are described in U.S. Pat. No. 8,087,284, and U.S. application Ser. Nos. 12/305,733 and 12/927,031 incorporated in their entirety by reference. The referenced teachings form the basis for certain commercial particle measurement instruments.
In some embodiments, a pressure drop may be applied across the microchannel, causing the fluid containing the suspended particles to flow through the channel. The detection of the particles may be used to determine their velocity as they are carried by the flow through the microchannel by measuring the interval between the time a particle enters and exits the resonant microchannel. Averaging over a plurality of particles gives a precise measure of flow rate. With the knowledge of the pressure drop and flow rate, the fluid viscosity can be determined.
This final step can be done by using precisely known geometries of the microchannel and the known flow characteristics through channels. For example, Poiseuille-Hagen flow through a circular channel relates flow rate, pressure drop, channel dimensions, and viscosity (ref), and can be extended to channels of other geometries.
In alternative embodiments, a reference fluid of known viscosity (for example, water) may be first flowed through the microchannel using a given pressure drop, and the flow rate determined from the particle transit times as described above. A second, target fluid is then flowed through the microchannel at the same pressure drop, and the flow rate measured for that fluid. The ratio of this flow rate vs. the flow rate of the reference fluid yields the viscosity of the target fluid relative to that of the reference fluid. This approach has the advantage that it does not require knowledge of the absolute values of the pressure drops or of the microchannel dimensions.
In other embodiments, fluids that contain no native particles can be spiked with suitable particles, making the method applicable to any fluid.
The method described herein has been demonstrated to give viscosity values precise and accurate to better than 5% of a range from 0.8 cP to 100 cP in just a few minutes, and could be extended to higher viscosities as needed. In addition, by measuring the corresponding flow rates over a range of pressure drops, shear thickening and shear thinning can be measured.
This description primarily describes embodiments using resonant mass measurement to determine the particle motion and flow rate. However, the principles of the invention can be extended to other embodiments that employ a method that detects flow of particles through a channel, including optical methods and electrozone methods. In the latter, particle motion is detected by change in the electrical impedance of a conductive fluid due to the volume displaced by the particle (the so-called Coulter principle). Measuring particle motion with these methods, using the motion to determine flow rate, and combining this knowledge with pressure drop measurements, constitutes a novel embodiment for measuring viscosity.
The specification will be better understood by referring to the Figures.
This specification discloses a method for measuring fluid flow rate and viscosity by monitoring a fluid flowing through a sensor comprising a microfluidic channel.
b shows a representative time evolution of frequency measurements when a particle suspended in the fluid passes through the resonant portion of the microchannel, with the numbers on the resonant response graph corresponding to the labeled positions of the particle in the microchannel. Because the particle displaces the fluid in the resonator, if its density is greater than that of the fluid, the overall mass of the resonator increases as the particle passes through. This causes the sensor resonant frequency to decrease, then return to its baseline value when the particle exits the sensor. Particle measurement instruments based on such sensors measure the frequency excursion of a series of particles as they pass through the sensor, and from this determine the masses and other physical properties of the particles. For such measurements, and for the measurements described in the embodiment below, the concentration of particles is assumed to be low enough that, for the great majority of the time, at most one particle is present in the sensor at any given time.
For particles having size less than the channel size, the transit time, and hence the measured particle velocity, can vary from particle to particle, even when the actual fluid flow rate is held constant. This is because the flow velocity is not uniform across the width of the channel. For example, the velocity profile at low Reynolds numbers for flow through a circular channel is parabolic, with a maximum velocity at the channel center, and falling to zero at the channel walls. Therefore, particles that pass through the center of the channel travel faster than those near the walls. By averaging the transit times for several particles, the volumetric flow rate Q (units ml/s) can be determined as Vol/Avg(Δt), where Vol is the volume of the active region of the sensor. For resonant microchannels fabricated using MEMS the volume can be known very precisely from the dimensions of the channel.
In coordination with the pressure applied to vial (2), a pressure regulated with pressure regulator (7) is applied to vials (6). The sensor channel (5) connects the inlet reservoir channel (4) to a similar reservoir at its outlet. At this point, a pressure P_Inlet, controlled by regulator (1), is applied at the inlet of sensor (5), and a pressure P_Outlet, controlled by regulator (7), is applied at the sensor outlet. If P_Outlet<P_Inlet, the sample fluid will flow through the resonator. By using the pressure regulators to control the pressure difference ΔP=P_Inlet-P_Outlet, the flow rate through the sensor can be controlled precisely. The pressures ΔP, P_Inlet, and P_Outlet can be measured precisely either by using precision calibrated voltage-controlled regulators, or by monitoring the applied pressures using pressure sensors (8) and (9). Precision regulators and pressure sensors can control or monitor pressures to 0.01 PSI or better, allowing great precision when compared to typically applied pressures and pressure drops from 0.5-100 PSI typical of such a configuration in practice.
The embodiment of
The embodiment of
From this information, the viscosity of the sample fluid can be determined using two methods: 1) absolute and 2) relative, as follows:
(1) The absolute method uses the quantitative relationship between pressure, flow rate, channel geometry, and viscosity. For example, for a circular pipe, the flow rate is give by the Hagen-Poiseuille equation:
Here, Q is the volumetric flow rate, r is the radius of the pipe, L is the length of the pipe, ΔP is the pressure drop across the pipe, and μ is the dynamics viscosity of the fluid. By applying a known pressure drop ΔP determining the flow rate using the particle transit time measurements, and known sensor dimensions r and L, the viscosity μ can be determined quantitatively using Equation (1). This approach can be extended to channel geometries other than circular pipes by modifying Equation (1) as appropriate, which can be done for simple channel cross-sections (references to be provided).
(2) The relative method utilizes a reference fluid of known viscosity. First, a reference fluid having viscosity μref is flowed through the sensor using a known pressure drop ΔPref, and its flow rate Qref is measured using particle transit times. Then the sample fluid is flowed at a pressured drop ΔPs and its flow rate Qs is also measured using particle transit times. The sample viscosity is then given by
μs=μref*(Qref/Qs)*(ΔPs/ΔPref) Equation (2)
The relative approach has the advantage that the sensor geometry does not have to be known precisely, nor does the exact equation for flow rate vs. geometry. In fact, the sensor volume Vol is not needed either, since the averages of the article transit times for the reference and sample fluids provide enough information to determine the ratio of the flow rates. That is, the sample viscosity can be determined by these simple ratios:
μs=μref*((Avg(Δts)/(Avg(Δtref))*(ΔPs/ΔPref) Equation (3)
Modified embodiments of
In one modification, the resonant mass sensor is replaced by a microfluidic channel coupled with an alternate means of determining the transit time of particles passing through it. For example, a microfluidic channel having optical access could be observed with a high resolution camera capable of detecting the position and motion of particles passing through the channel. Measurement of the particle transit times, combined with pressure measurements similar to those in
In other modifications, the fluidics may not have the same configuration as in
Other modifications are contemplated. For example, many fluids exhibit a sensitive dependence of viscosity on temperature. Controlling and/or measuring the temperature of the fluid during the measurement of flow rate and viscosity would allow an automatic determination of the viscosity of the reference fluid in the relative method describe above. It would also allow more reproducibility of measurements if, for example, the fluid temperature were held constant between measurements.
Another modification relates to determining the time of entry of a particle into the sensor, and its time of exit. In
Other embodiments measure the shear thickening or shear thinning of a fluid, that is, the non-Newtonian fluid characteristic wherein the shear is not linearly dependent on the strain. By changing the pressure drop and flow rate through the microchannel, a range of shear values can be accessed. In addition, the pressure drop provides a measure of the strain applied to the fluid. Thus, a profile of shear vs. strain can be obtained for a fluid to determine if there is shear thickening or thinning present and to measure its magnitude. Due to their small cross section, microfluidic channels can introduce significant shear into the flow if desired. For example, for a channel with cross section of 8 μm and length 400 μm, and a flow rate that causes a particle to pass through in 100 ms (a typical value), the shear is approximately 1300 ŝ−1. Exploring shears in a range above and below this value finds application in many shear thinned and thickened fluids.
This application claims priority to U.S. Provisional Application Ser. No. 61/818,174, filed May 1, 2013
Number | Date | Country | |
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61818174 | May 2013 | US |