Claims
- 1. Apparatus for determining integrated nucleation probability for an ink jet system that uses thermal energy generated by a heat generating element that is responsive to a heating drive signal so as to generate bubbles in ink, said apparatus comprising:a memory to store programmed calculation steps including steps by which integrated nucleation probability is determinable; a central processing unit for executing said programmed calculation steps stored in said memory so as to determine integrated nucleation probability; wherein said programmed calculation steps include (a) a temperature calculation step to calculate a temperature distribution of ink on the heat generating element, (b) a rate calculation step to calculate rate of nucleation of bubbles based on the temperature distribution of ink calculated in said temperature calculation step, and (c) an integrating step to integrate the rate of nucleation from said rate calculation step with respect to time, so as to obtain integrated nucleation probability as a function of time of the heating drive signal.
- 2. A system according to claim 1, wherein said memory is comprised by a random access memory.
- 3. A system according to claim 1, wherein said programmed calculation steps further include a control program by which said central processing unit controls itself.
- 4. A system according to claim 1, wherein said rate calculation step includes steps to calculate a nucleation rate per unit area and further includes at least one of a a homogeneous nucleation rate and a a heterogeneous nucleation rate.
- 5. A system according to claim 1, wherein said memory is comprised at least in part by a read only memory.
- 6. A system according to claim 1, further comprising a data output port connected with a printer, and wherein said central processing unit is adapted to output the integrated nucleation probability from said integrating step to said data output port.
- 7. A system according to claim 1, further comprising a data output port connected with display means, and wherein said central processing unit is adapted to output the integrated nucleation probability from said integrating step to said data output port.
- 8. A system according to claim 1, wherein said rate calculating step includes steps to calculate both a homogeneous nucleation rate and a heterogeneous nucleation rate, and wherein rate of nucleation is comprised by at least a sum thereof.
- 9. A system according to claim 8, wherein the homogeneous nucleation rate Kho is calculated by integrating Jho with respect to distance, where Jho is given by: Jho=NAρlml(3NAσπ m1)12exp[-Δ GhokBT],Δ Gho=16 πσ33(pv-pl)2,pv=psexp[pamb-psρlRvT-Xa]+pambxaxsa,where NA is the Avogadro number, kB is the Boltzmann constant, m is the molecular weight of the liquid, ρ is the density of the ink, σ is the surface tension of the ink, Pv is the pressure in the critical size bubble, Pamb, Ps is the saturated vapor pressure, Rv (=NAKB/m2is) is the gas constant of the vapor, xa is the mole ratio of the dissolved air, xsa is the mole ratio of the dissolved air in saturation, and T is the temperature distribution in said temperature calculating step.
- 10. A system according to claim 8 or 9, wherein the heterogeneous nucleation rate Khe is calculated by Khe=(NAρlml)23(ψ(3NAσπ mlφ))12exp[-Δ GhekBT],Δ Ghe=16 πσ3φ3(pv-pamb)2,φ=2+3 cos θ-cos3 θ4,ψ=1+cos θ2,where NA is the Avogadro number, kB is the Boltzmann constant, m is the molecular weight of the liquid, ρ is the density of the ink, σ is the surface tension of the ink, pv is the pressure in the critical size bubble, pamb is ambient pressure, θ is a contact angle, and T is the temperature distribution in said temperature calculating step.
- 11. Computer-executable process steps stored on a computer-readable memory medium, the steps to determine integrated nucleation probability in an ink jet system that uses thermal energy generated by a heat generating element that is responsive to a heating drive signal so as to generate bubbles in ink, the steps comprising:a temperature calculation step to calculate a temperature distribution of ink on the heat generating element; a rate calculation step to calculate rate of nucleation of bubbles based on the temperature distribution of ink calculated in said temperature calculation step; and an integrating step to integrate the rate of nucleation from said rate calculation step with respect to time, so as to obtain integrated nucleation probability as a function of time of the heating drive signal.
- 12. Computer-executable process steps according to claim 11, wherein said rate calculation step includes steps to calculate a nucleation rate per unit area and further includes at least one of a step to calculate a homogeneous nucleation rate and a step to calculate a heterogeneous nucleation rate.
- 13. Computer-executable process steps according to claim 11, wherein said rate calculating step includes steps to calculate both a homogeneous nucleation rate and a heterogeneous nucleation rate, and wherein rate of nucleation is comprised by at least a sum thereof.
- 14. Computer-executable process steps according to claim 13, wherein the homogeneous nucleation rate Kho is calculated by integrating Jho with respect to distance, where Jho is given by: Jho=NAρlml(3NAσπ m1)12exp[-Δ GhokBT],Δ Gho=16 πσ33(pv-pl)2,pv=psexp[pamb-psρlRvT-Xa]+pambxaxsa,where NA is the Avogadro number, kB is the Boltzmann constant, m is the molecular weight of the liquid, ρ is the density of the ink, σ is the surface tension of the ink, pv is the pressure in the critical size bubble, Pamb, ps is the saturated vapor pressure, Rv (=NAKB/m2is) is the gas constant of the vapor, xa is the mole ratio of the dissolved air, xsa is the mole ratio of the dissolved air in saturation, and T is the temperature distribution in said temperature calculating step.
- 15. Computer-executable process steps according to claim 13 or 14, wherein the heterogeneous nucleation rate Khe is calculated by Khe=(NAρlml)23(ψ(3NAσπ mlφ))12exp[-Δ GhekBT],Δ Ghe=16 πσ3φ3(pv-pamb)2,φ=2+3 cos θ-cos3 θ4,ψ=1+cos θ2,where NA is the Avogadro number, kB is the Boltzmann constant, m is the molecular weight of the liquid, ρ is the density of the ink, σ is the surface tension of the ink, Pv is the pressure in the critical size bubble, pamb is ambient pressure, θ is a contact angle, and T is the temperature distribution in said temperature calculating step.
Priority Claims (1)
Number |
Date |
Country |
Kind |
1-095397 |
Apr 1989 |
JP |
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Parent Case Info
This application is a continuation of application Ser. No. 8/528,605, filed Sep. 15, 1995, which is a continuation of application Ser. No. 08/274,376, filed Jul. 13, 1994, which was a continuation of application Ser. No. 07/908,614, filed Jun. 29, 1992, which was a continuation of application Ser. No. 07/724,455, filed Jul. 3, 1991, which was a continuation of application Ser. No. 07/509,759, filed Apr. 17, 1990, all now abandoned.
US Referenced Citations (6)
Foreign Referenced Citations (1)
Number |
Date |
Country |
11170 |
Jan 1983 |
JP |
Non-Patent Literature Citations (4)
Entry |
Allen et al; Thermodynanics and Hydrodynamics of Thermal Ink Jets; Hewlett-Packard Journal, vol. 36, May 1985, No. 5, Table of Contents and pp. 21-27. |
Hsu, “On the Size Range of Active Nucleation Cavities on a Heating Surface”, Journal of Heat Transfer, Aug. 1962, pp. 207-216. |
Ward et al., “On the Thermodynamics of Nucleation in Weak Gas-Liquid Solutions”, Journal of Basic Engineering, Dec. 1970, pp. 695-704. |
Bender et al., “Advanced Mathematical Methods for Scientists and Engineers”, McGraw-Hill 1978, Table of Contents and pp. 484-543. |
Continuations (5)
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Number |
Date |
Country |
Parent |
08/528605 |
Sep 1995 |
US |
Child |
08/896543 |
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US |
Parent |
08/274376 |
Jul 1994 |
US |
Child |
08/528605 |
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US |
Parent |
07/908614 |
Jun 1992 |
US |
Child |
08/274376 |
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US |
Parent |
07/724455 |
Jul 1991 |
US |
Child |
07/908614 |
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US |
Parent |
07/509759 |
Apr 1990 |
US |
Child |
07/724455 |
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US |