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Non-isothermal spreading of liquid drops on horizontal plates

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Non-isothermal spreading of liquid drops on horizontal plates

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    1. Non-isothermal spreading of liquid drops on horizontal plates A paper by P. Ehrhard and S. Davis Presented by Lael Fisher Tuesday January 28, 2003

    2. Why is this important? coating technology mould filling performance of fuel tanks in space cited 66 times (Web of Science) innovative heat pipe systems (Zhang 2001) spin coating (Kitamura 2001) fluid dispensing process (Chen et. al. 2000)

    3. What’s new? angle v. speed generalized: U = ? (?-?A)m gravity plate uniformly heated or cooled

    4. Mobility Exponent found empirically m = 1 (Greenspan) m = 3 (Schwartz & Tejeda) m = infinity (constant contact angle)

    5. Problem Formulation & B.C.’s Navier - Stokes Continuity Equation Energy Equation no-slip at rigid boundary relaxed to avoid the appearance of shear-stress singularity at moving contact line

    6. Procedure I.C.’s symmetry conditions smoothness conditions conservation of volume contact angle conditions non-dimensionalize variables O(1) problem gives ‘lubrication approximation’ dimensionless parameters appear

    7. Evolution Equation lubrication approx. gives evolution eq’n solve for velocity field experiment agreement Marangoni number = 0 > 0 < 0

    8. Results: Isothermal Spreading M = 0 modified Bessel functions (1st kind) gravity no fluid motion at steady state

    9. Results: Isothermal Spreading

    10. Results: Non-Isothermal Spreading (heating) fluid flow always present no gravity as M increases, heating slows drop spreading and limits drop size

    11. Results: Non-Isothermal Spreading (Cooling) thermocapillary flow reversed flatter drops no gravity aids spreading

    12. Results: Cooling and Heating top ?A = 0 bottom ?A = 0.5 top line on each figure is an approximation (which breaks down)

    13. Molecular Connection (de Gennes) small-scale physics of contact lines model long-range van der Waals repulsion no contact line nearby drop precursor film from main drop do not consider film edge contact line

    14. Conclusions non-isothermal heating retards spreading cooling augments spreading ?A= 0 isothermal drop goes to infinity plate heated, drop will spread finitely far plate cooled, drop goes to infinity faster gravity important at large times determines power law for unlimited spreading

    15. Bibliography P. Ehrhard & S.H. Davis 1991 Non-isothermal spreading of liquid drops on horizontal plates. Journal of Fluid Mechanics. 229 365-388 Gennes, P.J. DE 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57 827 Zhang N.L. Innovative heat pipe systems using a new working fluid. Int Commun Heat Mass. 28(8): 1025-1033 Nov 2001 Kitamura A. Thermal effects on liquid film flow during spin coating. Phys. Fluids 13(10): 2788-2794 Oct. 2001 Chen X.B., Schoenau G., Zhan W.J. Modeling of time-pressure fluid dispensing processes. IEEE T Electron Pa M. 23 (4): 300-305 Oct. 2000

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