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Nonisothermal spreading of liquid drops on horizontal plates

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Non-isothermal spreading of liquid drops on horizontal plates. A paper by P. ... Gennes, P.J. DE 1985 Wetting: statics and dynamics. Rev. Mod. Phys. 57 827 ... – PowerPoint PPT presentation

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Title: Nonisothermal spreading of liquid drops on horizontal plates


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
Whats 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 eqn
  • solve for velocity field
  • experiment agreement
  • Marangoni number
  • 0
  • gt 0
  • lt 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
ResultsCooling 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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