Non-isothermal spreading of liquid drops on horizontal plates

A viscous-liquid drop spreads on a smooth horizontal surface, which is uniformly heated or cooled. Lubrication theory is used to study thin drops subject to capillary, thermocapillary and gravity forces, and a variety of contact-angle-versus-speed conditions. It is found for isothermal drops that gravity is very important at large times and determines the power law for unlimited spreading. Predictions compare well with the experimental data on isothermal spreading for both two-dimensional and axisymmetric configurations. It is found that heating (cooling) retards (augments) the spreading process by creating flows that counteract (reinforce) those associated with isothermal spreading. For zero advancing contact angle, heating will prevent the drop from spreading to infinity. Thus, the heat transfer serves as a sensitive control on the spreading.

[1]  D. v.,et al.  The moving contact line: the slip boundary condition , 1976, Journal of Fluid Mechanics.

[2]  M. Nishioka,et al.  Some observations of the subcritical transition in plane Poiseuille flow , 1985, Journal of Fluid Mechanics.

[3]  S. Rosenblat,et al.  How Do Liquid Drops Spread on Solids , 1985 .

[4]  L. M. Hocking.  SLIDING AND SPREADING OF THIN TWO-DIMENSIONAL DROPS , 1981 .

[5]  John Kim,et al.  On the structure of wall‐bounded turbulent flows , 1983 .

[6]  L. M. Hocking,et al.  On the nonlinear evolution of three-dimensional disturbances in plane Poiseuille flow , 1974, Journal of Fluid Mechanics.

[7]  L. M. Hocking.  THE SPREADING OF A THIN DROP BY GRAVITY AND CAPILLARITY , 1983 .

[8]  L. M. Hocking,et al.  The spreading of a drop by capillary action , 1982, Journal of Fluid Mechanics.

[9]  Clarence A. Miller,et al.  Spreading kinetics of liquid drops on solids , 1976 .

[10]  E. B. Dussan,et al.  LIQUIDS ON SOLID SURFACES: STATIC AND DYNAMIC CONTACT LINES , 1979 .

[11]  H. P. Greenspan,et al.  On the motion of a small viscous droplet that wets a surface , 1978, Journal of Fluid Mechanics.

[12]  Michael J. Miksis,et al.  The effect of the contact line on droplet spreading , 1991, Journal of Fluid Mechanics.

[13]  S. Orszag.  Accurate solution of the Orr–Sommerfeld stability equation , 1971, Journal of Fluid Mechanics.

[14]  C. Ngan.  On the dynamics of liquid spreading on solid surfaces , 1989, Journal of Fluid Mechanics.

[15]  J. T. Stuart,et al.  Stability of viscous motion between parallel planes for finite disturbances , 1951, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[16]  D. Henningson,et al.  Turbulent spots in plane Poiseuille flow-flow visualization , 1986 .

[17]  S. Tejada,et al.  Studies of dynamic contact angles on solids , 1972 .

[18]  J. Jiménez.  Bifurcations and bursting in two-dimensional Poiseuille flow , 1987 .

[19]  S. G. Bankoff,et al.  Nonlinear stability of evaporating/condensing liquid films , 1988, Journal of Fluid Mechanics.

[20]  P. Saffman,et al.  Two-dimensional superharmonic stability of finite-amplitude waves in plane Poiseuille flow , 1988, Journal of Fluid Mechanics.

[21]  L. M. Hocking.  A moving fluid interface. Part 2. The removal of the force singularity by a slip flow , 1977, Journal of Fluid Mechanics.

[22]  S. H. Davis,et al.  Steady thermocapillary flows in two-dimensional slots , 1982, Journal of Fluid Mechanics.

[23]  T. Herbert.  Finite amplitude stability of plane parallel flows , 1977 .

[24]  P. G. Saffman,et al.  VORTICES, STABILITY, AND TURBULENCE * , 1983 .

[25]  P. Gennes.  Wetting: statics and dynamics , 1985 .

[26]  S. H. Davis,et al.  On the motion of a fluid-fluid interface along a solid surface , 1974, Journal of Fluid Mechanics.

[27]  R. Hoffman.  A study of the advancing interface. I. Interface shape in liquid—gas systems , 1975 .

[28]  Anthony T. Patera,et al.  Secondary instability of wall-bounded shear flows , 1983, Journal of Fluid Mechanics.

[29]  D. O. Gough,et al.  Nonlinear cellular motions in Poiseuille channel flow , 1974, Journal of Fluid Mechanics.

[30]  A. Cazabat,et al.  Dynamics of wetting: Effects of surface roughness. , 1986 .

[31]  Jing-den Chen.  Experiments on a spreading drop and its contact angle on a solid , 1988 .

[32]  H. Reichardt,et al.  Über die Geschwindigkeitsverteilung in einer geradlinigen turbulenten Couetteströmung , 1956 .

[33]  D. Barkley.  Theory and predictions for finite‐amplitude waves in two‐dimensional plane Poiseuille flow , 1990 .

[34]  S. H. Davis.  Moving contact lines and rivulet instabilities. Part 1. The static rivulet , 1980, Journal of Fluid Mechanics.

[35]  Steven A. Orszag,et al.  Transition to turbulence in plane Poiseuille and plane Couette flow , 1980, Journal of Fluid Mechanics.

[36]  Sheila E. Widnall,et al.  A flow-visualization study of transition in plane Poiseuille flow , 1982, Journal of Fluid Mechanics.

[37]  Contact-line problems in fluid mechanics , 1983 .

[38]  S. G. Yiantsios,et al.  Rayleigh–Taylor instability in thin viscous films , 1989 .