Marangoni‐driven liquid films rising out of a meniscus onto a nearly‐horizontal substrate

We revisit the situation of a thin liquid film driven up an inclined substrate by a thermally induced Marangoni shear stress against the opposing parallel component of gravity. In contrast to previous studies, we focus here on the meniscus region, in a case where the substrate is nearly horizontal. Our numerical simulations show that the time‐dependent lubrication model for the film profile can reach a steady state in the meniscus region that is unlike the monotonic solutions investigated earlier. A systematic investigation of the steady states of the lubrication model is carried out by studying the phase space of the corresponding third‐order ODE system. We find a rich structure of the phase space including multiple non‐monotonic solutions with the same far‐field film thickness. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

[1]  T. Witelski,et al.  Localized Marangoni forcing in driven thin films , 2005 .

[2]  A. Münch.  Pinch-off transition in Marangoni-driven thin films. , 2003, Physical review letters.

[3]  Andreas Münch,et al.  The Thickness of a Marangoni-Driven Thin Liquid Film Emerging from a Meniscus , 2002, SIAM J. Appl. Math..

[4]  L. M. Hocking.  Meniscus draw-up and draining , 2001, European Journal of Applied Mathematics.

[5]  L. Schwartz.  On the asymptotic analysis of surface-stress-driven thin-layer flow , 2001 .

[6]  M. Schneemilch,et al.  Shock Separation in Wetting Films Driven by Thermal Gradients , 2000 .

[7]  M. Schneemilch and,et al.  Wetting Films in Thermal Gradients , 2000 .

[8]  Andreas Münch,et al.  Shock transitions in Marangoni gravity-driven thin-film flow , 2000 .

[9]  Andrea L. Bertozzi,et al.  Undercompressive shocks in thin film flows , 1999 .

[10]  A. Bertozzi,et al.  Rarefaction–undercompressive fronts in driven films , 1999 .

[11]  V. Alexiades,et al.  Undercompressive waves in driven thin film flow: Theory, computation, and experiment , 1999 .

[12]  A. Münch,et al.  Numerical and asymptotic results on the linear stability of a thin film spreading down a slope of small inclination , 1999, European Journal of Applied Mathematics.

[13]  Andrea L. Bertozzi,et al.  CONTACT LINE STABILITY AND UNDERCOMPRESSIVE SHOCKS IN DRIVEN THIN FILM FLOW , 1998 .

[14]  Troian,et al.  Stabilizing the Advancing Front of Thermally Driven Climbing Films. , 1998, Journal of colloid and interface science.

[15]  S. Troian,et al.  A Theoretical Study of Instabilities at the Advancing Front of Thermally Driven Coating Films , 1997, Journal of colloid and interface science.

[16]  D. Quéré,et al.  Thickness and Shape of Films Driven by a Marangoni Flow , 1996 .

[17]  A. Cazabat,et al.  The Thickness of Surface-Tension-Gradient-Driven Spreading Films , 1993 .

[18]  L. E. Scriven,et al.  Rising and falling film flows: Viewed from a first-order approximation , 1992 .

[19]  F. Heslot,et al.  Fingering instability of thin spreading films driven by temperature gradients , 1990, Nature.

[20]  L. Landau,et al.  Dragging of a Liquid by a Moving Plate , 1988 .

[21]  S. Wilson,et al.  The drag-out problem in film coating theory , 1982 .

[22]  John E. Buchanan,et al.  Dynamics of thin liquid films in the presence of surface tension gradients , 1973 .