Fingering phenomena for driven coating films


Eres, M.H., Schwartz, L.W. and Roy, R.V. (2000) Fingering phenomena for driven coating films. Physics of Fluids, 12, (6), 1278-1295. (doi:10.1063/1.870382).

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Original Publication URL: http://dx.doi.org/10.1063/1.870382

Description/Abstract

A theoretical and numerical model is formulated to describe the instability and the long-time evolution of both gravity-driven and surface-shear-stress-driven thin coating films. A single evolution equation, of higher-order diffusive type, models the flow for either problem. It is derived using the lubrication approximation. For partially wetting systems, the effect of finite contact angle is incorporated in the equation using a particular disjoining pressure model. The base state, in each case, is a two-dimensional steadily propagating capillary front. Slight perturbations of the base state, applied along the front, initiate the fingering instability. Early-time results accurately reproduce the wavelengths of fastest growth and the corresponding eigenmodes as reported in published linear stability analyses. As time proceeds, depending on parameter values, various fingering patterns arise. For conditions of perfect wetting with the substrate downstream of the moving front covered with a thin precursor layer, predicted nonlinear finger evolution agrees well with published experiments. The ultimate pattern, in this case, is a steadily translating pattern of wedge-shaped fingers. Alternatively, for partially wetting systems that exhibit sufficiently large static contact angles, long straight-sided fingers or rivulets are formed. Finally, for larger contact angles, or at relatively low speeds, we predict that the flowing rivulets will become unstable and break up into strings of isolated droplets.

Item Type: Article
ISSNs: 1070-6631 (print)
Related URLs:
Keywords: thin liquid-films, direct numerical-simulation, rotating cylinder, spreading films, contact line, instability, surface, dynamics, flows, stability
Subjects: T Technology > TJ Mechanical engineering and machinery
Q Science > QA Mathematics
Q Science > QC Physics
Divisions: University Structure - Pre August 2011 > School of Engineering Sciences > Computational Engineering and Design
ePrint ID: 46403
Date Deposited: 29 Jun 2007
Last Modified: 27 Mar 2014 18:30
URI: http://eprints.soton.ac.uk/id/eprint/46403

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