Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

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Gaskell, P.H. ; Jimack, P.K. ; Sellier, M. ; Thompson, H.M. ; Wilson, M.C.T. (2004)
  • Publisher: Cambridge University Press
  • Subject:
    arxiv: Physics::Fluid Dynamics

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver.\ud \ud Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography.\ud \ud Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decré & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function.\ud \ud An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decré & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.\ud
  • References (37)
    37 references, page 1 of 4

    Aksel, N. 2000 Influence of the capillarity on a creeping flow down an inclined plane with an edge. Arch. Appl. Mech. 70, 81-90.

    Bertozzi, A. & Brenner, M. P. 1997 Linear stability and transient growth in driven contact lines. Phys. Fluids 9, 530-539.

    Brandt, A. 1977 Multi-level adaptive solutions to boundary-value problems. Maths Comput. 31-138, 333-390.

    Christodoulou, K. N., Kistler, S. F. & Schunk, P. R. 1997 Advances in computational methods for free surface flows. In Liquid Film Coating (ed. S. F. Kistler & P. M. Schweizer), pp. 297-366. Chapman and Hall.

    Christodoulou, K. N. & Scriven, L. E. 1989 The fluid mechanics of slide coating. J. Fluid Mech. 208, 321-354.

    Decre´, M. M. J. & Baret, J.-C. 2003 Gravity-driven flows of low-viscosity liquids over twodimensional topographies. J. Fluid Mech. 487, 147-166.

    Decre´, M. M. J., Fernandez-Parent, C. & Lammers, J. H. 1998 Flow of a gravity driven thin liquid film over one-dimensional topographies. Philips Research, Unclassified Report NL-UR 823/98.

    Decre´, M. M. J., Fernandez-Parent, C. & Lammers, J. H. 1999 Flow of a gravity driven thin liquid film over one-dimensional topographies: a tripartite approach. Proc. 3rd European Coating Symposium (ed. F. Durst & H. Raszillier), pp. 151-156. Springer.

    Fawehinmi, O. B., Gaskell, P. H. & Thompson, H. M. 2002 Finite element analysis of flow in a cavity with internal blockages. Proc. Inst. Mech. Engrs C 216, 517-530.

    Gaskell, P. H., Jimack, P. K., Sellier, M. & Thompson, H. M. 2004 Efficient and accurate time-adaptive multigrid simulations of droplet spreading. Intl J. Numer. Meth. Fluids (In press).

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