×

zbMATH — the first resource for mathematics

Three-dimensional thin film and droplet flows over and past surface features with complex physics. (English) Zbl 1433.76017
Summary: This paper describes, in the main, the benefits of using a general Newton globally convergent solver within an adaptive multigrid framework for solving discretised forms of lubrication models of three-dimensional, free-surface flow over and/or past substrate topography, involving complex physics. The two illustrative gravity-driven problems considered address solute mixing in a continuous thin film flow and droplet migration down an inclined substrate. The computational price paid for the flexibility offered by the solver is investigated alongside the overall benefits of adaptive local mesh refinement and multigridding.
MSC:
76A20 Thin fluid films
Software:
FILMPAR
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Craster, R.V.; Matar, O.K., Dynamics and stability of thin liquid films, Rev mod phys, 81, 3, 1131-1197, (2009)
[2] Dècre, M.M.J.; Baret, J.C., Gravity-driven flows of viscous liquids over two-dimensional topographies, J fluid mech, 487, 147-166, (2003) · Zbl 1049.76004
[3] Blyth, M.G.; Pozrikidis, C., Film flow down an inclined plane over a three-dimensional obstacle, Phys fluids, 18, 5, 052104, (2006) · Zbl 1185.76437
[4] Baxter, S.J.; Power, H.; Cliffe, K.A.; Hibberd, S., Three-dimensional thin film flow over and around an obstacle on an inclined plane, Phys fluids, 21, 3, 032102, (2009) · Zbl 1183.76085
[5] Oron, A.; Davis, S.H.; Bankov, S.G., Long-scale evolution of thin liquid films, Rev mod phys, 69, 931-980, (1997)
[6] Schwartz, L.W.; Eley, R.R., Simulation of droplet motion on low-energy and heterogeneous surfaces, J colloid interf sci, 202, 173-188, (1998)
[7] Gaskell, P.H.; Jimack, P.K.; Sellier, M.; Thompson, H.M., Efficient and accurate time adaptive multigrid simulation of droplet spreading, Int J num meth fluids, 45, 11, 1161-1186, (2004) · Zbl 1060.76617
[8] Becker, J.; Grun, G.; Seemann, R.; Mantz, H.; Jacobs, K.; Mecke, K.R.; Blossey, R., Complex dewetting scenarios captured by thin-film models, Nat mater, 2, 1, 59-63, (2003)
[9] Lee, Y.C.; Thompson, H.M.; Gaskell, P.H., An efficient adaptive multigrid algorithm for predicting thin film flow on surfaces containing localised topographic features, Comput fluids, 36, 5, 838-855, (2007) · Zbl 1194.76157
[10] Gaskell, P.H.; Jimack, P.K.; Sellier, M.; Thompson, H.M.; Wilson, M.C.T., Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography, J fluid mech, 509, 253-280, (2004) · Zbl 1163.76322
[11] Sellier, M.; Lee, Y.C.; Thompson, H.M.; Gaskell, P.H., Thin film flow on surfaces containing localized arbitrary occlusions, Comput fluids, 38, 1, 171-182, (2009) · Zbl 1237.76012
[12] Howison, S.D.; Moriarty, J.A.; Ockendon, J.R.; Terril, E.L.; Wilson, S.K., A mathematical model for drying paint layers, J eng math, 32, 377-394, (1997) · Zbl 0910.76006
[13] Gaskell, P.H.; Jimack, P.K.; Sellier, M.; Thompson, H.M., Flow of evaporating gravity-driven thin liquid films over topography, Phys fluids, 18, 1, 013601, (2006) · Zbl 1185.76440
[14] Lee, Y.C.; Thompson, H.M.; Gaskell, P.H., Thin film flow over flexible membranes containing surface texturing: bio-inspired solutions, J eng tribo imeche part J, 223, 3, 337-345, (2009)
[15] Lee, Y.C.; Thompson, H.M.; Gaskell, P.H., FILMPAR: a parallel algorithm designed for the efficient and accurate computation of thin film flow on functional surfaces containing micro-structure, Comput phys commun, 180, 12, 2634-2649, (2009)
[16] Podgorski, T.; Flesselles, J.-M.; Limat, L., Corners, cusps and pearls in running drops, Phys rev, 87, 3, 036102, (2001)
[17] Koh, Y.Y.; Lee, Y.C.; Gaskell, P.H.; Jimack, P.K.; Thompson, H.M., Droplet migration: quantitative comparisons with experiment, Euro phys J - special topics, 166, 117-120, (2009)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.