TY - JOUR
T1 - Comparison of Navier-Stokes simulations with long-wave theory
T2 - Study of wetting and dewetting
AU - Mahady, K.
AU - Afkhami, S.
AU - Diez, J.
AU - Kondic, L.
N1 - Funding Information:
This research was partly supported by NSF Grant Nos. DMS-1320037 (S.A.) and CBET-1235710 (L.K.) and by Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET, Argentina) Grant No. PIP 844/2011 (J.D.). The authors acknowledge many useful discussions with J. Fowlkes, A. González, and P. Rack.
PY - 2013/8/30
Y1 - 2013/8/30
N2 - The classical long-wave theory (also known as lubrication approximation) applied to fluid spreading or retracting on a solid substrate is derived under a set of assumptions, typically including small slopes and negligible inertial effects. In this work, we compare the results obtained by using the long-wave model and by simulating directly the full two-phase Navier-Stokes equations employing a volume-of-fluid method. In order to isolate the influence of the small slope assumption inherent in the long-wave theory, we present a quantitative comparison between the two methods in the regime where inertial effects and the influence of gas phase are negligible. The flow geometries that we consider include wetting and dewetting drops within a broad range of equilibrium contact angles in planar and axisymmetric geometries, as well as liquid rings. For perfectly wetting spreading drops we find good quantitative agreement between the models, with both of them following rather closely Tannerss law. For partially wetting drops, while in general we find good agreement between the two models for small equilibrium contact angles, we also uncover differences which are particularly evident in the initial stages of evolution, for retracting drops, and when additional azimuthal curvature is considered. The contracting rings are also found to evolve differently for the two models, with the main difference being that the evolution occurs on the faster time scale when the long-wave model is considered, although the ring shapes are very similar between the two models.
AB - The classical long-wave theory (also known as lubrication approximation) applied to fluid spreading or retracting on a solid substrate is derived under a set of assumptions, typically including small slopes and negligible inertial effects. In this work, we compare the results obtained by using the long-wave model and by simulating directly the full two-phase Navier-Stokes equations employing a volume-of-fluid method. In order to isolate the influence of the small slope assumption inherent in the long-wave theory, we present a quantitative comparison between the two methods in the regime where inertial effects and the influence of gas phase are negligible. The flow geometries that we consider include wetting and dewetting drops within a broad range of equilibrium contact angles in planar and axisymmetric geometries, as well as liquid rings. For perfectly wetting spreading drops we find good quantitative agreement between the models, with both of them following rather closely Tannerss law. For partially wetting drops, while in general we find good agreement between the two models for small equilibrium contact angles, we also uncover differences which are particularly evident in the initial stages of evolution, for retracting drops, and when additional azimuthal curvature is considered. The contracting rings are also found to evolve differently for the two models, with the main difference being that the evolution occurs on the faster time scale when the long-wave model is considered, although the ring shapes are very similar between the two models.
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U2 - 10.1063/1.4828721
DO - 10.1063/1.4828721
M3 - Article
AN - SCOPUS:84888816216
SN - 1070-6631
VL - 25
JO - Physics of Fluids
JF - Physics of Fluids
IS - 11
M1 - 112103
ER -