Numerical simulation of spreading drops

Abstract

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in : http://oatao.univ-toulouse.fr/ Eprints ID : 10539Any correspondance concerning this service should be sent to the repository administrator: staff-oatao@listes-diff.inp-toulouse.fr g r a p h i c a l a b s t r a c t• Numerial simulation of spreading drops on a wettable surface.• We discuss the effect of the main parameters (density, viscosity, surface tension, drop radius and wettability).• Power law evolutions observed in experiments (t 1 /2, t 1 /10) are recovered and discussed.• The combined effect of viscosity and wettability has a significant effect on the spreading. Keywords:Drop spreading Numerical simulation a b s t r a c tWe consider a liquid drop that spreads on a wettable surface. Different time evolutions have been observed for the base radius r depending of the relative role played by inertia, viscosity, surface tension and the wetting condition. Numerical simulations were performed to discuss the relative effect of these parameters on the spreading described by the evolution of the base radius r(t) and the spreading time t S . Different power law evolutions r(t) ∝ t n have been observed when varying the parameters. At the early stage of the spreading, the power law t 1/2 (n = 1/2) is observed as long as capillarity is balanced by inertia at the contact line. When increasing the viscosity contribution, the exponent n is found to increase despite the increase of the spreading time. The effect of the surface wettability is observed for liquids more viscous than water. For a small contact angle, the power law t 1/2 is then followed by the famous Tanner law t 1/10 once the drop shape has reached a spherical cap. IntroductionWhen a liquid drop contacts a wettable surface, the liquid spreads over the solid to minimize the total surface energy. The first moments of spreading tend to be rapid (some milli-seconds for millimeter sized water drops) while it takes a much longer time for viscous liquids to completely spread. From the literature [22,17,9,1,6,3,2,24,7], it appears that several time evolutions can be observed for the base radius depending if inertia, viscosity and/or * Corresponding authors.

Effects of surface wettability and liquid viscosity on the dynamic wetting of individual drops

“…This is consistent with theoretical predictions [9,11] and experimental results [8,9,11,12,17] from literature. Recently, Legendre and Maglio numerically calculated that if the early wetting was dominated by viscous dissipation, the spreading should follow a power law with α = 2/3 [38]. However, in our experiments we found that the maximum α for all liquids was 0.5 and that α was only dependent on θ eq .…”

Comparison between numerical models for the simulation of moving contact lines

“…As a consequence, a sub-grid model as described in Dupont and Legendre [10] has to be introduced in order to make possible macroscopic simulations. Based on this approach, the modeling developed in recent works [23,21,17] appears to be the more -the wall condition seen by the fluid is a non slip condition, -the interface shape is connected by a dynamic relation to the characteristics of the contact line at the nanoscale.…”

“…The main difference with experiments is due to the oscillations observed at the end of the drop spreading. Such oscillations are induced by the propagation of capillary wave resulting in some cases of a droplet ejection [26,23]. In the simulations, the top of the drop is free to Table 5 Grid used in the simulations reported in Section 5. move and oscillate due to the capillary waves while in the experiments the drop remains pinned to the needle used for the deposit.…”

Inertial coalescence of droplets on a partially wetting substrate

“…The second method used adopts a volume-of-fluid (VOF) approach. 15,16 In the version of the VOF method employed in the present study, there is no interface reconstruction but the interface is limited to 2 to 3 grid cells, thanks to an accurate flux-corrected transport algorithm. The shear stress singularity at the wall is removed by using the Navier slip boundary condition.…”