Axisymmetric model of drop spreading on a horizontal surface

Spreading of an initially spherical liquid drop over a textured surface is analyzed by solving an integral form of the governing equations. The mathematical model extends Navier-Stokes equations by including surface tension at the gas-liquid boundary and a force distribution at the three phase contact line. While interfacial tension scales with drop curvature, the motion of the contact line depends on the departure of instantaneous contact angle from its equilibrium value. The numerical solution is obtained by discretizing the spreading drop into disk elements. The Bond number range considered is 0.01-1. Results obtained for sessile drops are in conformity with limiting cases reported in the literature [J. C. Bird et al., Short-time dynamics of partial wetting, Phys. Rev. Lett. 100, 234501 (2008)]. They further reveal multiple time scales that are reported in experiments [K. G. Winkels et al., Initial spreading of low-viscosity drops on partially wetting surfaces, Phys. Rev. E 85, 055301 (2012) and A. Eddi et al., Short time dynamics of viscous drop spreading, Phys. Fluids 25, 013102 (2013)]. Spreading ofwater and glycerin drops over fully and partially wetting surfaces is studied in terms of excess pressure, wall shear stress, and the dimensions of the footprint. Contact line motion is seen to be correctly captured in the simulations. Water drops show oscillations during spreading while glycerin spreads uniformly over the surface. (C) 2015 AIP Publishing LLC.