A semi-analytical method to estimate the slip length of spreading cap-shaped droplets using Cox theory

Martin Wörner, Xuan Cai, Hocine Alla, Pengtao Yue

Published 2016-05-20Version 1

The Cox-Voinov law on dynamic spreading relates the difference between the cubic values of the apparent contact angle (theta) and the equilibrium contact angle to the instantaneous contact line speed (U). Comparing spreading results with this law requires accurate data of theta and U during the entire process. We consider the case when gravitational forces are negligible and transform the general Cox law in a relationship for the temporal evolution of the spreading radius. For cap-shaped droplets, this enables a comparison of experimental or computational results with Cox theory without the need for instantaneous data of theta and U. The fitting of Cox theory against measured or computed base-radius-over-time curves allows estimating the effective slip length. This is useful for establishing relationships between slip length and parameters in numerical methods for moving contact lines. The procedure is illustrated by numerical simulations for partially wetting droplets employing the coupled level-set volume-of-fluid and phase field methods.