Modeling the effects of contact angle hysteresis on the sliding of droplets down inclined surfaces

Contact angle hysteresis is an important phenomenon that occurs both in natural and industrial droplet spreading/sliding applications. As they slide, droplets adopt a different contact angle at the front and rear, the advancing and a receding contact angles, respectively. This work investigates the different stages involved in the motion of droplets down inclined surfaces in the lubrication approximation framework. A simplified hysteresis model is proposed, implemented, and tested. This model automatically locates the section of the contact line which is advancing and the section which is receding. This enables the application of different contact angles at the advancing and receding fronts and therefore takes into account contact angle hysteresis. For validation purposes, experiments of fluid droplet spreading/sliding on inclined surfaces have also been performed to measure the terminal sliding velocity. With the inclusion of contact angle hysteresis, simulation results are shown to be in much better agreement with the experimental ones. This paper also presents a simple model based on Newton's second law which is shown to have reproduced remarkably well the steady and dynamic results if the shape of the droplets does not depart too much from a spherical cap configuration.