Forces Acting on Sessile Droplet on Inclined Surfaces

Although many analytical, experimental and numerical studies have focused on droplet motion, the mechanics of the droplet while still in its static state, and just before motion starts, are not well understood. A study of static droplets would shed light on the threshold voltage (or critical inclination) for initiating electrically (or gravitationally) induced droplet motion. Before the droplet starts to move, the droplet shape changes such that the forces acting at the triple contact line balance the actuation forces. These contact line forces are governed by the contact angles along the contact line. The contact angle varies from an advancing angle at the leading edge to a receding angle at the trailing edge of the droplet. The present study seeks to understand and predict these forces at the triple contact line. The droplet shape, as well as the advancing and receding contact angles, is experimentally measured as a function of droplet size under the action of a gravitational force at different inclination angles. The advancing and receding contact angles are correlated with static contact angle and Bond number. A Volume of Fluid Continuous Surface Force model with varying contact angles along the triple contact line is developed to predict the same. The model is first verified against a twodimensional analytical solution. It is then used to simulate the shape of a sessile droplet on an incline at various angles of inclination and to determine the critical angle of inclination as a function of droplet size. Good agreement is found between experimental measurements and predictions. The contact line profile and contact area are also predicted. The contact area predictions based on a spherical-cap assumption are also compared against the numerical predictions. NOMENCLATURE A area Bo Bond number D diameter F volumetric force g gravitational vector n normal vector n̂ unit normal vector p pressure R radius of semi-circular droplet t time t̂ unit tangential vector v velocity vector Greek  volume fraction β surface inclination angle  interface curvature μ viscosity φ azimuthal angle  contact angle ρ density Subscripts adv advancing contact angle crit critical h hysteresis norm normalized rec receding contact angle w wall Proceedings of the ASME 2009 Heat Transfer Summer Conference HT2009 July 19-23, 2009, San Francisco, California USA