An Analytical Two-Dimensional Linearized Droplet Shape Model for Combined Tangential and Normal Body Forces

In view of emerging research on forced wetting under complex applied forces, a simple model for a droplet shape evolution is developed here. In particular, the model refers to droplet spreading under quasisteady conditions. The corresponding linearized two-dimensional Young–Laplace equation is solved analytically resulting in a system of two equations that relates the droplet shape features to each other. Despite its simplicity, the final model produces a wealth of droplet behaviors when combined with the physical requirement that the contact angle should be within a particular range of values. Indicative results of the droplet behavior under several forces scenarios are examined here exhibiting why the present model is useful for designing experimental campaigns on forced spreading.