The motion of a drop in a rigid surface

The assumptions of a region of slip near a moving contact line (to remove the force singularity) and a constant contact angle are used to obtain the equation for the shape of a thin drop of liquid resting on a rigid plane. Three asymptotic expansions are matched together to obtain an expression for the rate at which the drop spreads. Some cases of sliding motion are also examined. Although the technique is presented here for thin drops only, it can also be applied to drops of arbitrary size.