Axisymmetric spreading of a thin liquid drop with suction or blowing at the horizontal base

The axisymmetric spreading under gravity of a thin liquid drop on a horizontal plane with suction or blowing of fluid at the base is considered. The thickness of the liquid drop satisfies a non-linear diffusion equation with a source term. For a group invariant solution to exist the normal component of the fluid velocity at the base, v_n, must satisfy a first-order quasi-linear partial differential equation. The general form of the group invariant solution for the thickness of the liquid drop and for v_n is derived. Two particular solutions are considered. Each solution depends essentially on only one parameter which can be varied to yield a range of models. In the first solution, v_n is proportional to the thickness of the liquid drop. The base radius always increases even for suction. In the second solution, v_n is proportional to the gradient of the thickness of the liquid drop. The thickness of the liquid drop always decreases even for blowing. A special case is the solution with no spreading or contraction at the base which may have application in ink-jet printing.