The evolution and bifurcation of a pendant drop

Abstract

In this paper we calculate how a pendant drop evolves at the end of a nozzle when the volume of the drop increases steadily with time. We find that the character of the evolution is strongly dependent on the growth rate of the drop and the radius of the nozzle. Typically we find that once the drop has become unstable, two bifurcations occur shortly after each other when the growth rate of the drop is slow. For large growth rates the bifurcations are well-separated in time. We are able to calculate the volumes of the drops after the bifurcations. A comparison with experimental data shows a satisfactory agreement.