Critical behavior of drop breakup in axisymmetric viscous flow

The critical behavior of a liquid droplet immersed in a host fluid under external axisymmetric viscous flow is studied. It is well known that when the external extensional flow is weak the system approaches a steady-state flow, but when the shear rate is increased beyond some critical value a steady state is never attained and the droplet is stretched to infinity. This behavior is explained qualitatively by a simple semianalytic argument. The critical power law behavior of the droplet shape and its time dependence when the shear rate approaches the critical value is studied and is verified by numerical simulations for linear axisymmetric flows. For biaxial extensional flow (negative elongational flow) it is known that another critical point appears, and the droplet goes over into a toroidal shape. Similar critical behavior is predicted at that point also. (C) 1999 American Institute of Physics. [S1070-6631(99)03105-0].