Breakup of liquid threads in linear flows

We study, theoretically, the surface-tension-driven breakup of a long filament of fluid in a general linear flow, v = L·x. By analyzing the problem in a moving frame and assuming a circular cross section we find that the flow around the filament is an axisymmetric extensional flow with a time-dependent strength, which can be calculated from the rate of rotation of the filament and a contribution to the axial velocity which varies with the azimuthal angle. The analysis of the axisymmetric time-dependent case does not appear to be overly restrictive: the asymmetric variation may be small even in the case of a simple shear flow, in which the asymmetry is the greatest among all possible linear flows, depending on the initial orientation of the filament. We present calculations for two special cases: hyperbolic extensional flow and simple shear flow. The results indicate that under similar conditions, the drop fragments produced on breakup in simple shear flow are larger than those in hyperbolic extensional flow. The predictions of the theory also compare reasonably well with some previous experimental data in hyperbolic extensional flow and simple shear flow.