The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers

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Abstract
Transient effects associated with the deformation and breakup of a drop following a step change from critical to suberitical flow conditions are studied experimentally and numerically. In the experiments, we consider step changes in both the shear rate and flow type for two-dimensional linear flows generated in a four-roll mill. Numerically we consider step changes in shear rate only for a uniaxial extensional flow. Depending upon the degree of deformation prior to the change in flow conditions, the drop may either return to a steady deformed shape, or continue to stretch at a reduced rate, or, for intermediate cases, the drop may break without large-scale stretching. This behaviour is a consequence of the complicated interaction between changes of shape due to interfacial tension and changes of shape due to the motion of the suspending fluid. This mode of breakup is most pronounced for high viscosity ratios, because very large extensions are necessary to guarantee breakup if the flow is stopped abruptly. For drops that are not too deformed, the sudden addition of vorticity to the external flow is characterized by rapid rotation of the drop to a new steady orientation followed by deformation and/or breakup according to the effective flow conditions at the new orientation. Finally, for viscous drops in flows with vorticity, it is demonstrated experimentally that breakup can be achieved if the initial shape is sufficiently non-spherical even though the same drop could not be made to break in the same flow at any capillary number when beginning with a near-spherical shape.