Abstract
A boundary-integral method for periodic arrays of drops, threads or sheets between parallel walls is presented. The Green’s functions take the form of a far-field Hele-Shaw description, which is used to generate periodic Green’s functions for the parallel-wall configuration. The method is applied to study the effect of confinement on the breakup of threads. A comparison is made with classical Tomotika’s theory and growth rates parallel and perpendicular to the walls are determined as a function of confinement ratio. Contrary to existing belief, we find that confined threads are not stable, but that the time for breakup increases with confinement and viscosity ratio, at least for threads whose diameter is smaller than the wallspacing. We also show the in-phase and out-of-phase breakup for an array of threads, as well as the stabilizing effect of shear flow.
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