In selective withdrawal, the interface between two layers of liquid is deformed by a spatially converging withdrawal flow imposed in the upper layer. When the imposed flow is sufficiently strong, liquid from the lower layer is entrained by the withdrawal flow in the upper layer. A thin liquid spout forms. Such thin liquid spouts are being used to encapsulate biological cells and to create thin fibers and monodisperse drops in microfluidic channels via axisymmetric flow-focusing. But the spout formation dynamics are poorly understood.
Here, we re-examine measurements that suggest spout formation via the interface approaching a singular cusp shape as the withdrawal flow strengthens. We analyze the interface evolution in a minimal model whose results agree well with experimental measurements but extend over a larger dynamic range. We identify the transition as a discontinuous saddle-node bifurcation. The large increase in the interface curvature near transition is not associated with an approach towards a singularity but instead remains smooth.
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