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arXiv · 1806.05446

Edge states control droplet break-up in sub-critical extensional flows

Giacomo Gallino·Tobias M. Schneider·François Gallaire
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Abstract

A fluid droplet suspended in an extensional flow of moderate intensity may break into pieces, depending on the amplitude of the initial droplet deformation. In subcritical uniaxial extensional flow the non-breaking base state is linearly stable, implying that only a finite amplitude perturbation can trigger break-up. Consequently, the stable base solution is surrounded by its finite basin of attraction. The basin boundary, which separates initial droplet shapes returning to the non-breaking base state from those becoming unstable and breaking up, is characterized using edge tracking techniques. We numerically construct the edge state, a dynamically unstable equilibrium whose stable manifold forms the basin boundary. The edge state equilibrium controls if the droplet breaks and selects a unique path towards break-up. This path physically corresponds to the well-known end-pinching mechanism. Our results thereby rationalize the dynamics observed experimentally [Stone & Leal, J. Fluid Mech. 206, 223 (1989)]

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Giacomo Gallino, Tobias M. Schneider, François Gallaire. 2018-06-14. Edge states control droplet break-up in sub-critical extensional flows. https://doi.org/10.1103/physrevfluids.3.073603

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