Patterns in viscoplastic films

Neil Balmforth

University of British Columbia, Canada

Abstract

In narrow slots (Hele-Shaw cells), when a more viscous fluid is displaced by a less viscous one, the interface between them becomes prone to the Saffman-Taylor instability, prompting the creation of labyrinthian patterns. If the more viscous fluid is replaced by a yield-stress fluid, one expects the viscoplastic version of this instability. However, if the displacing fluid is water, another instability takes over, whose appearance is more reminiscent of a pattern of fractures. This alternative instability even appears when the water is displaced by the yield-stress fluid (the opposite of the Saffman-Taylor configuration, which is expected to be stable). Similarly, when a viscoplastic fluid is extruded onto a flat plate, the resulting gravity current expands axisymmetrically when the surface is dry. However, when the plate is wet by a thin coating of water, fractures again appear to create a distinctive flower-like pattern. In this talk, I will report an exploration of these patterns and suggest that they arise from the solid-mechanical fracturing of the complex fluid, exacerbated by the presence at the surface of the solvent making up the fluid (i.e. water) which reduces the fracture toughness.

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