Fracture patterns in viscoplastic gravity currents

Abstract

Constant-flux gravity currents of viscoplastic fluid remain axisymmetric when extruded onto a dry horizontal plane. However, if the plane is coated with a shallow layer of water, the current suffers a dramatic non-axisymmetric instability in which localized $v$ -shaped cuts appear in the outer edge where the viscoplastic fluid is in contact with water. These ‘fractures’ lengthen and guide the subsequent radial outflow, leading to distinctive flower-like patterns. This pattern formation process is illustrated for two viscoplastic materials, an aqueous suspension of Carbopol, and a mixture of water and joint compound (a kaolin-based, commercially available product). The fracturing spreads over the entire upper surface of the current when deeper water baths are used, complicating the extrusion patterns. The instability can be removed entirely when the ambient water layer is replaced by an immiscible liquid of comparable viscosity, indicating that the presence of water at the surface is key to the pattern formation process. We conjecture that the underlying mechanism is the fracture under tension of the viscoplastic material, exacerbated by the ambient water.