Fingers and Fractures: Instabilities in Viscoplastic Fluid Films – Thomasina Ball, U. Warwick

November 8, 2021 @ 1:00 pm – 2:00 pm
Dr. Jerome Neufeld

The study of gravity currents has long been of interest due to their prevalence in industry and in nature, one such example being the spreading of viscoplastic (yield-stress) fluid films. When a viscoplastic fluid is extruded onto a flat plate, the resulting gravity current expands axisymmetrically when the surface is dry and rough. For such a case, the flow above the non-slip surface is dominated by shear stresses. In this talk, I will discuss two instabilities that arise when the two conditions of a dry and rough surface are relaxed.

1) Firstly, when the underlying surface is replaced by a free-slip surface, the fluid film spreads with little traction, the main resistance to flow now stemming from the extensional stresses of the material. Experiments with radially spreading sliding viscous films have suggested these flows are stable towards non-axisymmetric disturbances. However, recent analysis of the stability of radially expanding two-dimensional flow of a shear-thinning power-law fluid suggests the presence of an extensional flow instability. We extend this analysis to three-dimensional spreading films with a viscoplastic rheology in the thin-film limit, confirming the existence of instability if the fluid has a yield stress or is sufficiently shear-thinning.

2) Second, when experiments are performed with a viscoplastic fluid (Carbopol) extruded onto a flat plate wet by a thin coating of water, fractures appear to create a distinctive flower-like pattern. However, by performing a number of variations on the experiments, we demonstrate that the shear-thinning extensional-flow instability above is not responsible. Instead, further investigation suggests that these patterns 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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