Instability to elastic turbulence; freezing soft particles; confined viscous flows

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• Miguel Beneitez, Pallav Kant, Ashleigh Hutchinson - DAMTP
• Friday 21 October 2022, 16:00-17:00
• MR2, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Prof. Jerome Neufeld.

Miguel Beneitez – Linear instability leading to elastic turbulence in plane Couette flow

It is known that a simple, Newtonian fluid may experience transition to turbulence in the presence of inertia. In contrast, viscoelastic fluids, solutions of flexible long-chain polymers, have been shown to exhibit chaotic dynamics even in the absence of inertia, entirely sustained by its elastic properties. The origin of such ‘elastic turbulence’ has often been linked to a linear instability of curved streamlines. In this talk, we present a new viscoelastic rectilinear instability in one of the most fundamental flow configurations, plane Couette flow. This instability, found in the inertialess limit, stems from a finite polymeric diffusion, caused by the molecular diffusion of the polymer chains, and relies on a novel instability mechanism. We perform the first numerical simulation of the nonlinear evolution of the associated eigenmodes and we show that it leads to self-sustained elastic turbulence in parallel flow.

Pallav Kant – Interaction of soft particles with moving solidification front

Freezing of dispersions is omnipresent in science and technology. While the passing of a freezing front over a solid particle is reasonably understood, this is not so for soft particles. In the present investigations, using an oil-in-water emulsion as a model system, we show that when engulfed into a growing crystal, a soft particle severely deforms, even forming pointy-tip shapes in extreme situations. We show that such singular deformations are mediated by interfacial flows in nanometric thin liquid films separating the non-solidifying dispersed droplet and the solidifying bulk. We model the fluid flow in these intervening thin films using a lubrication approximation and then relate it to the deformation sustained by the dispersed droplet.

Ashleigh Hutchinson – The evolution of a viscous gravity current in a confined geometry

The aim of this talk is to present a theoretical and experimental study of an axisymmetric viscous gravity current with a constant flux confined to the space between two horizontal parallel plates. The effect of confinement is to produce two regions of flow: an inner region where the fluid is in contact with both plates and an outer annular region where the fluid forms a gravity current along the lower plate. I will outline a simple theoretical model that describes the flow dynamics by a single dimensionless parameter which is the ratio of the characteristic height of an unconfined gravity current to the height of the confined space. Theoretical height profiles display the same characteristics as unconfined gravity currents until this ratio reaches approximately a half, where a rapid change in behaviour occurs as confinement comes into effect. For larger values of this ratio, the confined viscous gravity current gradually tends to Hele-Shaw flow, with the transition essentially complete by a value of 2. The findings from the theoretical model are compared to the results of a series of experiments using golden syrup with various fluxes and gap spacings. Although the data aligns with the major aspects of the model, it is clear that other physics is at play and a single non-dimensional parameter is not sufficient to capture the flow behaviour fully. Possible mechanisms that may be responsible for this mismatch will be briefly discussed.

This talk is part of the Fluid Mechanics (DAMTP) series.

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