Folding instabilities in non-Newtonian viscous sheets: shear thinning and shear thickening effects

TL;DR

This study investigates how shear thinning and shear thickening behaviors influence folding instabilities in non-Newtonian viscous sheets, combining simulations, experiments, and analysis to reveal effects on amplitude, frequency, and onset of folding.

Contribution

It extends previous Newtonian analyses by exploring non-Newtonian shear effects on folding instabilities using a combined numerical, experimental, and theoretical approach.

Findings

Shear thickening increases folding amplitude and decreases frequency.

Shear thinning suppresses folding instabilities.

Folding onset and cessation are influenced by non-Newtonian rheology.

Abstract

In this work, we extend the analyses devoted to Newtonian viscous fluids previously reported by Ribe [Physical Review E 68, 036305 (2003)], by investigating shear thickening (dilatant) and shear thinning (pseudoplastic) effects on the development of folding instabilities in non-Newtonian viscous sheets of which viscosity is given by a power-law constitutive equation. Such instabilities are trigged by compression stresses acting on viscous sheets that leave a channel at a very small initial velocity, fall, and then hit a solid surface or a fluid substrate. Our study is conducted through a mixed approach combining direct numerical simulations, energy budget analyses, scaling laws, and experiments. The numerical results are based on an adaptive variational multi-scale method for multiphase flows, while Carpobol gel sheets are considered for the conducted experiments. Two folding regimes are observed: (1) the viscous regime; and (2) the gravitational one. Interestingly, only the latter is affected by shear thinning/thickening manifestations within the material. In short, when gravity is balanced by viscous forces along the non-Newtonian viscous sheet, both the folding amplitude and the folding frequency are given by a power-law function of the sheet slenderness, the Galileo number (the ratio of the gravitational stress to the viscous one), and the flow behaviour index. Highly shear thickening materials develop large amplitude (and low frequency) instabilities, which, in contrast, tend to be suppressed by shear thinning effects, and eventually cease. Lastly, nonNewtonian effects on folding onset/cessation are also carefully explored. As a result, non-Newtonian folding onset and cessation criteria are presented.