| Title: |
Instability of falling films of discontinuously shear-thickening fluid |
| Authors: |
Balmforth, Neil J. |
| Source: |
Journal of Fluid Mechanics ; volume 1002 ; ISSN 0022-1120 1469-7645 |
| Publisher Information: |
Cambridge University Press (CUP) |
| Publication Year: |
2025 |
| Description: |
Aqueous suspensions of cornstarch abruptly increase their viscosity on raising either shear rate or stress, and display the formation of large-amplitude waves when flowing down inclined channels. The two features have been recently connected using constitutive models designed to describe discontinuous shear thickening. By including time-dependent relaxation and spatial diffusion of the frictional contact density responsible for shear thickening, an analysis of steady sheet flow and its linear stability is presented. The inclusion of such effects is motivated by the need to avoid an ill-posed mathematical problem in thin-film theory and the resulting failure to select any preferred wavelength for unstable linear waves. Relaxation, in particular, eliminates an ultraviolet catastrophe in the spectrum of unstable waves and furnishes a preferred wavelength at which growth is maximized. The nonlinear dynamics of the unstable waves is briefly explored. It is found that the linear instability saturates once disturbances reach finite amplitude, creating steadily propagating nonlinear waves. These waves take the form of a series of steep, shear-thickened steps that translate relatively slowly in comparison with the mean flow. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| DOI: |
10.1017/jfm.2024.1184 |
| Availability: |
https://doi.org/10.1017/jfm.2024.1184; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112024011844 |
| Rights: |
http://creativecommons.org/licenses/by/4.0 |
| Accession Number: |
edsbas.2A43AD2C |
| Database: |
BASE |