Year: 2024
Type: article
Abstract: Liquid flowing down a fibre readily destabilises into a train of beads, commonly called a bead-on-fibre pattern. Bead formation results from capillary-driven instability and gives rise to patterns with constant velocity and time-invariant bead frequency $f$ whenever the instability is absolute. In this study, we develop a scaling law for $f$ that relates the Strouhal number $St$ and capillary number $Ca$ for Ostwaldian power-law liquids with Newtonian liquids recovered as a limiting case. We validate our proposed scaling law by comparing it with prior experimental data and new experimental data using xanthan gum solutions to produce a low capillary number $Ca \leq 10^{-2}$ regime. The experimental data encompasses both Ostwaldian and Newtonian flow, as well as symmetric and asymmetric patterns, and we find the data collapses along the predicted trend across seven orders of magnitude in $Ca$ . Our proposed scaling law is a powerful tool for studying and applying bead-on-fibre flows where $f$ is critical, such as heat and mass transfer systems.
Source: Journal of Fluid Mechanics
Authors: Chase T. Gabbard, James T. Rhoads, Jean-Marc Delhaye, Joshua B. Bostwick
Institutions: Brown University, Clemson University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4405784378