Shearing Liquids of Unequal Viscosity: Can Mixing be Independent of Stirring Rate at a Large Viscosity Ratio?
Year: 2024
Type: article
Abstract: Mixing liquids with unequal viscosity involves complex flows and a nontrivial diffusive feedback. As an insightful reference case, we study the deformation of a spherical blob with viscosity $\ensuremath{\lambda}\ensuremath{\eta}$, sheared in a miscible bath with viscosity $\ensuremath{\eta}$. Experiments resolve the transition from unbounded stretching, at low $\ensuremath{\lambda}$, to rollinglike motion, at large $\ensuremath{\lambda}$. In between the blob is transiently substretched before destabilizing into swirling structures. Exact solutions of the flow recover all three regimes and predict a transition ratio ${\ensuremath{\lambda}}_{c}\ensuremath{\simeq}3.975$. We discuss the dramatic impact of the flow transition on mixing and propose scaling laws for the blob mixing time in the limit of large P\'eclet numbers, suggesting mixing could be independent of shear rate at large $\ensuremath{\lambda}$.
Source: Physical Review Letters
Authors: I. Castaldi, B. Metzger, H. Lhuissier
Institution: Aix-Marseille Université
Language: English
Subfield: Fluid Flow and Transfer Processes
Field: Chemical Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403224998