Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell

Tools

Rajamanickam, Prabakaran (2025) Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell. Quarterly Journal of Mechanics and Applied Mathematics. ISSN 0033-5614 (In Press) (https://doi.org/10.1093/qjmam/hbaf007)

[thumbnail of Rajamanickam-QJMAM-2025-Shear-induced-force-and-dispersion-due-to-buoyancy] Text. Filename: Rajamanickam-QJMAM-2025-Shear-induced-force-and-dispersion-due-to-buoyancy.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 1 January 2099.
Download (442kB) | Request a copy

Abstract

This paper investigates shear flow in a Hele-Shaw cell, driven by varying horizontal buoyancy forces resulting from a horizontal density gradient induced by a scalar field. By employing asymptotic methods and taking the dependence of density and transport coefficients on the scalar field into account, effective two-dimensional hydrodynamic equations coupled with the scalar conservation equation are derived. These equations determine an effective diffusion coefficient for the scalar field accounting for shear-induced diffusion, and an effective shear-induced buoyancy force that modifies the classical Darcy's law. The derived equations provide a foundation for future research into various problems involving scalar transport in horizontal Hele-Shaw cells.

ORCID iDs

Rajamanickam, Prabakaran ORCID logoORCID: https://orcid.org/0000-0003-1240-0362;
CORE (COnnecting REpositories)