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

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Rajamanickam, Prabakaran (2025) Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell. Quarterly Journal of Mechanics and Applied Mathematics, 78 (2). hbaf007. ISSN 0033-5614 (https://doi.org/10.1093/qjmam/hbaf007)

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Abstract

This article 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)