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arXiv · 2411.04619

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

Prabakaran Rajamanickam
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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.

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Prabakaran Rajamanickam. 2024-11-07. Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell. https://doi.org/10.1093/qjmam%2Fhbaf007

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