Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell
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.
Keywords
Cite
@article{arxiv.2411.04619,
title = {Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell},
author = {Prabakaran Rajamanickam},
journal= {arXiv preprint arXiv:2411.04619},
year = {2025}
}