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

TL;DR

This study derives effective two-dimensional equations for shear flow and scalar transport in a horizontal Hele-Shaw cell influenced by buoyancy, highlighting shear-induced diffusion and buoyancy effects.

Contribution

It introduces a novel set of coupled equations accounting for shear-induced diffusion and buoyancy in a Hele-Shaw cell with variable density.

Findings

Effective diffusion coefficient for scalar transport derived

Shear-induced buoyancy force modifies Darcy's law

Framework for future scalar transport studies in Hele-Shaw cells

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.