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.

References in corpus (3)

• A thick reaction zone model for premixed flames in two-dimensional channels
• Effects of thermal expansion on Taylor dispersion-controlled diffusion flames
• Effect of a shear flow on the Darrieus-Landau instability in a Hele-Shaw channel

Cited by in corpus (1)

• Hydrodynamic origin of Korteweg stresses from shear-induced horizontal buoyancy