Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell
Rajamanickam, Prabakaran (2025) Shear-induced force and dispersion due to buoyancy in a horizontal Hele-Shaw cell. Quarterly Journal of Mechanics and Applied Mathematics. ISSN 0033-5614 (In Press) (https://doi.org/10.1093/qjmam/hbaf007)
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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.
ORCID iDs
Rajamanickam, Prabakaran
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Item type: Article ID code: 92913 Dates: DateEvent5 May 2025Published5 May 2025AcceptedSubjects: Technology > Mechanical engineering and machinery
Science > MathematicsDepartment: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 21 May 2025 13:37 Last modified: 28 May 2025 06:46 Related URLs: URI: https://strathprints.strath.ac.uk/id/eprint/92913