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arXiv · 2607.08509

Hele-Shaw Flow With Pressure and Shear Rate Dependent Viscosity

Benedetta Calusi·Liviu Iulian Palade
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Abstract

This paper investigates the behaviour of a fluid characterized by a viscosity simultaneously depending on pressure and shear rate within a Hele-Shaw cell featuring a sharp corner geometry. The study extends previous analyses conducted on purely pressure-dependent (piezo-viscous) and yield-stress fluids, providing a new perspective on confined complex flows. Motivated by practical applications related to designing biomedical devices and flows of relevance to biomedicine area, thin film technologies, injection molding -- to name only a few -- the flow configuration considered here can highlight essential features of complex fluid behavior in narrow-gap geometries around a sharp edge. Starting from the governing equations for an incompressible generalized Newtonian fluid and employing an appropriate rheological model, we derive the modified flow equations adapted to the Hele-Shaw flow. A particular solution is obtained near the corner region. Numerical simulations complement the theoretical results, illustrating the influence of the rheological parameters on the flow behavior.

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Benedetta Calusi, Liviu Iulian Palade. 2026-07-09. Hele-Shaw Flow With Pressure and Shear Rate Dependent Viscosity. https://doi.org/10.1515/tp-2026-0002

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