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arXiv · 2603.10942

Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform

Abdallah Daddi-Moussa-Ider
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Abstract

Understanding fluid flow in wedge-shaped geometries is essential for predicting hydrodynamic interactions in confined systems, such as microfluidic devices and near-corner transport phenomena. This article reviews analytical methods and techniques for addressing wedge problems in low-Reynolds-number hydrodynamics, focusing on solutions of the Stokes equations for a point force (Stokeslet) and a point torque (rotlet). The formulation is based on the Papkovich-Neuber representation, which uses four harmonic functions to characterize the fluid flow. A concise overview of the Fourier-Kontorovich-Lebedev (FKL) transform method is provided, highlighting key properties and steps employed in deriving these solutions. This offers a versatile framework for predicting particle dynamics in wedge confinements and for designing microfluidic systems with corner geometries.

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Abdallah Daddi-Moussa-Ider. 2026-03-11. Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform. https://arxiv.org/abs/2603.10942

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