Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform
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.
Cite
@article{arxiv.2603.10942,
title = {Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform},
author = {Abdallah Daddi-Moussa-Ider},
journal= {arXiv preprint arXiv:2603.10942},
year = {2026}
}
Comments
15 pages, 2 figures, review article