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

TL;DR

This paper reviews spectral methods, especially the Fourier-Kontorovich-Lebedev transform, for solving low-Reynolds-number fluid flow problems in wedge-shaped geometries, aiding microfluidic device design.

Contribution

It provides a comprehensive overview of the FKL transform approach for analyzing Stokes flow in wedge geometries, emphasizing its application to microfluidics.

Findings

Derivation of solutions for Stokeslet and rotlet in wedge geometries.

Highlighting the versatility of the FKL transform in fluid flow analysis.

Framework for predicting particle behavior in corner confinements.

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.