Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911578699333632 |
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| author | Daddi-Moussa-Ider, Abdallah |
| author_facet | Daddi-Moussa-Ider, Abdallah |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_10942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform Daddi-Moussa-Ider, Abdallah Fluid Dynamics Soft Condensed Matter 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. |
| title | Spectral methods for wedge and corner flows: The Fourier-Kontorovich-Lebedev integral transform |
| topic | Fluid Dynamics Soft Condensed Matter |
| url | https://arxiv.org/abs/2603.10942 |