Stokes flow with Oseen tensors

Stokes' law, force fields, and flow near a wall

Journal Article (2025)
Author(s)

Timon Idema (TU Delft - BN/Timon Idema Lab, Kavli institute of nanoscience Delft)

Research Group
BN/Timon Idema Lab
DOI related publication
https://doi.org/10.1088/1361-6404/adc357
More Info
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Publication Year
2025
Language
English
Research Group
BN/Timon Idema Lab
Issue number
3
Volume number
46
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Abstract

The quintessential example of a fluid flow problem with a known solution is the drag force required to move a sphere through a stationary fluid. While the equation describing this Stokes drag is simple, deriving it from the Stokes equations requires several pages of mathematics. In this paper, I present an alternative, more intuitive approach, based on the Oseen tensor, which gives the fluid flow due to an applied point force. For completeness, we first derive the expression for the Oseen tensor, then use it to re-derive Stokes law. As an additional application, we also study fluid flow near a wall, using a mirror images technique similar to the one used in electrostatics problems.