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Spherical particle in Poiseuille flow between planar walls
1Department of Physics, Queen Mary, University of London, London E1 4NS, United Kingdom. r.b.jones@qmul.ac.uk
The Journal of Chemical Physics
|July 21, 2004
Summary
We derived an analytic Green tensor for Stokes flow of a sphere between walls. This allows precise calculation of friction and mobility, revealing translation-rotation coupling that drives sideways particle migration.
Area of Science:
- Fluid dynamics
- Stokes flow
- Mesoparticle dynamics
Background:
- Studying particle behavior in confined flows is crucial for microfluidics and materials science.
- Creeping flow around particles in confined geometries presents significant analytical challenges.
Purpose of the Study:
- To develop an analytic solution for the Green tensor of Stokes flow for a sphere between parallel walls.
- To derive the friction and mobility matrices for a sphere in this geometry.
- To investigate the impact of translation-rotation coupling on particle migration.
Main Methods:
- Utilized a two-dimensional Fourier transform technique to derive the Green tensor.
- Employed a vector harmonic basis for calculating matrix elements.
- Performed numerical integration and Stokesian dynamics simulations.
Main Results:
- Obtained a symmetric analytic expression for the Green tensor.
- Derived 13 scalar friction and mobility functions, showing good convergence and agreement with prior numerical results.
- Demonstrated that translation-rotation coupling induces sideways migration perpendicular to the flow direction.
Conclusions:
- The analytic Green tensor provides an accurate method for calculating hydrodynamic interactions of spheres in confined flows.
- Translation-rotation coupling is a significant factor influencing particle dynamics and migration in channel flows.
- The derived functions are essential for accurate simulations of particle suspensions in microfluidic devices.