Perturbations of the Coupled Jeffery-stokes Equations
نویسنده
چکیده
This paper seeks to provide clues as to why experimental evidence for the alignment of fibers in semi-dilute suspensions under shear flows does not match theoretical predictions. This paper posits that it is the coupling between Jeffery’s equation and Stokes’ equation that causes the deviation from theory. It is proposed that if the initial data is slightly non-uniform, then there is feedback via Stokes’ equation that causes these non-uniformities to grow significantly in short amounts of time, so that the standard uncoupled Jeffery’s equation becomes a poor predictor. This paper provides numerical evidence, involving spectral analysis of the linearization of the perturbation equation, to support this theory.
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