Singular Perturbation Methods Applied to the Dynamics and Rheology of Suspensions.
Final rept. 1 Jul 73-30 Apr 77,
STANFORD UNIV CALIF DEPT OF AERONAUTICS AND ASTRONAUTICS
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Non-linear hydrodynamic interaction on particles suspended in viscous flows was investigated analytically by the method of matched expansions. In particular, three problems of fundamental importance were analyzed. The first problem involves the motion of a particle in an oscillating viscous shear flow. It was found that because of the inertia of the fluid, a lift force is produced on the particle. This force has a d-c component which tends to cause a sidewise drift of the particle. The second problem involves the extension of Jefferys classical work on the motion of ellipsoidal particle immersed in a viscous shear flow. It was found that the first order outer solution corresponds to gyrating dipoles in a shear flow. The effect of the shear produces a higher order effect than the one caused by the second order non-linear effect in the near field. The third problem dealt with the motion of a spherical particle in a viscous compressible flow. The flow field was calculated in terms of a near field and a far field. The flow pattern is rather complex because of the combined effects of heat conduction and viscosity. Author
- Fluid Mechanics