Session MB - Drops I. Emulsions & Drops.
MIXED session, Tuesday afternoon, November 23
Grand II, Westin Seattle
An analytical solution for the motion of a slightly deformed sphere in creeping flows with the assumption of slip on the particle surface is presented. Explicit expressions are obtained for the hydrodynamic force and torque exerted by the fluid on the deformed sphere. A perturbation method, based on previous work done by Brenner [1964] and Lamb[1945], is used to solve for the motion of a fluid influenced by the presence of a deformed sphere. Slip is assumed at the surface of the particle. Hydrodynamic force and torque exerted by the fluid on the deformed sphere are expressed explicitly for a translational and rotational deformed sphere. The equation governing the motion and orientation of a spheroid induced by homogenous flows is also presented. This evolution equation for the orientation of the spheroid is similar to the equation derived by Jeffery [1922]. Solutions of this equation show that the period of rotation of the particle with slip is longer than for the same particle without slip. Furthermore, when the slip coefficient is sufficiently low, the particle rotates to a fixed angle that corresponds to a quasi-steady state in the flow.
REFERENCES Brenner, H. 1964 The Stokes resistance of a slightly deformed sphere. Chemical Engineering Science 19, 519-539 Jeffery, G.B.1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. Soc. Lond. Math., 102, 161-179 Lamb, H. 1945 Hydrodynamics, sixth version, Dover, New York, U.S.A