Inhomogeneous viscosity fluid flow in a wide-gap Couette apparatus: Shear-induced migration in suspensions

The first portion of this two-part paper investigates the short time evolut ion of a low Reynolds number flow characterized by a spatially inhomogeneou s viscosity within the annular domain between two widely separated concentr ic circular cylinders undergoing relative rotation. The viscosity is regard ed as a material property and as such is convected with the fluid. Any poss ible "diffusion" of this viscosity is supposed negligible, at least in the short times of interest in our calculation. The initial viscosity field, as sumed to be only slightly inhomogeneous, is expanded into a Fourier series with respect to the polar angle, and the contributions of the zeroth and fi rst harmonics are subsequently addressed. Approximate short-time analytic s olutions for the velocity and viscosity fields are obtained. In the second part of this paper the results of the preceding analysis are employed in an attempt to gain insight into the experimentally observed shear-induced mig ration of particles in suspensions being sheared in a wide-gap Couette appa ratus. The connection of the inhomogeneous viscosity problem studied in the first part to such shear-induced migration phenomena lies in the assumptio n that the local viscosity of a suspension of (non-Brownian) particles is f unctionally dependent only upon the local suspended particle volumetric fra ction. In such circumstances, the local transport of suspended particles co rresponds to a concomitant transport of the local suspension viscosity and vice-versa. Subject to the foregoing interpretation and limited by algebrai c tractability to short times, a global radial migration is predicted. It i ncreases with an increase in the annular gap size between the cylinders and depends upon the phase angle between the rotating outer and inner cylinder s, but not upon their relative circumferential velocity-a conclusion consis tent with experimental observations. Further, to leading order, particle mi gration is found to be independent of purely radial viscosity disturbances (the zeroth harmonic) and to arise entirely from coupling between circumfer ential disturbances in the velocity and viscosity (i.e., particle concentra tion) fields. The solution also indicates that the high shear-rate region, proximate to the inner wall, may either become less viscous on average (the reby predicting net radial migration away from the high shear rate region) or, conversely, more viscous (corresponding to migration toward the high sh ear rate region migration). The latter case arises in circumstances that in volve a large positive radial gradient in the viscosity's first harmonic. ( C) 2000 American Institute of Physics. [S1070-6631(00)00212-9].