Hostname: page-component-7c8c6479df-ws8qp Total loading time: 0 Render date: 2024-03-27T08:53:20.068Z Has data issue: false hasContentIssue false

The shear-induced migration of particles in concentrated suspensions

Published online by Cambridge University Press:  21 April 2006

David Leighton
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305–5025, USA Present address: Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA.
Andreas Acrivos
Affiliation:
Department of Chemical Engineering, Stanford University, Stanford, CA 94305–5025, USA

Abstract

In the course of viscometric measurements of concentrated suspensions of spheres in Newtonian fluids using a Couette device, Gadala-Maria & Acrivos (1980) observed a decrease in the suspension viscosity after long periods of shearing even though the viscosity of the pure suspending fluid remained constant under identical conditions. In the present work we demonstrate that this phenomenon is due to the shear-induced migration of particles out of the sheared Couette gap and into the fluid reservoir, which reduces the particle concentration in the gap and thereby the observed viscosity. We show further that this rate of viscosity decrease is consistent with a gap-limited shear-induced diffusion process normal to the plane of shear, with the relevant diffusion coefficient being proportional to $a^2\dot{\gamma}$, where a is the particle radius and $\dot{\gamma}$ is the applied shear rate.

Additional experiments also uncovered a new phenomenon - a short-term increase in the viscosity upon initial shearing of a suspension in a Couette device - which was attributed to the diffusive migration of particles across the width of the Couette gap and thus was used to infer values of the corresponding diffusion coefficient within the plane of shear parallel to gradients in fluid velocity.

In the theoretical part we demonstrate that the particle migrations that led to these observed phenomena may be explained in terms of the irreversible interparticle interactions that occur in these suspensions. From simple arguments, these interactions are shown to lead to effective diffusivities both normal to the plane of shear and normal to the direction of fluid motion within the plane of shear whose estimated magnitudes are comparable with those that were inferred from the experimental measurements. Furthermore, these interactions should induce, within a shear flow, particle drifts from regions of high to low shear stress, which are estimated to be of sufficient intensity to account for the observed initial viscosity increase mentioned above.

Type
Research Article
Copyright
© 1987 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arp, P. A. & Mason, S. G. 1977 The kinetics of flowing dispersions. IX. Doublets of rigid spheres (experimental). J. Colloid Interface Sci. 61, 44.Google Scholar
Bossis, G. & Brady, J. 1984 Dynamic simulation of sheared suspensions. I. General method. J. Chem. Phys. 80, 5141.Google Scholar
Eckstein, E. C., Bailey, D. G. & Shapiro, A. H. 1977 Self-diffusion of particles in shear flow of a suspension. J. Fluid Mech. 79, 191.Google Scholar
Gadala-Maria, F. A. 1979 The rheology of concentrated suspensions. Ph.D. thesis, Stanford University.
Gadala-Maria, F. & Acrivos, A. 1980 Shear-induced structure in a concentrated suspension of solid spheres. J. Rheol. 24, 799.Google Scholar
Ho, B. & Leal, L. 1974 Inertial migration of rigid spheres in two-dimensional uni-directional flows. J. Fluid Mech. 65, 365.Google Scholar
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The kinetics of flowing dispersions. I. Concentrated suspensions of rigid particles. J. Colloid Interface Sci. 22, 531.Google Scholar
Karnis, A. & Mason, S. G. 1967 The flow of suspensions through tubes. I. Meniscus effects. J. Colloid Interface Sci. 23, 120.Google Scholar
Leighton, D. 1985 The shear induced migration of particulates in concentrated suspensions. Ph.D. thesis, Stanford University.
Leighton, D. & Acrivos, A. 1987 Measurement of self-diffusion in concentrated suspensions of spheres. J. Fluid Mech. 177, 109.Google Scholar