Migration and structure formation in sheared slurries
This thesis is concerned with the sheared flow of medium dense slurries, consisting rigid particles in a Newtonian fluid. The particles are rough. The interaction between rough particles in the lubrication limit is studied and expanded on. In a shear gradient geometry a migration phenomenon occurs, in which the particles congregate in the low shear rate region. The literature on this phenomenon is reviewed and for each model that is available a sample calculation of channel flow is calculated. Two models appear to yield realistic results. They incorporate the fluctuations in particle motion (which is a necessary feature of sheared dense slurries). These two models require further attention. The first is the granular temperature model. This model is studied as an isotropic cell model, which permits first order estimates for its many parameters, thus making the model more suitable for practical calculations. The second is the anisotropy-induced model for which in the literature only a phenomenological version is available. The latter model is studied by setting up an analytical continuum calculation that entails explicit fluctuations. It is shown that in steady-state shear a linear approximation never leads to a stable result, unless a substantial repulsive particle interaction is present. The theory is then modified to include a non-linear term (associated with a rough particle interaction), elaboration of which yields stability, but at the same time structures formation. The latter problem (in two dimensions) is then further studied by carrying out numerical simulations employing the Discrete Element Method. The analytical results are qualitatively replicated: structures form when the particle interaction does not involve a substantial repulsive element; they disappear when a repulsive elastic interaction is implemented. Thus the understanding of the physics of medium dense slurry flow is improved.