Lattice-Boltzmann simulations of particle suspension flows

We have used the lattice-Boltzmann (LB) simulation code developed earlier [1] to study rheological properties and flow behaviour of liquid-particle suspensions. The code is three dimensional and fully parallellized. It can include particles of different sizes and interactions between the suspended particles (these features are not utilized in this study, however). The advantage of the present method of direct numerical simulation is that we can study in detail both the basic particle-scale phenomena and their macroscopic consequences i.e. the measurable mean properties of the flow. In particular, we can study the different microscopic phenomena that contribute to the apparent rheological properties of the suspension, namely the momentum transfer due to viscous stress of the carrier fluid, due to elastic stress in particles caused by interactions with fluid and by particle-particle collisions, and due to fluctuating motion of both phases. Similarly, we can study important macroscopic flow phenomena such as mean flow profile, slip at the tube wall and formation of concentration gradients due to migration of particles. The results are particularly useful in analysing the experimental results obtained by rheological measurements of particulate suspensions and thereby in gaining better understanding of the actual material properties of the suspension. This information is essential in e.g. developing numerical models for processes involving flow of such suspensions. Here, we demonstrate the use of the LB method starting from a study of very basic particle scale phenomena that contribute to the observed shear thickening of non-colloidal particulate suspensions in simple shear flow, namely the effect of a single suspended particle and the effect of a single chain-like cluster of suspended particles. By a cluster we mean here a compact group of particles, formed as a result of hydrodynamic forces that bring suspended particles to close contact with each other. Short-range lubrication forces between these particles are then responsible for binding together such otherwise temporary aggregates. We then calculate the dependence on particle concentration of the apparent viscosity of the suspension. Since this dependence is well known from earlier theoretical and experimental studies, this results gives an excellent benchmarking test for the method used here. Another benchmarking case is provided by the study of strain hardening, for which we find good qualitative agreement with the data found in the literature. These results are reported in more detail in references [2-3]. Finally, we apply the the method in analysing the flow in capillary viscometer and compare the numerical results with measured data, and thereby seek to use the method as an advanced data-analysis tools for the experiments.