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In this study, the Lattice Boltzmann (LB) method is applied for computer simulation of suspension flow in Couette systems. Typical aspects of Couette flow such as wall effects and non-zero Reynolds numbers can be studied well with the LB method because of its time-dependent character. Couette flow of single, two and multi-particle systems was studied, where two-dimensional (2D) systems were compared with three-dimensional (3D) systems. Computations on multi-particle 3D suspensions, for instance to assess the viscosity or shear-induced diffusivity, were found to be very intensive. This was only partly a consequence of the 3D system size. The critical particle grid size, necessary for accurate results, was found to be relatively large, increasing the system to impractical sizes. It is however demonstrated that it is possible to carry out computer simulations on 2D suspensions and use relatively simple, linear scaling relations to translate these results to 3D suspensions, in this way avoiding intensive computations. By doing so, the LB method is shown to be well-suited for study of suspension flow in Couette systems, particularly for aspects as particle layering near solid walls, hydrodynamic particle interactions and viscous stresses at non-zero Reynolds numbers, which cannot be easily solved with alternative methods. It also opens the way to employ the LB method for other unexplored aspects, such as particle polydispersity and high Reynolds number flow, with large relevance to practical processing of suspensions.

By extending the concept of an effective temperature, earlier introduced for sheared monodisperse suspensions, we propose a continuum theory for sheared bidisperse suspensions. We show the theory for sheared suspensions can be constructed from the theory for Brownian suspensions by replacing the temperature with the effective temperature. Furthermore, we explore the validity of closure relations based on mean field/free volume theory, by comparison with experimental data obtained for Brownian bidisperse suspensions. In a recent paper, we have shown that the new theory, combined with the discussed closure relations, is indeed a predictive theory.

In this paper we review simulation methods, which address suspension flows at different length scales. Taking the multiscale problem of confined suspension flow in fractionation and sorting applications as a guiding example, we discuss these numerical methods for use in a multiscale simulation framework. We have classified the methods in terms of dimensionless numbers, governing the physics of confined suspension flows, and the resolution of particles on the computation grid. From our literature review, we conclude, that for suspension flows at Peclet numbers larger than unity, Lattice Boltzmann is a good method to implement for all levels of the multiscale simulation framework.

A new computer simulation model is proposed for suspension flow in microfiltration systems. In this model, the diffusion of the suspended microparticles is governed by the mechanism of shear-induced migration. Using an Euler–Euler approach, hydrodynamics and convection–diffusion are simultaneously resolved according to the lattice Boltzmann method. The new suspension flow model allows the complete solution of the flow field (including calculation of the actual local shear rate) in systems with complex geometries and the application of a pressure gradient over he feed flow channel as well as over he membrane. The cake layer dimensions and permeability are explicitly taken into account. For a simple cross-flow system, a comparison is made between the new suspension flow model and existing models. The more realistic approach of the suspension flow model is found to be especially significant for the calculation of the cake layer profile at the beginning and the end of the membrane. Also the effect of narrowing of the flow channel by cake formation on the suspension flow pattern (at a constant pressure gradient over the flow channel) is more realistically predicted. Finally, some examples are presented of the concentration polarisation and cake layer formation in microfiltration systems with more complex geometries. The newly developed suspension flow model has generic applicability as a design tool for microfiltration membranes, systems and processes. Extensions of the model o three-dimensional systems (including parallel computations), as well as adaptations of the diffusion model to anisotropic diffusivity can be relatively easily achieved.

We review existing mixture models for shear-induced migration (SIM) in flowing viscous, concentrated particle suspensions via an analysis of the models from the perspective of a two-fluid formulation. Our analysis shows that particle suspensions in strong non-linear shear fields are a prime example of a driven soft matter system. The driving forces for particle migration can be expressed in terms of non-equilibrium osmotic pressure and chemical potential. Using the linear scaling of the effective temperature with the shear stress, we show that the osmotic pressure and shear-induced diffusion coefficients can be written in identical equations. This is similar to the equations for Brownian motion - with the temperature replaced by the effective temperature. As a guiding application we have taken crossflow microfiltration, where the driving is very strong and there is formation of a jammed state, cake layer, coexisting with the fluid state. The question whether the SIM mixture models holds for this application is investigated. Another questions is how SIM models can be extended for bidisperse suspensions, which is relevant for microfiltration applications involving particle fractionation. Analysis of existing closures of SIM mixture models from the two-fluid perspective learns us that the theory seems to be extendable towards bidisperse suspensions by means of the effective medium theory