SCS colloquium: Multi-scale Simulations of Suspension Flow

Suspensions show complex rheological behaviour dependent on numerous aspects of domain geometry, solid fraction, sizes, shape and deformability of the particles, and strength of additional particle-particle interactions. As a function of these parameters the (local) apparent viscosity can change drastically with the (local) shear rate which has considerable impact on the flow of the suspension. The actual parameter space to be considered is high-dimensional and only a few models exist that bridge some of the dimensions in a limited range. A fully resolved model that realistically mimicks individual particles and still spans the whole domain is not feasible with today's computing capacity.

 

We investigate the applicability of the Hierarchical Multi-scale Method (HMM) for this type of problem. Based on the assumption that local gradients are not too large, instead of simulating the whole macroscopic domain at a microscopic resolution we split the spatial scale to a macro-region where we introduce a model for the macroscopic flow and concentration fields, and a microscopical "pocket" system in which simulations of a fully resolved micromodel can be carried out in which all aspects of particle-fluid interaction can be realised. Given the local parameters of the macro-system, through such pocket experiments apparent viscosity and a particle diffusivity tensor are obtained. With this approach we not only gain massive reduction of computational effort by splitting the scales, we also can make efficient use of rotational and Galilean symmetries.

 

An additional reduction of the computational effort is achieved by the implementation of a database and an extra/inter-polation scheme to retrieve viscosity and diffusivity values from it for a given point in the parameter space. Filling the database on-the-fly means only the actually visited parameter space needs to be sampled.

 

As a proof of concept we successfully applied this approach to the simulation of monodisperse neutrally-buoyant suspensions of hard spheres in a wide 2d channel. Profiles of velocity and particle concentration agree well with experimental results and predictions from the diffusive flux and suspension balance models.