Using a coupled lattice Boltzmann and discrete element method, we have developed a new tool for the numerical characterisation of dense suspension rheology. This approach has been implemented using a shared memory, multicore, parallel architecture which allows for rapid and inexpensive evaluation of model results. Where model capabilities include non-Newtonian rheology, turbulence, fluid-solid interactions, and lubricated solid-solid interactions. Through consideration of the fundamental phenomena of flow and contact mechanics this model is able to accurately capture the suspension rheology.

Using this coupled framework we have implemented a numerical couette flow rheometer, discrete element particles are packed into a cubic lattice Boltzmann domain which is periodic in the lateral directions. Using either stress or shear rate control, this model then simulates the shearing of the particulate suspension. The resultant hydrodynamic and mechanical forces on the shearing plane are recovered once the model has achieved a steady state, where these results are used to compute an effective suspension viscosity. The results from this analysis have been validated against existing semi-empirical expressions.


Simulation of particle transport often occurs at a scale orders of magnitude larger than the size of the particulate inclusions. Where previous work in this field has focused on development of constitutive equations to describe the effective viscosity of suspensions with a specific solid volume fraction [1]. The rheology specified by such expressions is then typically used to calibrate a power-law based rheological model [2]. However, work by Lyon & Leal has shown that even in a relatively simple poiseuille flow the distribution of solid particulates is not uniform across the aperture [3]. This spatially varying solid volume fraction shows the need to directly simulate both the fluid and particles in order for correct flow behaviour to be accurately represented.

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