Lattice Boltzmann modeling of Bingham plastics

A new lattice Boltzmann model within the framework of D2Q9 lattices for Bingham plastics is proposed. The essence of the present model lies in incorporation of the effect of local shear rate into the lattice equilibrium distribution function. With this arrangement, particle distribution functions are able to relax to the states containing proper local shear-rate information during collisions that makes the proposed scheme a more efficient and stable one. Macroscopically, consistency of the proposed lattice Boltzmann model with the equations of motion for Bingham plastics are demonstrated through the technique of Chapman–Enskog multi-scale expansion. The benchmark problem of a 2:1 sudden expansion flow in a planar channel for a wide range of Bingham numbers, 0≤Bn≤20000≤Bn≤2000, and Reynolds numbers, 0.2≤Re≤200, are executed to verify the applicability of the present model. It is shown that both the extent and shape for yielded/unyielded regions and for corner vortexes are accurately captured and their numerical values are also in good agreement with existing results.