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Numerical simulation of pressure-driven displacement of a viscoplastic material by a Newtonian fluid using the lattice Boltzmann method. (English) Zbl 1408.76017
Summary: The pressure-driven displacement of a non-Newtonian fluid by a Newtonian fluid in a two-dimensional channel is investigated via a multiphase lattice Boltzmann method using a non-ideal gas equation of state well-suited for two incompressible fluids. The code has been validated by comparing the results obtained using different regularized models, proposed in the literature, to model the viscoplasticity of the displaced material. Then, the effects of the Bingham number, which characterizes the behaviour of the yield-stress of the fluid and the flow index, which reflects the shear-thinning/thickening tendency of the fluid, are studied. It is found that by increasing the Bingham number and the flow index, the size of the unyielded region of the fluid in the downstream portion of the channel increases as well as the thickness of the residual layer of the fluid resident initially in the channel; the latter is left behind on the channel walls by the propagating ‘finger’ of the displacing fluid. This, in turn, reduces the growth rate of interfacial instabilities and the speed of finger propagation.

##### MSC:
 76A05 Non-Newtonian fluids 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 76M28 Particle methods and lattice-gas methods 76E05 Parallel shear flows in hydrodynamic stability
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