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The non-homogeneous flow of a thixotropic fluid around a sphere

The non-homogeneous flow of a thixotropic fluid around a settling sphere is simulated. A four-parameter Moore model is used for a generic thixotropic fluid and discontinuous Galerkin method is employed to solve the structure-kinetics equation coupled with the conservation equations of mass and momentum. Depending on the normalized falling velocity $U^{*}$, which compares the time scale of structure formation and destruction, flow solutions are divided into three different regimes, which are attributed to an interplay of three competing factors: Brownian structure recovery, shear-induced structure breakdown, and the convection of microstructures. At small $U^{*}( \ll 1)$, where the Brownian structure recovery is predominant, the thixotropic effect is negligible and flow solutions are not too dissimilar to that of a Newtonian fluid. As $U^{*}$ increases, a remarkable structural gradient is observed and the structure profile around the settling sphere is determined by the balance of all three competing factors. For large enough $U^{*}(\gg 1)$, where the Brownian structure recovery becomes negligible, the balance between shear-induced structure breakdown and the convection plays a decisive role in determining flow profile. To quantify the interplay of three factors, the drag coefficient Cs of the sphere is investigated for ranges of $U^{*}$. With this framework, the effect of the destruction parameter, the confinement ratio, and a possible nonlinearity in the model-form on the non-homogeneous flow of a thixotropy fluid have been addressed.