  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.
