Polymer Flow Through Porous Media: Numerical Prediction of the Contribution of Slip to the Apparent Viscosity.

The flow of polymer solutions in porous media is often described using Darcy’s law with an apparent viscosity capturing the observed thinning or thickening effects. While the macroscale form is well accepted, the fundamentals of the pore-scale mechanisms, their link with the apparent viscosity, and their relative influence are still a matter of debate. Besides the complex effects associated with the rheology of the bulk fluid, the flow is also deeply influenced by the mechanisms occurring close to the solid/liquid interface, where polymer molecules can arrange and interact in a complex manner. In this paper, we focus on a repulsive mechanism, where polymer molecules are pushed away from the interface, yielding a so-called depletion layer in the vicinity of the wall. This depletion layer acts as a lubricating film that may be represented by an effective slip boundary condition. Here, our goal is to provide a simple mean to evaluate the contribution of this slip effect to the apparent viscosity. To do so, we solve the pore-scale flow numerically in idealized porous media with a slip length evaluated analytically in a tube. Besides its simplicity, the advantage of our approach is also that it captures relatively well the apparent viscosity obtained from core-flood experiments, using only a limited number of inputs. Therefore, it may be useful in many applications to rapidly estimate the influence of the depletion layer effect over the macroscale flow and its relative contribution compared to other phenomena, such as non-Newtonian effects

Effect of tube diameter and capillary number on platelet margination and near-wall dynamics

The effect of tube diameter $D$ and capillary number $Ca$ on platelet margination in blood flow at $\approx 37\%$ tube haematocrit is investigated. The system is modelled as three-dimensional suspension of deformable red blood cells and nearly rigid platelets using a combination of the lattice-Boltzmann, immersed boundary and finite element methods. Results show that margination is facilitated by a non-diffusive radial platelet transport. This effect is important near the edge of the cell-free layer, but it is only observed for $Ca > 0.2$, when red blood cells are tank-treading rather than tumbling. It is also shown that platelet trapping in the cell-free layer is reversible for $Ca \leq 0.2$. Only for the smallest investigated tube ($D = 10 \mu\text{m}$) margination is essentially independent of $Ca$. Once platelets have reached the cell-free layer, they tend to slide rather than tumble. The tumbling rate is essentially independent of $Ca$ but increases with $D$. Tumbling is suppressed by the strong confinement due to the relatively small cell-free layer thickness at $\approx 37\%$ tube haematocrit.Comment: 16 pages, 10 figure

Renal structure and function in hypothyroidism and hyperparathyroidism : an experimental study in the pig

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