We study the shape differentiability of a cost function for the steady flow of an incompressible viscous fluid of power-law type. The fluid is confined to a bounded planar domain surrounding an obstacle. For smooth perturbations of the shape of the obstacle we express the shape gradient of the cost function which can be subsequently used to improve the initial design.

The growth rate of fingers of a Newtonian fluid can be modeled by a power law dependence on time. In this experiment, we examine whether the model can be adapted to describe a fluid with changing viscosity. We provide two possible interpretations. For PVA and a PVA/glycerol solution, we show that by assuming a constant exponent, the changing behavior of the fluid can be captured by a coefficien...

We have studied the drainage of foams made from Newtonian and non-Newtonian solutions of different viscosities. Forced-drainage experiments first show that the behavior of Newtonian solutions and of shear-thinning ones (foaming solutions containing either Carbopol or Xanthan) are identical, provided one considers the actual viscosity corresponding to the shear rate found inside the foam. Second...

A refined model is presented which numerically resolves the fluid flow within a fracture inside saturated poroelastic material. At discontinuity, mass balance of solved using velocity profile fracture, with being determined from momentum in integration points at discontinuity. The resolution and discontinuity coupled to surrounding material two-scale approach. resulting monolithic scheme allows...