Impact of osmotic pressure on the stability of Taylor vortices

We use linear stability analysis and direct numerical simulations to investigate the coupling between centrifugal instabilities, solute transport and osmotic pressure in a Taylor–Couette configuration that models rotating dynamic filtration devices. The geometry consists of a Taylor–Couette cell with a superimposed radial throughflow of solvent across two semi-permeable cylinders. Both cylinders totally reject the solute, inducing the build-up of a concentration boundary layer. The solute retroacts on the velocity field via the osmotic pressure associated with the concentration differences across the semi-permeable cylinders. Our results show that the presence of osmotic pressure strongly alters the dynamics of the centrifugal instabilities and substantially reduces the critical conditions above which Taylor vortices are observed. It is also found that this enhancement of the hydrodynamic instabilities eventually plateaus as the osmotic pressure is further increased. We propose a mechanism to explain how osmosis and instabilities cooperate and develop an analytical criterion to bound the parameter range for which osmosis fosters the hydrodynamic instabilities.

Experimental Analysis of Turbulent Wake Development Behind a Permeable Cylinder

To investigate the effect of permeability on turbulent wake behind a cylinder in uniform flow, we conduct particle image velocimetry on turbulent wake behind permeable cylinders, which are made of mesh sheets, of different permeabilities and compare the results with those for a solid cylinder. For relatively lower permeability, turbulent wake is quite similar to the case for a solid cylinder except for a slight shift in the streamwise direction of the reversed flow region implying turbulent Kármán vortex shedding. On the other hand, for higher permeability, the structure of turbulence is qualitatively different. More concretely, turbulent Kármán vortices disappear. Interestingly, however, the momentum deficit for such flow is comparable with that of a solid cylinder. This considerable momentum deficit can be understood with isotropic turbulence caused by the flow penetrating through the mesh constructing the cylinders. These results imply that turbulent wake behind a permeable cylinder involves dynamics both of wake and grid turbulence and the latter one dominates when permeability is sufficiently high.

Instability of an inviscid flow between porous cylinders with radial flow

The stability of a two-dimensional inviscid flow in an annulus between two permeable cylinders is examined. The basic flow is irrotational, and both radial and azimuthal components of the velocity are non-zero. The direction of the radial flow can be from the inner cylinder to the outer one (the diverging flow) or from the outer cylinder to the inner one (the converging flow). It is shown that, independent of the direction of the radial flow, the basic flow is unstable to small two-dimensional perturbations provided that the ratio of the azimuthal component of the velocity to the radial one is sufficiently large. The instability is oscillatory and persists if the viscosity of the fluid is taken into consideration.