(435i) Flow of a Power-Law Fluid across an Asymmetrically Confined Rotating Cylinder

The present study is motivated by the potential application of a rotating cylinder in the area of drying, filtration of slurries, and calendering process in paper making and polymer industries, cylindrical cooling devices in the glass and plastics industries etc. In addition, such model configurations also advance our understanding of the underlying fluid mechanical issues like wake characteristics, hydrodynamic forces etc. The flow field far away from the cylinder is influenced very little by its rotation and/or by the severity of confinement of the cylinder. Thus, in this work, the combined effects of rotation and asymmetric confinement on the momentum transfer aspects in power-law fluids are investigate numerically.

In particular, this work endeavours to study the momentum transfer characteristics for the flow of shear-thinning fluids, modelled here as a power-law fluid, across a confined, rotating cylinder in between two parallel walls. The cylinder rotational velocity is maintained same as the bulk fluid velocity. The flow is assumed to be laminar, 2-dimensional and incompressible. The flow field is visualized in terms of streamlines, hydrodynamic forces and torque acting on the rotating cylinder. In general, for fixed values of the Reynolds number, power-law index and asymmetry ratio, the drag and lift coefficients and torque are seen to increases steeply with the rising confinement. On the other hand, the shear thinning fluid shows a negative effect on the drag and lift coefficients and torque for a particular value of Reynolds number and cylinder confinement and asymmetry parameter. For the symmetric case, the effective rate of shearing is likely to be high close to the cylinder and close to the walls (due to the no-slip condition) whereas these two regions of low viscosity are separated by a fluid of effectively higher viscosity. For asymmetric positioning, the high viscosity region shrinks and finally disappears for the case when the rotating cylinder is situated close to the channel wall. The velocity field near the cylinder surface is strongly influenced by the Reynolds number, power-law index and degree of confinement and asymmetry due to the low and high viscosity regions depending upon the conditions. Therefore, it is likely that the flow behaviour will exhibit non-monotonic dependence on some of these variables.

For symmetrically placed highly confined cylinder, lubrication analysis holds true. The geometrical and dynamic conditions for the lubrication approximation are generalized for shear-thinning fluids. For Newtonian fluids, an analytical expression for the velocity profile and the torque correction factor in the narrow gap are obtained within the framework of lubrication approximation. For shear-thinning fluids, the resulting velocity profile is more complex due to the existence of non-linear viscous term in the momentum equations. The analytical results in the narrow gap are matched perfectly with the numerical results for all values power-law index