Slow Ono-Newtonian Flow in a Zone of Separation

Slow motions of purely viscous fluids in a two-dimensional conduit expansion are investigated using a finite-difference numerical scheme. The important concepts in the general theory leading to the governing differential equations of the flow are briefly discussed, and the equations are reduced to a convenient form for numerical solution. Contours of stream function, vorticity, and viscosity function in the zone of separation are compared for different values of the flow behavior index, which vary from the shear-thinning, pseudoplastic, range to the shear-thickening, dilatant, range, at four values of the generalized Reynolds number: 0, 16, 32, and 48. The results of the investigation indicate that for the separated flow of power-law fluids, shear-thinning fluids develop shorter, less intense, and more viscous eddies than do shear-thickening fluids at the same Reynolds number. It is also found that the influence of the flow behavior index is different for creeping flows than for flows at higher Reynolds numbers, i.e., at R = 0 the deviation of the eddy characteristics from Newtonian behavior is greater than at higher values of the Reynolds number.