Shear augmented dispersion of a solute in a Casson fluid flowing in a conduit

The unsteady dispersion of a solute in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model of Gill an d Sankarasubramanian. With this approach, the entire dispersion process is described appropriately in terms of a simple diffusion process with the eff ective diffusion coefficient as a function of time, in addition to its depe ndence on the yield stress of the fluid. The results are accurate up to a f irst approximation for small times, but verified with Sharp to be exact for large rimes. The model brings out mainly the effect of yield stress, or eq uivalently, the plug Row region on the overall dispersion process. It is fo und that the rate of dispersion is reduced (i.e., the effective diffusivity decreases) due to the yield stress of the fluid, or equivalently, the plug flow region in the conduit. Also, the effective diffusivity increases with time, bur eventually attains its steady state value below a critical time [0.48(a(2)/D-m) for dispersion in a pipe and 0.55(a(2)/D-m) for dispersion in a channel-the critical transient time for a Newtonian fluid-where ''a" i s the radius of the pipe and D-m is the molecular diffusivity]. At steady s tate, for dispersion in a pipe with the plug Row radius one tenth of the ra dius of the pipe, the effective diffusivity is reduced to about 0.78 times of the corresponding value for a Newtonian fluid at equivalent flow rates; for dispersion in a channel, the reduction factor is about 0.73 confirming the earlier result of Sharp. Further, the location of the center of mass of a passive species over a cross section is found to remain unperturbed duri ng the course of dispersion and for different values of the plug flow param eter (i.e., the yield stress of the fluid). The study can be used as a star ting first approximate solution for studying the dispersion in the cardiova scular system or blood oxygenators. (C) 2000 Biomedical Engineering Society .