Effect of boundary absorption in dispersion in Casson fluid flow in a tube

The combined effect of yield stress and irreversible boundary reaction on dispersion process in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model proposed by Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115-132, 1973). The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, viz., exchange, convection, and dispersion coefficients. The exchange coefficient does not depend on yield stress but the convection and dispersion coefficients depend on yield stress or equivalently plug flow region. For large times, when the plug flow radius is one-tenth of pipe radius, the convective coefficient is reduced by 0.41 times of the corresponding value for a Newtonian fluid at equivalent wall absorption parameter; in channel case the reduction is by 39%. It is seen that the asymptotic dispersion coefficient decreases with increase in wall absorption parameter and yield stress of the fluid. When the plug radius in pipe (channel) is 0.1, depending upon the values of wall absorption parameter, say (0.01-100) the reduction factor in dispersion coefficient is in the range (0.1-0.3) in comparison to the values of the Newtonian case. The results reduce to those of Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115-132, 1973) when there is no yield stress for the pipe flow analysis and to those of Dash et al. (Dash, R. K., G. Jayaraman, and K. N. Mehta. Ann. Biomed. Eng. 28:373-385, 2000) when there is no interphase mass transfer. The study can be used as a starting first approximation solution for studying the dispersion in the cardiovascular system.