Dispersion of a solute in a Herschel–Bulkley fluid flowing in a conduit

Abstract

The dispersion of a solute in a Herschel-Bulkley fluid is studied by using the generalized dispersion model in both pipe and channel. With this method the entire dispersion process is described as a simple diffusion process with the effective diffusion coefficient as a function of time. The results for Newtonian fluid, power law fluid and Bingham fluid are obtained as special cases by giving appropriate values to the power law index and yield stress. The effects of power law index, yield stress on the dispersion coefficient and mean concentration have been discussed computationally and graphically. The effect of power law index and yield stress is found to reduce the dispersion coefficient. It is observed that the critical time for dispersion coefficient to reach the steady state is varying with the yield stress and power law index. It is noticed that time to assume the critical value in Newtonian case is 0.5 and in the channel case the corresponding value of time is 0.55 which are in agreement with the existed results. It is also observed that in the non- Newtonian fluids this time is less than that of Newtonian fluid case and in Bingham fluid the critical value of time in pipe flow analysis (channel flow analysis) is attained at 0.45 (0.52) while in power law fluid it is at 0.43(0.48) and in the case of Herschel-Bulkley fluid it is 0.41 (0.45).