DISPERSION OF SOLUTE IN A FLUID FLOWING THROUGH A CURVED TUBE WITH ABSORBING WALLS

The dispersion of solute in a fluid flowing through a curved tube with absorbing walls is studied using a mathematical model of an infinitel y long conduit defined by two concentric curved circular pipes. The an nular wall is comprised of a stationary homogeneous medium, and the in ner cylinder is the flowing fluid phase. The solute is soluble in the annular region and is assumed to satisfy a linear equilibrium relation ship at the interface. A series expansion is derived for the effective longitudinal diffusivity, D-eff, valid when both the Dean number N-1/ 2 and the product sigma N (sigma is the Schmidt number) are sufficient ly small. The theory is extended numerically using a spectral finite-d ifference method to widen the validity of the results to more realisti c problems in which sigma N can take large values although N remains s mall. The results are consistent with the experimental findings of Kay e et al. (1, 2) that the influence of secondary flows on dispersion is reduced if the tracer is very soluble in the wall. It is found that D -eff falls below its straight-tube value by an amount which depends on the absorption coefficient beta and the diffusivity in the wall. The minimum ratio is about 0.28, in the absence of absorption, and this ag rees with the corresponding result of Johnson and Kamm (3). Relative t o the case with a non-absorbing wall, D-eff goes through a very large maximum as beta is varied.