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 infinitely long conduit defined by two concentric curved circular pipes. The annular wall is comprised of a stationary homogeneous medium, and inner cylinder is the flowing phase. The solute is soluble in the annular region and is assumed to satisfy a linear equilibrium relationship at the interface. A series expansion is derived for the effective longitudinal diffusivity, Deff, valid when both the Dean number N^1/2 and the product σN (σ is the Schmidt number) are sufficiently small. The theory is extended numerically using a spectral finite-difference method to widen the validity of the results to more realistic problems in which σN can take large values although N remains small. The results are consistent with the experimental findings of Kaye 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 Deff falls below its straight-tube value by an amount which depends on the absorption coefficient β and the diffusivity in the wall. The minimum ratio is about 0.28, in the absence of absorption, and this agrees with the corresponding result of Johnson and Kamm (3). Relative to the case with a non-absorbing wall, Deff goes through a very large maximum as β is varied.