Transport of a solute in primary and secondary flows through a rotating channel with an absorbing wall

This study uses a multi-scale homogenization technique to provide an analytical solution for solute transport in a viscous fluid flowing between rotating parallel plates. The analytical solutions for the mean and vertical concentration distributions of the solute are derived up to second-order approximations. The channel undergoes rotation around an axis perpendicular to its walls with uniform angular velocity, resulting in a secondary flow. Most previous literature focused on determining the dispersion coefficient for the primary flow. Apart from the dispersion coefficient, we also found the mean and vertical concentration distributions for both primary and secondary flows. The effects of a dimensionless rotation parameter (a) and boundary absorption parameters on solute mean and vertical concentration distributions in both flow directions are discussed. Results reveal that, for the primary flow, the peak of the mean concentration distribution of the solute increases until a = 2:2, then becomes flat with higher a. This phenomenon is due to the emergence of the Coriolis force, which shifts the maximum velocity toward the walls, thereby increasing velocity variation across the channel, whereas for secondary flow, the mean concentration increases with increasing a. However, in the secondary flow direction, the vertical concentration distribution reaches uniformity over significantly longer timescales (e.g., dimensionless s ~ 10⁵, for a = 2) than the primary flow (dimensionless s ~ 10).