Effects of bulk and wall chemical reactions on hydrodynamic dispersion of a solute in a couple stress fluid

This paper presents an analytical exploration of the two-dimensional concentration distribution of a solute under the influence of first-order bulk and wall chemical reactions in a viscous, couple stress fluid flowing between two parallel plates. The analytical expressions for mean and transverse concentration distributions up to third order are derived using Mei and Vernescu's multiscale homogenization technique. This paper meticulously investigates the impact of a couple stress parameter (α) and the chemical reaction parameters on Taylor dispersion through a reactive solute's dispersion coefficient, mean, and transverse concentration distributions. Results reveal that the effect of couple stress is most significant for smaller values of α (i.e., 20>α≥1), in which the dispersion increases and the tracer particle's mean concentration decreases. As α increases, there is a decreasing trend in dispersion, and for a large value of α a subtle decrease in dispersion is observed, which implies that the increment in viscosity impacts the dispersion coefficient. However, the negligible effect of couple stress (α≫20) results in a subtle increase in the mean concentration distribution. Increasing the value of the bulk chemical reaction parameter uniformly decreases the transverse concentration more effectively for smaller values of α. Both couple stress and wall reactions significantly impact the concentration variation by inducing nonuniformity. Interestingly, at the center of the channel cross section, the bulk chemical reaction is more efficient in decreasing the transverse concentration profile when compared to wall chemical reactions, especially for smaller values of α where the couple stress is notably high. The results are effective as they are pivotal in advancing the design and performance of microfluidic devices, enhancing the separation of fluids and components, and improving fluid mixing efficiency.