The integration of electro-osmotic effect to the underlying flow enhances solute dispersion precision in microfluidic systems, which is crucial for applications such as drug delivery and on-chip fluidic functionalities. We investigate, in this study, the solute dispersion characteristics of couple-stress fluids in a two-dimensional microchannel configuration under the combined effects of electro-osmotic actuation and applied pressure gradients. We consider both homogeneous and heterogeneous reactions in the present analysis. Couple-stress fluids, which account for additional stresses due to the presence of the microstructures in the fluids, offer a more accurate model to describe the rheological behaviour of biofluids. While previous studies have addressed longitudinal Gaussianity and transverse uniformity of solute distribution, we focus uniquely in this endeavour on longitudinal uniformity. Using Mei’s multiscale homogenisation technique, we solve a two-dimensional convection–diffusion model, extending it to third-order approximation to analyse the dispersion coefficient, concentration profiles, and variation rates of concentration within microchannel flow. Results show that forcing and couple-stress parameters enhance the gradients of the longitudinal variation rate, while boundary absorption reduces this variation rate near the walls. The couple-stress parameter exhibits dual behaviour: initially, it enhances solute dispersion, but beyond a certain value of couple-stress parameter $B_{cr}$ (which depends on forcing comparison and the Debye–Hückel parameter), it reduces dispersion. In the absence of pressure, solute distribution remains longitudinally uniform. However, as the pressure gradient increases, concentration levels drop sharply, and the distribution shifts to a parabolic profile, underscoring the significant influence of pressure on flow behaviour in electro-osmotic flow.