Taylor dispersion for coupled electroosmotic and pressure-driven flows in all time regimes

The dispersion behaviour of solutes in flow is crucial to the design of chemical separation systems and microfluidics devices. These systems often rely on coupled electroosmotic and pressure-driven flows to transport and separate chemical species, making the transient dispersive behaviour of solutes highly relevant. However, previous studies of Taylor dispersion in coupled electroosmotic and pressure-driven flows focused on the long-term dispersive behaviour and the associated analyses cannot capture the transient behaviour of solute. Further, the radial distribution of solute has not been analysed. In the current study, we analyse the Taylor dispersion for coupled electroosmotic and pressure-driven flows across all time regimes, assuming a low zeta potential (electric potential at the shear plane), the Debye–Hückel approximation and a finite electric double layer thickness. We first derive analytical expressions for the effective dispersion coefficient in the long-time regime. We also derive an unsteady, two-dimensional (radial and axial) solute concentration field applicable in the latter regime. We next apply Aris’ method of moments to characterise the unsteady propagation of the mean axial position and the unsteady growth of the variance of the solute zone in all time regimes. We benchmark our predictions with Brownian dynamics simulations across a wide and relevant dynamical regime, including various time scales. Lastly, we derive expressions for the optimal relative magnitudes of electroosmotic versus pressure-driven flow and the optimum Péclet number to minimise dispersion across all time scales. These findings offer valuable insights for the design of chemical separation systems, including the optimisation of capillary electrophoresis devices and electrokinetic microchannels and nanochannels.