Optimization of zeta potential distributions for minimal dispersion in an electroosmotic microchannel

Optimization of the zeta potential distributions at the walls for minimal dispersion in an electroosmotic microchannel is performed based on the variational approach. In the present problem, the governing equations are the steady flow equations and the unsteady mass transport equation. Based on the calculus of variations and the method of Lagrange multiplier, the Euler–Lagrange equations are derived in the form of coupled partial differential equations. The coupled equations of the state variables and the adjoint variables are solved by the FDM method iteratively. The original and adjoint flow equations are reformulated using the streamfunction-vorticity method to eliminate the pressure and the adjoint pressure in the equations. It is found that the dispersion can be reduced drastically by controlling the zeta potentials at the channel walls in an optimal way. The results of the optimal solutions are expected to provide an insight for the design of zeta potential control systems. The methodology used in this work may find various applications in the area of the micro-total-analysis-system (μTAS).