Estimation of inhomogeneous zeta potential in the electroosmotic flow by means of mode reduction

A reduced-order model is derived for electroosmotic flows in a microchannel of nonuniform cross-section. The model is constructed based on the Karhunen–Loève Galerkin (KLG) procedure which can reduce nonlinear partial differential equations to sets of minimal number of ordinary differential equations. The reduced-order model of the present investigation is carefully constructed such that it is not necessary to re-evaluate any coefficient of the model even though the inhomogeneous zeta potential ζ(x) and the dielectric constant ε vary. This feature reduces the computational time greatly when employed in the estimation and control of electroosmotic flows, where repeated solution of governing equations is required. Using the present reduced-order model, a practical method is devised to estimate inhomogeneous zeta potential ζ(x) from velocity measurements of the electroosmotic flow in the microchannel. The proposed method is found to estimate ζ(x) with reasonable accuracy even using noisy velocity measurements.