Electroosmotic flows in microchannels with finite inertial and pressure forces

Emerging microfluidic systems have spurred an interest in the study of electrokinetic flow phenomena in complex geometries and a variety of flow conditions. This paper presents an analysis of the effects of fluid inertia and pressure on the velocity and vorticity field of electroosmotic flows. In typical on-chip electrokinetics applications, the flow field can be separated into an inner flow region dominated by viscous and electrostatic forces and an outer flow region dominated by inertial and pressure forces. These two regions are separated by a slip velocity condition determined by the Helmholtz-Smoulochowski equation. The validity of this assumption is investigated by analyzing the velocity field in a pressure-driven, two-dimensional flow channel with an impulsively started electric field. The regime for which the inner/outer flow model is valid is described in terms of nondimensional parameters derived from this example problem. Next, the inertial forces, surface conditions, and pressure-gradient conditions for a full-field similarity between the electric and velocity fields in electroosmotic flows are discussed. A sufficient set of conditions for this similarity to hold in arbitrarily shaped, insulating wall microchannels is the following: uniform surface charge, low Reynolds number, low Reynolds and Strouhal number product, uniform fluid properties, and zero pressure differences between inlets and outlets. Last, simple relations describing the generation of vorticity in electroosmotic flow are derived using a wall-local, streamline coordinate system.