Electroosmotic flow is fluid motion driven by an electric field acting on the net fluid charge produced by charge separation at a fluid−solid interface. Under many conditions of practical interest, the resulting fluid velocity is proportional to the local electric field, and the constant of proportionality is everywhere the same. Here we show that the main conditions necessary for this similitude are a steady electric field, uniform fluid and electric properties, an electric Debye layer that is thin compared to any physical dimension, and fluid velocities on all inlet and outlet boundaries that satisfy the Helmholtz−Smoluchowski relation normally applicable to fluid−solid boundaries. Under these conditions, the velocity field can be determined directly from the Laplace equation governing the electric potential, without solving either the continuity or momentum equations. Three important consequences of these conditions are that the fluid motion is everywhere irrotational, that fluid velocities in two-dimensional channels bounded by parallel planes are independent of the channel depth, and that such flows exhibit no dependence on the Reynolds number. Similitude is demonstrated by comparing measured and computed fluid streamlines with computed electric flux lines.

Analytical and numerical methods are employed to determine the electric potential, fluid velocity, and late-time solute distribution for electroosmotic flow in a tube and channel at zeta potentials that are not necessarily small. The electric potential and fluid velocity are in general obtained by numerical means. In addition, new analytical solutions are presented for the velocity in a tube and channel in the extremes of large and small Debye layer thickness. The electroosmotic fluid velocity is used to analyze late-time transport of a neutral nonreacting solute. Zero- and first-order solutions describing axial variation of the solute concentration are determined analytically. The resulting expressions contain eigenvalues representing the dispersion and skewness of the axial concentration profiles. These eigenvalues and the functions describing transverse variation of the concentration field are determined numerically using a shooting technique. Results are presented for both tube and channel geometries over a wide range of the normalized Debye layer thickness and zeta potential. Simple analytical approximations to the eigenvalues are also provided for the limiting cases of large and small values of the Debye layer thickness.

Analytical methods are employed to determine the axial dispersion of a neutral nonreacting solute in an incompressible electroosmotic flow. In contrast to previous approaches, the dispersion is obtained here by solving the time-dependent diffusion−advection equation in transformed spatial and temporal coordinates to obtain the two-dimensional late-time concentration field. The coefficient of dispersion arises as a separation eigenvalue, and its value is obtained as a necessary condition for satisfying all of the required boundary conditions. Solutions based on the Debye−Hückel approximation are presented for both a circular tube and a channel of infinite width. These results recover the well-known solutions for dispersion in pressure-driven flows when the Debye length is very large. In this limit, the axial dispersion is proportional to the square of the Peclet number based on the characteristic transverse dimension of the tube or channel. In the limit of very small Debye lengths, we find that the dispersion varies as the square of the Peclet number based on the Debye length. Simple approximations to the coefficient of dispersion as functions of the Debye length and Peclet number are also presented.

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Analytical and numerical methods are employed to investigate species transport by electrophoretic or electroosmotic motion in the curved geometry of a two-dimensional turn. Closed-form analytical solutions describing the turn-induced diffusive and dispersive spreading of a species band are presented for both the low and high Peclet number limits. We find that the spreading due to dispersion is proportional to the product of the turn included angle and the Peclet number at low Peclet numbers. It is proportional to the square of the included angle and independent of the Peclet number when the Peclet number is large. A composite solution applicable to all Peclet numbers is constructed from these limiting behaviors. Numerical solutions for species transport in a turn are also presented over a wide range of the included angle and the mean turn radius. On the basis of comparisons between the analytical and numerical results, we find that the analytical solutions provide very good estimates of both dispersive and diffusive spreading provided that the mean turn radius exceeds the channel width. These new solutions also agree well with data from a previous study. Optimum conditions minimizing total spreading in a turn are presented and discussed.