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.

Numerical methods are employed to examine the transport of charged species in pressure-driven and electroosmotic flow along nanoscale channels having an electric double-layer thickness comparable to the channel size. In such channels, the electric field inherent to the double layer produces transverse species distributions that depend on species charge. Flow along the channel thus yields mean axial species speeds that also depend on the species charge, enabling species separation and identification. Here we characterize field-flow separations of this type via the retention and plate height. For pressure-driven flows, we demonstrate that mean species speeds along the channel are uniquely associated with a single species charge, allowing species separation based on charge alone. In contrast, electroosmotic flows generally yield identical speeds for several values of the charge, and these speeds generally depend on both the species charge and electrophoretic mobility. Coefficients of dispersion for charged species in both planar and cylindrical geometries are presented as part of this analysis.

Comparisons are made among Molecular Dynamics (MD), Classical Density Functional Theory (c-DFT), and Poisson–Boltzmann (PB) modeling of the electric double layer (EDL) for the nonprimitive three component model (3CM) in which the two ion species and solvent molecules are all of finite size. Unlike previous comparisons between c-DFT and Monte Carlo (MC), the present 3CM incorporates Lennard-Jones interactions rather than hard-sphere and hard-wall repulsions. c-DFT and MD results are compared over normalized surface charges ranging from 0.2 to 1.75 and bulk ion concentrations from 10 mM to 1 M. Agreement between the two, assessed by electric surface potential and ion density profiles, is found to be quite good. Wall potentials predicted by PB begin to depart significantly from c-DFT and MD for charge densities exceeding 0.3. Successive layers are observed to charge in a sequential manner such that the solvent becomes fully excluded from each layer before the onset of the next layer. Ultimately, this layer filling phenomenon results in fluid structures, Debye lengths, and electric surface potentials vastly different from the classical PB predictions.

Numerical methods are employed to optimize the geometry of two-dimensional microchannel turns such that the turn-induced spreading of a solute band is minimized. An inverted numerical method is first developed to compute the electric potential and local species motion in turns of arbitrary geometry. The turn geometry is then optimized by means of a nonlinear least-squares minimization algorithm using the spatial variance of the species distribution leaving the turn as the object function. This approach yields the turn geometry producing the minimum possible dispersion, subject only to prescribed constraints. The resulting low-dispersion turns provide an induced variance 2-3 orders of magnitude below that of a comparable conventional turns. Sample results are presented for 180 and 90 degrees turns, and the use of these turns to form wyes and tees is discussed. A sample 45 degrees wye is presented. The use of low-dispersion turns in folding separation columns is also discussed, and sample calculations are presented for folding a column 100 microm in width and up to 900 mm in length onto a region of only 10 by 10 mm. These low-dispersion geometries are applicable to electroosmosis, electrophoresis, and some pressure-driven flows.