Nonlinear Electrokinetic Phenomena

I. Ravina and D. Zaslavsky, Nonlinear electrokinetic phenomena. Part II Experiments with electrophoresis of clay particles. Soil Sci. 106 94 (1968). I. C. Callaghan and R. H. Ottewill, Interparticle forces in montmorillonite gels, Faraday Disc. Chem. Soc. 57 110(1974). P. F. Low, The swelling of clay. Ill Dissociation of exchangeable cations, Soil Sci. Soc. Am. J. 45 1074 (1981). 

Mathematical models of ACEO follow other examples of ICEO, as described in the article on nonlinear electrokinetic phenomena. A major simplification in the case of small voltages is to assume sinusoidal response to sinusoidal AC forcing and solve only for the complex amplitudes of the potential and velocity components at a single frequency co (Fourier mode) [2]. In this regime, the basic scaling of time-averaged ACEO flow is... 

Nonlinear electrokinetic phenomena, such as the electrokinetic motion of polarizable particles, have only been studied for a few decades, and attention is just begiiming to be paid to the nonlinear motion of heterogeneous particles due to induced-charge electrophoresis [7-9]. Recent theoretical work has relaxed assumptions 1-3, but much remains to be done. Surprising new possibilities include particles that rotate continuously or translate perpendicular to a uniform AC field [9]. 

The underlying physical mechanisms for the electrokinetic motion of particles are described in other entries on Electroosmotic How (DC), Electrophoresis, Dielectrophoresis, Nonlinear Electrokinetic Phenomena, and Electrokinetic Motion of Polarizable Particles, along with various mathematical models. The effects of relaxing the assumptions above in these models, however, are often unexpected and have not yet been firUy explored, either theoretically or experimentally. Here, we simply give a few examples of how heterogeneous particles can move in electric fields. 

Transverse ICEP motion of metallo-dielectric Janus particles in a uniform AC field has recently been observed by Gangwal et al. [10]. Consistent with theoretical predictions in Fig. 3, the particles align and translate perpendicular to the field in the direction of the less polarizable (light) end, as shown in Fig. 4. Larger particles move faster than smaller ones, as expected from Eq. 2, and the velocity scales like the field squared in dilute NaCl solutions. The ICEP velocity decays at higher concentrations, extrapolating to zero around 10 mM. The same concentration dependence is also observed in AC electroosmotic flow and other nonlinear electrokinetic phenomena, which, although poorly understood, further reinforces that the motion is indeed due to ICEP. 

Since all materials are polarizable to some degree, the surface charge is generally not fixed. This leads to a broad class of nonlinear electrokinetic phenomena, where bulk electric fields interact with induced diffuse charge in solution to produce nonlinear electrophoretic motion, U = f(E). In electrolytes, such effects of induced-charge electrophoresis (ICEP) occur in addition to the purely electrostatic effect of... 

Compared to the vast literature on linear electrophoresis, the study of nonlinear electrokinetic motion is still its early stages. As indicated above, much remains to be done, in both making theoretical predictions and systematically testing them (or discovering new effects) in experiments. Modern mathematical methods and computational power now allow more sophisticated analysis, going beyond linear and weakly nonlinear approximations, as well as large-scale simulations of interacting colloidal particles. Similarly, the advent of microfluidics provides new opportunities to observe and exploit nonlinear electrokinetic phenomena, since polarizable particles can now be fabricated with complicated shapes and material properties and electric fields controlled with submicron precision. 

Electroosmosis of the second kind Nonlinear electrokinetic phenomena Nonlinear electroos-motic flow The secondary electroosmotic flow... 

Nonlinear electrokinetic phenomena Nonlinear electroosmotic flow Nonlinear electrophoresis... 

Nonlinear electrokinetic phenomena are electrically driven fluid flows or particle motions, which depend nonlinearly on the applied voltage. The term is also used more specifically to refer to induced-charge electroosmotic flow, driven by an electric field acting on diffuse charge induced near a polarizable surface. 

The possibility of nonlinear electroosmotic flow, varying as m oc E, seems to have been first described by Murtsovkin [1, 2], who showed that an alternating electric field can drive steady quadrupolar flow around a polarizable particle (Fig. la). This effect has recently been unified with other nonlinear electrokinetic phenomena in microfluidics [3], such as AC electro-osmotic flow (ACEO) at microelectrodes [4, 7, 8] (Fig. lb), DC electrokinetic jets at dielectric corners [5] (Fig. Ic), and nonlinear flows around metal posts [9] (Fig. Id-e). These are all cases of induced-charge electroosmosis (ICEO) - the nonlinear electroosmotic flow resulting firom the action of an electric field on its own induced diffuse charge near a polarizable surface. 

Nonlinear Electrokinetic Phenomena, Fig. 4 Sketch of space charge formation and second-kind flow at the junction between a nanopore and a micropore in a microfluidic device or porous material (From Leinweber and Tallarek [15]). (a) In equilibrium, the micropore contains neutral electrolyte, while the nanopore has overlapping double layers containing mostly counterions. 

Induced-charge and second-kind electrokinetic phenomena arise due to electrohydrodynamic effects in the electric double layer, but the term nonlinear electrokinetic phenomena is also sometimes used more broadly to include any fluid or particle motion, which depends nonlinearly on an applied electric field, fit the classical effect of dielectrophoresis mentioned above, electrostatic stresses on a polarized dielectric particle in a dielectric liquid cause dielectro-phoretic motion of particles and cells along the gradient of the field intensity (oc VE ). In electrothermal effects, an electric field induces bulk temperature gradients by Joule heating, which in turn cause gradients in the permittivity and conductivity that couple to the field to drive nonlinear flows, e.g., via Maxwell stresses oc E Ve. In cases of flexible solids and emulsions, there can also be nonlinear electromechanical effects coupling the... 

Nonlinear Electrokinetic Phenomena, Fig. 5 Some experimental data rm induced-charge electrokinetic phenomena. (a) The fluid velocity at different points around a tin particle in an AC field versus the applied electric field, demonstrating the quadratic scaling of Eq. 4 (From Murtsovkin [1] and references therein), (b) The veloeity... 

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