Transport of fluids and particles at the microscale is an important theme both in fundamental and applied science. One of the most successful approaches is to use an electric field, which requires the system to carry or induce electric charges. We describe a versatile approach to generate electrokinetic flows by using a liquid crystal (LC) with surface-patterned molecular orientation as an electrolyte. The surface patterning is produced by photo-alignment.In the presence of an electric field, the spatially varying orientation induces space charges that trigger flows of the LC. The active patterned LC electrolyte converts the electric energy into the LC flows and transport of embedded particles of any type (fluid, solid, gaseous) along a predesigned trajectory, posing no limitation on the electric nature (charge, polarizability) of these particles and interfaces. The patterned LC electrolyte exhibits a quadratic field dependence of the flow velocities; it induces persistent vortices of controllable rotation speed and direction that are quintessential for micro-and nanoscale mixing applications.

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order parameter tensor. The model extends the previously developed director-based theory and accounts for presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic, characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electro-osmotic effect that occurs in an isotropic electrolyte when an applied field acts on the ionic charge it induces near a polarizable surface.

Liquid crystal electrolytes enable nonlinear electrophoresis of colloidal particles with velocities proportional to the square of the applied field. We demonstrate that the magnitude and even the polarity of electrophoretic mobility can be controlled by the anisotropy of electric conductivity and dielectric permittivity of the liquid crystal. In particular, reversal of electrophoretic mobility can be triggered either by temperature or composition changes that alter the signs of the conductivity and permittivity anisotropies. Controllable reversal of mobility adds to the list of advantages of anisotropic electrolytes over their isotropic counterparts. † olavrent@kent.edu

We study ionic and mass transport in a liquid crystalline fluid film in its nematic phase under an applied electrostatic field. Both analytic and numerical solutions are given for some prototypical configurations of interest in electrokinetics: Thin films with spatially nonuniform nematic director that are either periodic or comprise a set of isolated disclinations. We present a quantitative description of the mechanisms inducing spatial charge separation in the nematic, and of the structure and magnitude of the resulting flows. The fundamental solutions for the charge distribution and flow velocities induced by disclinations of topological charge m = −1/2, 1/2 and 1 are given. These solutions allow the analysis of several designer flows, such as "pusher" flows created by three colinear disclinations, the flow induced by an immersed spherical particle (equivalent to an m = 1 defect) and its accompanying m = −1 hyperbolic hedgehog defect, and the mechanism behind nonlinear ionic mobilities when the imposed field is perpendicular to the line joining the defects.

Electrokinetic phenomena in a nematic suspension are considered when one or more dielectric particles are suspended in a liquid crystal matrix in its nematic phase. The long-range orientational order of the nematic constitutes a fluid with anisotropic properties. This anisotropy enables charge separation in the bulk under an applied electric field, and leads to streaming flows even when the applied field is oscillatory. In the cases considered, charge separation is seen to result from director field distortions in the matrix that are created by the suspended particles. We use a recently introduced electrokinetic model to study the motion of a single-particle hyperbolic hedgehog pair. We find this motion to be parallel to the defect-particle center axis, independent of field orientation. For a two-particle configuration, we find that the relative force of electrokinetic origin is attractive in the case of particles with perpendicular director anchoring, and repulsive for particles with tangential director anchoring. The study reveals large scale flow properties that are respectively derived from the topology of the configuration alone and from short scale hydrodynamics phenomena in the vicinity of the particle and defect.

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We develop a formal analogy between configurational stresses in physically distinct systems, and study the flows that they induce when the configurations of interest include topological defects. Our primary focus is on electrokinetic flows in a nematic fluid under an applied electrostatic field, which we compare with a class of systems in which internal stresses are generated due to configurational changes (e.g., active matter, liquid crystal elastomers). The mapping allows the extension, within certain limits, of existing results on transport in electrokinetic systems to active transport. We study motion induced by a pair of point defects in a dipole configuration, and steady rotating flows due to a swirling vortex nematic director pattern. The connection presented allows the design of electrokinetic experiments that correspond to particular active matter configurations that may be easier to conduct and control in the laboratory.

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