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We report a model to predict equilibrium density profiles for different shaped colloids in two-dimensional liquid, nematic, and crystal states in nonuniform external fields. The model predictions are validated against Monte Carlo simulations and optical microscopy experiments for circular, square, elliptical, and rectangular colloidal particles in AC electric fields between parallel electrodes. The model to predict the densities of all states of different shaped particles is based on a balance of the local quasi-2D osmotic pressure against a compressive force due to induced dipole-field interactions. The osmotic force balance employs equations of state for hard ellipse liquid, nematic, and crystal state osmotic pressures, which are extended to additional particle shapes. The resulting simple analytical model is shown to accurately predict particle densities within liquid, liquid crystal, and crystal states for a broad range of particle shapes, system sizes, and field conditions. These findings provide a basis for quantitative design and control of fields to assemble and reconfigure colloidal particles in interfacial materials and devices. 

Abstract Induced‐charge electroosmosis (ICEO) offers a practical approach to drive microscale flows by application of AC electric fields across polarizable surfaces, enabling diverse functions including microfluidic pumping, active cargo transport, and biosensing. While ICEO along pristine surfaces is well‐understood, practical applications of ICEO often require surface modifications that affect ICEO flows in a manner that is poorly understood. Here, this study introduces dielectrophoretic (DEP) polarizability measurement, DPM, as a method to study effects of surface modifications on surface polarizability and ICEO flows. The method entails DEP trapping of probe particles and analysis of their equilibrium motions to measure polarizability. This DPM‐generated polarizability data is then used to predict effects of surface modifications on ICEO flows and reveal the contribution of additional factors affecting ICEO. It compares predictions with experimentally observed changes to the speed of Janus particles traveling by ICEO‐driven induced‐charge electrophoresis. This study shows that DPM enables prediction of decreased particle speed upon protein capture by functional Janus particles and reveals that increased speed of polymer‐modified Janus particles likely arises from hydrodynamic factors. Overall, this work lays the foundation for investigating new ICEO‐driven systems with applications in complex environments, potentially including those encountered in biosensing, remediation, or cargo delivery.