In-plane electrophoresis in nonpolar liquids: Measurements and simulations

In this paper we describe electrophoresis of charged particles in a thin layer of a nonpolar liquid between two insulating substrates because this configuration is common in recently developed in-plane electronic paper. In the in-plane electrophoresis experiments a model system of charged inverse micelles in dodecane has been used which is well understood from studies of out-of-plane electrophoresis. The transient current due to drift and diffusion of charged inverse micelles is measured in thin in-plane devices upon application of a voltage step. For the modelling of the transient dynamics of charged inverse micelles without chemical reactions or convection a 1-dimensional approximation of the Poisson–Nernst–Planck (PNP) equations is developed. This approximation is valid for a sufficiently thin in-plane device and allows much faster calculations. Firstly, it is verified in the case of a sufficiently thin in-plane device and high applied voltage that the 1-dimensional approximation is in good agreement with the solution of the full 2-dimensional PNP equations with finite elements implementation. Then, the 1-dimensional approximation is used to study the transient current and trajectories of trace amounts of charged colloidal particles in different regimes depending on the screening of the electric field. Also a comparison is made to the well-studied case of out-of-plane electrophoresis. Finally, it is verified that for voltages much larger than the thermal voltage the experimental results are in good agreement with the 1-dimensional approximation, indicating that the charge transport dynamics of charged inverse micelles in the bulk are described well by the model.