Electroosmotic flow through packed beds of granular materials

Electrical charges originate at most solid surfaces in contact with aqueous electrolytes which result in the formation of an electrical double layer. If an external electric field is tangentially applied to the double layer, an electroosmotic flow is induced which can be employed for various applications such as microfluidic pumps. Here, highly porous materials are especially suitable since they generate significant flow rates along with high pump pressures. The models which are currently used to describe the electroosmotic flow through porous substrates are based on the so-called parallel capillary flow model. In terms of packed beds of granular materials, these models have the disadvantages of oversimplifying the geometry to tortuous capillaries while neglecting intra- and inter-pore connections, varying pore cross-sectional geometries as well as the influence of the packed bed walls. In the current research, we employ dimensional reasoning (Buckingham theorem) to derive a phenomenological model which relates the electroosmotic flow to the averaged parameters of the packed bed as well as to the relevant physicochemical parameters. A comprehensive set of experiments is carried out to infer a semiempirical correlation which can be universally applied to packed beds of arbitrary granular materials. Additionally, we derive a dynamic model of the center-of-mass motion of the fluidic parts of the experimental setup. The model allows for an evaluation of the influence of Joule heating without monitoring the temperature in the bed.