Electrokinetic coupling in unsteady pressure-driven flow through a porous transducer: Fractal capillary bundle model

Abstract

• A fractal capillary bundle model is used to predict the frequency-dependent streaming potential coefficient of porous media. • The theoretical model of electrokinetic coupling in the unsteady pressure-driven flow is established to characterize the frequency response of the streaming potential coefficient. • An analytic solution of Poisson-Boltzmann equation is obtained for the capillary bundle of porous media with high zeta potential condition. • The proposed model shows satisfactory agreement with experiments and can optimize the parameter configuration of transducers. The liquid circular angular accelerometer (LCAA) is a novel fluid-mechanical device based on the principle of electrokinetic effect, which is featured as the streaming potential coefficient (SPC) to convert elastic wave energy into electromagnet energy within the porous transducer. To determine its dynamic response, we present an analytical expression for the frequency-dependent SPC of a porous transducer in the LCAA. The electrokinetic coupling process in unsteady pressure-driven flow is developed by using the fractal capillary bundle model. Electrical potential distribution in a torturous capillary of the arbitrary radius is modeled by a modified approximation for the Poisson-Boltzmann equation with high zeta potential condition. We present an apparatus for measuring the dynamic SPC of transducers that are sintered with glass beads and have high porosity. Measurements on natural and sintered porous samples validate the proposed model and demonstrate satisfactory agreement. According to the sensitivity analysis, changes in fluid and structural properties have a significant impact on the unsteady SPC response, particularly the solution concentration and mean particle size. The findings of this study can pave the way for the frequency-dependent SPC prediction of the porous transducer as well as a better understanding of the LCAA design optimization.