Non-linear electro-rheological model of a membrane immersed in Tanner-Power law fluids applied to outer hair cells: Shear-thinning mechanisms

Flexoelectric actuation employs an applied electric field to induce membrane curvature, which is the mechanism utilized by the outer hair cells (OHC) present in the inner ear. The model developed for this study, representing the OHC, integrates two key components: (i) an approximation of the flexoelectric membrane shape equation for circular membranes attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting liquid viscoelastic phases characterized by the Tanner-Power law rheological equation of state. A second-order non-linear differential equation for average curvature has been derived, and a robust numerical method has been programmed. This model simplifies to a linear model used previously. The main challenge involves identifying and describing the enhancement in curvature change rate. It was observed that low symmetry, low viscosity, and soft membrane and shear-thickening behavior of the phases enhance the curvature change rate. Additionally, there exists a critical electric field frequency value that maximizes the curvature change rate (resonance effect). The current theory, model, and computational simulations add to the ongoing development comprehension of how biological membrane shape actuation through electromechanical couplings.