Actuation of Flexoelectric Membranes in Viscoelastic Fluids with Application to Outer Hair Cells

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending and it is used by the Outer Hair Cells (OHC) located in the inner ear, whose role is to amplify sound through generation of mechanical power. Oscillations in the OHC membranes create periodic viscoelastic flows in the contacting fluid media. A key objective of this work on flexoelectric actuation relevant to OHC is to find the relations and impact of the electro-mechanical properties of the membrane, the rheological properties of the viscoelastic media, and the frequency response of the generated mechanical power output. The model developed and used in this work is based on the integration of: (i) the flexoelectric membrane shape equation applied to a circular membrane attached to the inner surface of a circular capillary, and (ii) the coupled capillary flow of contacting viscoelastic phases, such that the membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equation an analytical expression for the transfer function, associated to the curvature and electrical field, power dissipation elastic storage were found. The integrated flexoelectric/viscoelastic model and the novel findings contribute to the ongoing quest for a fundamental understanding of the functioning of outer hair cells (OHC), especially on the role of membrane deformation in delivering mechanical power through electromotility and its frequency-dependent power conversion efficiency.