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Fluids 2018, 3(2), 35; https://doi.org/10.3390/fluids3020035

Electrorheological Model Based on Liquid Crystals Membranes with Applications to Outer Hair Cells

1
Carrera de Ingeniería Química, Facultad de Estudios Superiores Zaragoza, Universidad Nacional Autónoma de México, Campus I: Av. Guelatao No. 66 Col. Ejercito de Oriente, Iztapalapa, Ciudad de México C.P. 09230, Mexico
2
Department of Chemical Engineering, McGill University, 3610 University Street, Montreal, QC H3A2B2, Canada
*
Author to whom correspondence should be addressed.
Received: 2 February 2018 / Revised: 8 May 2018 / Accepted: 16 May 2018 / Published: 22 May 2018
(This article belongs to the Special Issue Liquid Crystal Rheology)
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Abstract

Liquid crystal flexoelectric actuation uses an imposed electric field to create membrane bending, this phenomenon is found in outer hair cells (OHC) located in the inner ear, whose role is to amplify sound through the 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, which are characterized by the Jeffreys constitutive equation with different material conditions. The membrane flexoelectric oscillations drive periodic viscoelastic capillary flows, as in OHCs. By applying the Fourier transform formalism to the governing equations and assuming small Mach numbers, analytical equations for the transfer function, associated to the average curvature, and for the volumetric rate flow as a function of the electrical field were found, and these equations can be expressed as a third-order differential equation which depends on the material properties of the system. When the inertial mechanisms are considered, the power spectrum shows several resonance peaks in the average membrane curvature and volumetric flow rate. When the inertia is neglected, the system follows a non-monotonic behavior in the power spectrum. This behavior is associated with the solvent contributions related to the retardation-Jeffreys mechanisms. The specific membrane-viscoelastic fluid properties that control the power response spectrum are identified. The present theory, model, and computations contribute to the evolving fundamental understanding of biological shape actuation through electromechanical couplings. View Full-Text
Keywords: flexoelectric membrane actuation; flexoelectric-driven viscoelastic capillary flow; rheological transfer function in outer hair cells; electromotility; Fourier formalism; Jeffreys constitutive equation flexoelectric membrane actuation; flexoelectric-driven viscoelastic capillary flow; rheological transfer function in outer hair cells; electromotility; Fourier formalism; Jeffreys constitutive equation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Herrera Valencia, E.E.; Rey, A.D. Electrorheological Model Based on Liquid Crystals Membranes with Applications to Outer Hair Cells. Fluids 2018, 3, 35.

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