Electroconvective jets in liquid dielectrics

The principal feature of electroconvective jets in liquid dielectrics developing under the influence of a high-voltage external field is the large value of the EHD interaction parameter. This leads to the coupling of the hydrodynamic and electric problems. As formulated in [1, 2] the situation is reversed: the EHD interaction parameter is small. In these problems the interest is usually confined to finding the electric characteristics of the jet for a given velocity field. In [3] flows from sharp electrodes in liquid dielectrics were analyzed under two principal assumptions: nonlinear ohmic conductivity and point EHD interaction. This paper deals with the calculation of submerged electroconvective jets with ionic conductivity on the basis of the boundary-value problem formulated in [4]. In this case point EHD interaction is not assumed. It should be noted that in this formulation the problem is of practical as well as theoretical interest, for example, in connection with the problem of designing throttle EHD converters [5].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 13–19, November–December, 1984.     

Development of electroconvection in liquid dielectrics

The development of electroconvection in liquid dielectrics is analyzed theoretically from the standpoint of the dissociation-injection model of conductivity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 34–42, January–February, 1989.The author wishes to thank the participants in the G. A. Lyubimov seminar for discussing his work and making useful suggestions.     

Linear and nonlinear waves in liquid dielectrics

Fluid Dynamics - A study is made of linear and nonlinear waves in liquid dielectrics in strong external electric fields. In the case of linear waves, it is assumed that the liquid has bipolar...     

Electrohydrodynamics of liquid dielectrics on the basis of a dissociation-injection conductivity model

A physicochemical model of the electrical conductivity of liquid dielectrics is formulated on the basis of dissociation and injection charge generation with allowance for recombination processes [1, 2]. The corresponding boundary-value problem of eléctrohydrodynamics is written down. It is shown that it is consistent with the principal electrical and electrohydrodynamic effects in liquid dielectrics.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 3–13, July–August, 1986.The author wishes to thank seminar participants I. E. Tarapov and G. A. Lyubimov and the seminar at Perm State University for discussion of his results and useful comments.     

Investigation of electroconvection and electroconvective heat transfer in liquid dielectrics with unipolar injection conductivity

The characteristics of electroconvection and electroconvective heat transfer in liquid dielectrics possessing unipolar injection conductivity [1, 2] are investigated and certain types of EHD pumps are calculated. These investigations are necessary because so far there is no theoretical explanation for the slowing of heat transfer with increase in voltage in strong fields [3, 4]. Moreover, there is no satisfactory theory of EHD pumps that would make it possible not only to establish the basic operating principles of existing (grid [5], knife-edge [6] and other [7, 8]) equipment but also to predict the performance of high-pressure EHD pumps.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 14–20, March–April, 1988.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

On thermoelastic dielectrics

Constitutive equations for a linear thermoelastic dielectric are derived from the energy balance equation assuming dependence of the stored energy function on the strain tensor, the polarization vector, the polarization gradient tensor and entropy. A method is indicated for constructing a hierarchy of constitutive equations for materials with arbitrary symmetry by introducing various thermodynamic potentials. Maxwell's relations are constructed for the thermodynamic potential W^L. The entropy inequality is used to obtain stability conditions for an elastic dielectric in equilibrium under prescribed boundary constraints. Frequencies are explicitly determined for a plane wave propagating along the x₁-axis in an infinite centro-symmetric isotropic thermoelastic dielectric.     

Small elastoplastic strains of dielectrics

The theory of small elastoplastic strains of dielectrics in the presence of an electric field is developed in the work. An expression is obtained for the electric part of the stress tensor. Total free energy minimum theorems with constant temperature and simple proportional loading and unloading theorems are proved. Experiments to calculate the mass functions are discussed.     

Thermodynamics of apolar viscoelastic dielectrics

Summary In this paper we propose a thermodynamic theory for apolar viscoelastic dielectrics. Within this framework we discuss the possibility of accounting for the Maxwell effect, i.e., the birefringence phenomenon due to the motion of the continuum in study. To this end we show that the proposal made by Toupin, in order to account for the Maxwell effect, does not contrast with the second law of Thermodynamics.

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Sommario In questo lavoro viene formulata una teoria termodinamica dei dielettrici viscoelastici apolari. Nell'ambito di tale teoria viene esaminata la possibilità di descrivere l'effetto Maxwell, ossia il fenomeno della birifrangenza dovuta al moto del continuo. A questo proposito si mostra che il termine proposto da Toupin per tener conto dell'effetto Maxwell non è in contrasto con la seconda legge della Termodinamica.

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This work was supported by the Gruppo Nazionale per la Fisica Matematica of CNR.     

Relativistic thermodynamics of viscoelastic dielectrics

Archive for Rational Mechanics and Analysis -     

Moore-Gibson-Thompson theory for thermoelastic dielectrics

We consider the system of equations determining the linear thermoelastic deformations of dielectrics within the recently called Moore-Gibson-Thompson(MGT)theory.First,we obtain the system of equations for such a case.Second,we consider the case of a rigid solid and show the existence and the exponential decay of solutions.Third,we consider the thermoelastic case and obtain the existence and the stability of the solutions.Exponential decay of solutions in the one-dimensional case is also recalled.     

Representations for isotropic thermoelastic dielectrics

Using Chakrabarti and Wainwright's method, an integrity basis consisting of eighteen invariants is constructed for the energy function of deformation and polarization of Isotropic thermoelastic dielectrics. The minimality of the integrity basis is verified by group theoretic methods and this minimal integrity basis is employed to construct closed form irreducible polynomial representations for the electric tensor, the stress tensor and the electric and heat flux vectors.     

Instabilities in multilayered soft dielectrics

Experimental observations clearly show that the performance of dielectric elastomeric-based devices can be considerably improved using composite materials. A critical issue in the development of composite dielectric materials toward applications is the prediction of their failure mechanisms due to the applied electromechanical loads. In this paper we investigate analytically the influence of electromechanical finite deformations on the stability of multilayered soft dielectrics under plane-strain conditions. Four different criteria are considered: (i) loss of positive definiteness of the tangent electroelastic constitutive operator, (ii) existence of diffuse modes of bifurcation (microscopic modes), (iii) loss of strong ellipticity of the homogenized continuum (localized or macroscopic modes), and (iv) electric breakdown. While the formulation is developed for generic isotropic hyperelastic dielectrics, results are presented for the special class of ideal dielectrics incorporating a neo-Hookean elastic response. The effect of material properties and loading conditions is investigated, providing a detailed picture of the different possible failure modes.