Theory of electroviscoelasticity

Abstract

So far, three possible mathematical formalisms have been discussed related to the developed theory of electroviscoelasticity. The first is tension tensor model where the normal and tangential forces are considered regardless, only from mathematical point of view, of their origin (mechanical or electrical). The second is van der Pol integral-derivative model. Finally, the third model presents an effort to generalize the van der Pol integral–differential equation; the ordinary time derivative and integral are now replaced with corresponding fractional-order time derivative and integral of order 0 , p , 1. Each of these mathematical formalisms, although related to the same physical formalism, facilitate a better understanding of different aspects of a droplet existence (formation, life, and destruction). Tension tensor model discusses the force equilibrium at the interfaces, either deformable or rigid, but its solution is difficult because the tensor contain nonlinear and complex elements. van der Pol derivative model is convenient for discussion of the antenna output circuit, the resulting equivalent electrical circuit; but in the case of nonlinear oscillators, that is here the realistic one, the problem of determining the noise output is complicated by the fact that the output is fed back into the system, thus modifying the effective noise input in a complicated manner. The noise output appears as an induced anisotropic effect. The theory of electroviscoelasticity using fractional approach constitutes a new interdisciplinary approach to colloid and interface science. Hence, (1) more degrees of freedom are in the model, (2) memory storage considerations and hereditary properties are included in the model, and (3) history or impact to the present and future is in the game.