ABSTRACT
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
A. Electroviscosity-Electroviscoelasticity of Liquid-Liquid Interfaces . . . . . . . . 371
B. Previous Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
II. Theory: Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373
A. Electrified Interfaces: A New Constitutive Model of Liquids . . . . . . . . . . . . . 373
1. Classical Assumptions for Interfacial Tension Structure and for
Partition Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
2. Postulated Assumptions for an Electrical Analog . . . . . . . . . . . . . . . . . . . 377
III. Theory of Electroviscoelasticity: Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
A. Tension Tensor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378
B. van der Pol Derivative Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
C. van der Pol Derivative Model: Fractional Approach . . . . . . . . . . . . . . . . . . . . 383
1. Fundamentals of Fractional Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
2. Example of Analog Realization of a Fractional Element . . . . . . . . . . . . . . 384
3. Solution of the Representative Linear Model . . . . . . . . . . . . . . . . . . . . . . 385
4. Solution of the Representative Nonlinear Model . . . . . . . . . . . . . . . . . . . 388
a. Numerical Methods for Nonlinear Equations . . . . . . . . . . . . . . . . . . . 390
IV. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
Electroviscosity and electroviscoelasticity are terms that may be dealing with fluid flow effects on
physical, chemical, and biochemical processes. The hydrodynamic or electrodynamic motion is
considered in the presence of both potential (elastic forces) and nonpotential (resistance forces)
fields. The elastic forces are gravitational, buoyancy, and electrostatic or electrodynamic
(Lorentz), and the resistance forces are continuum resistance or viscosity and electrical resistance
or impedance.
