A new approach to the phenomena at the interfaces of finely dispersed systems

A new idea has been applied for the elucidation of the electron and momentum transfer phenomena, at both rigid and deformable interfaces, in finely (micro-, nano-, atto-) dispersed systems. The electroviscoelastic behavior of, e.g., liquid/liquid interfaces (emulsions and double emulsions), is based on three forms of "instabilities"; these are rigid, elastic, and plastic. The events are understood as interactions between the internal (immanent) and external (incident) periodical physical fields. Since the events at the interfaces of finely dispersed systems must be considered at the molecular, atomic, and/or entities level it is inevitable to introduce the electron transfer phenomenon beside the classical heat, mass, and momentum transfer phenomena commonly used in chemical engineering. Therefore, an entity can be defined as the smallest indivisible element of matter that is related to the particular transfer phenomena. Hence, the entity can be either differential element of mass/demon, ion, phonon as quanta of acoustic energy, infon as quanta of information, photon, and electron. Three possible mathematical formalisms have been derived and discussed related to this physical formalism, i.e., to the developed theory of electroviscoelasticity. The first is the stretching tensor model, where the normal and tangential forces are considered, only in mathematical formalism, regardless of their origin (mechanical and/or electrical). The second is the classical integer-order van der Pol derivative model. Finally, the third model comprises an effort to generalize the previous van der Pol differential equations, both linear and nonlinear, where the ordinary time derivatives and integrals are replaced by corresponding fractional-order time derivatives and integrals of order p < 2 (p = n - delta, n = 1,2,delta << 1). In order to justify and corroborate a more general approach the obtained calculated results were compared to those experimentally measured using the representative liquid/liquid system.