Study of the electroosmotic flow of a structured fluid with a new generalized rheological model

The electroosmotic flow of a viscoelastic fluid in a capillary system was investigated analytically. The rheology of the fluid was characterized by a novel generalized exponential model equation. The charge density obeys the Boltzmann distribution, which governs the electrical double-layer field and body force generated by the applied electrical field. Mathematically, this scenario can be modeled by the Poisson-Boltzmann partial differential equation, by assuming that the zeta potential is small, i.e., less than 25 mV (Debye-Hückel approximation). Considering a pulsating electric field, the shear viscosity and the alteration in the volumetric flow were presented as a function of the material parameters through the characteristic dimensionless numbers by using an exponential-type generalized rheological model. Thixotropy, shear thinning, yield stress mechanisms, and weight concentration were analyzed through numerical results. Finally, the flow properties and rheology were predicted using experimental data reported elsewhere for worm-like micellar solution of cetyl trimethyl ammonium tosilate (CTAT). The rheological equation of state proposed in this study describes the alterations in the structure resulting from applied forces (tangential and normal). These forces induced a structural evolution (kinetic model) due to the relaxation processes caused by shear strain. It is important to mention that in electroosmotic flows, complex behavior such as (i) thixotropy, (ii) rheopexy, and (iii) shear banding flow is scarcely explained in terms of the change in the structure of the fluid under flow. Graphical Abstract