Combined time-pressure gradient and electric field on the electroosmotic flow of a complex fluid (human blood data) in a concentric annular microchannel: Linear and non-linear cases with the exponential structure rheological constitutive equation

This study explores theoretically how a time-dependent, pulsatile pressure gradient combined with an electric field affects the flow of a structured electro-viscoelastic fluid in an annular space. The fluid's behavior is described using an extend version of the nonlinear viscoelastic constitutive equation with an exponential structure kernel (ESR-S). This updated ESR model incorporates solvent-related forces, resulting in the ESR-S formulation, which captures complex non-Newtonian behaviors such as shear thinning/thickening, thixotropy, yield stress, elasticity and normal stress differences. Dimensionless variables are introduced to characterize the geometry, material properties, and driving forces, In the linear viscoelastic regime, transfer functions are derived using Fourier analysis, revealing resonance behavior at specific frequencies governed by the Womersley and Deborah numbers. In the nonlinear regime, flow enhancement is predicted based on material characteristic and external mechanisms, including electric and thermal effects. The study shows that combination of a pulsatile pressure gradient and an electric field can significantly enhance flow, particularly when specific dimensionless parameters are met. This effect is demonstrated using rheological data from human blood samples with varying cholesterol levels, where high-cholesterol samples exhibited a distinct flow pattern suggesting a potential diagnostic indicator for hypercholesterolemia. The main objective is to theoretically evaluate the extended ESR-S model for predicting coupled flow behavior in both linear and nonlinear regimes.