Recent Advances in Complex Fluids Modeling

Abstract

In this chapter, we present a brief description of existing viscoelastic models, starting with the classical differential and integral models, and then focusing our attention on new models that take advantage of the enhanced properties of the Mittag-Leffler function (a generalization of the exponential function). The generalized models considered in this work are the fractional Kaye-Bernstein, Kearsley, Zapas (K-BKZ) integral model and the differential generalized exponential Phan-Thien and Tanner (PTT) model recently proposed by our research group. The integral model makes use of the relaxation function obtained from a step-strain applied to the fractional Maxwell model, and the differential model generalizes the familiar exponential Phan-Thien and Tanner constitutive equation by substituting the exponential function of the trace of the stress tensor by the Mittag-Leffler function. Since the differential model is based on local operators, it reduces the computational time needed to predict the flow behavior, and, it also allows a simpler description of complex fluids. Therefore, we explore the rheometric properties of this model and its ability (or limitations) in describing complex flows.

Insulator‐based dielectrophoretic focusing and trapping of particles in non‐Newtonian fluids

“…() and (), the fluid rheological effects on iDEP focusing and trapping of particles are both characterized by the two multiplying correction factors, that is, causes a reduction while enhances. To simplify the analysis in the results section, we further assume the wall and particle zeta potentials are both independent of the polymer addition, which is common in the theoretical analysis [31–42]. Thus, the particle mobility ratio, , remains identical among the tested fluids, and hence the observed variation in iDEP focusing and trapping can be attributed solely to the influence of fluid rheology via .…”

“…There have been a number of studies on fluid electroosmosis and particle electrophoresis in non‐Newtonian fluids through microchannels [31]. However, the vast majority of them are theoretical (or numerical), where various constitutive equations have been used to consider the fluid rheological properties [32–42]. Experimental investigations in this direction are much less.…”

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

“…It has also only considered a simple conduit. Important work in two-fluid electro-kinetic transport has been reported by Afonso et al [42], in slip electro kinetic flows also by Afonso et al [43] and in annular electro-osmotic pumping by Ferrás et al [44]. These complexities constitute interesting pathways for extending the current work and will be addressed imminently.…”

A generalised distributed-order Maxwell model

“…They introduced the Maxwell model by using a spring and a dashpot, as shown in figure 1(a) (for a more detailed explanation see [7][8][9][10] and for the derivation of the Maxwell model using molecular theory see [11][12][13]). When the same material shows different relaxations in different regions, the model is not able to deal with such complexity.…”