Recent Advances in Complex Fluids Modeling

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 MittagLeffler 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.