Advanced modelling material functions of the Phan-Thein-Tanner (PTT) and Large amplitude oscillation shear (LAOS) flow modules

Abstract

The material functions of the linear and exponential Phan-Thein-Tanner (PTT) and Large amplitude oscillation shear (LAOS) modules are analyzed. The behavior of the functions at inception and cessation are investigated using advanced mathematical modeling techniques. Starting with the affine PTT model expressions, they are further formulated using material function parameters for the steady, initiation, and cessation shear flows. Dimensionless variables are introduced and incorporated into the equations and further modeling using Wolfram Mathematica is done to produce analytical results. Further on, the formulations of the linear and exponential large-amplitude oscillation shear (LAOS) modules are considered. They are also formulated using dimensionless variables and material functions. With the aid of Mathematica, the equations are coded and plotted for a comprehensive analytical understanding of the behavior of the flow. Ewoldt grid is introduced to give a better understanding of the Deborah De and Weissenberg Wi numbers effect as they increase or decrease on the behavior of the flow. The results give a detail description of the behavior of these modules under specific conditions and can be used with further studies in various fields.