Mhr. Ghoreishy et V. Nassehi, MODELING THE TRANSIENT FLOW OF RUBBER COMPOUNDS IN THE DISPERSIVE SECTION OF AN INTERNAL MIXER WITH SLIP-STICK BOUNDARY-CONDITIONS, Advances in polymer technology, 16(1), 1997, pp. 45-68
The aim of this article is to describe the development of a mathematic
al model for the simulation of the flow of polymer melts inside intern
al mixers. The rheological behavior of the polymeric fluid is assumed
to be described by the Carreau equation. The flow regime is considered
to be non-isothermal. The set of the governing equations are solved u
sing the finite element method for both steady-state and transient con
ditions. In the steady state case, the flow equations are solved by th
e penalty method using the standard Galerkin technique. Petrov-Galerki
n schemes based on both consistent and inconsistent streamline upwindi
ng methods are employed to solve the energy equation and the obtained
results are compared. Transient velocity, pressure, and stress fields
are modeled using implicit theta method. Ln addition to implicit theta
method, two versions of the Taylor-Galerkin approach are used to solv
e the transient energy equation. Slip-stick on the solid walls, encoun
tered in the flow of viscous fluids, is incorporated in the model by t
he use of Navier's slip conditions. We describe two new methods for th
e inclusion of this condition in the working equation. Our simulations
yield the velocity field, distribution of pressure, stress and temper
ature in the steady state and the variations of these parameters with
respect to time under transient conditions. As an example of the appli
cability of the developed model, a typical mixing problem which involv
es convection of carbon black with flowing rubber in a domain represen
tative of the section under the blade of a tangential rotor mixer is s
imulated. Concentration profiles of carbon black in the rubber matrix
in this case is obtained by the solution of carbon mass continuity equ
ation in conjunction with the flow model. This solution gives the dist
ribution of filler volume fraction at different mixing times in the mi
xer. Comparison of the obtained results with the available experimenta
l data gives some indication of the validity of the model. (C) 1997 Jo
hn Wiley & Sons, Inc.