CREEPING FLOW OF VISCOELASTIC FLUIDS THROUGH TAPERED SLIT DIES: AN ANALYTICAL SOLUTION

Abstract

In the present study, it will be shown that at vanishingly small Reynolds numbers the extensional behavior of a fluid has a strong effect on its kinematics when flowing through a tapered slit die. To show this, the Cauchy equations of motion were simplified using the creeping flow approximation. Assuming the flow to be steady, laminar, two-dimensional, and incompressible, the governing PDEs were reduced to a set of coupled ODEs using a series solution in terms of the powers of 1/r. Two different constitutive equations, both incorporating an extensional parameter, were used in the analysis: (i) the Giesekus model and (ii) the Simplified Phan-Thien-Tanner (SPTT). An analytical solution was found for each fluid model clearly depicting the strong influence of the extensional parameter on the flow becoming non-radial within the channel.

Keywords:

• Converging flow
• Creeping flow
• Giesekus model
• Maxwell model
• Phan-Thien-Tanner model
• Secondary flow

Acknowledgments

The authors would like to thank the Research Council of the University of Tehran (RCUT) for supporting this work. Special thanks are also due to the reviewers of the original manuscript for their constructive comments.