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.
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