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RESEARCH PAPERS: Non-Newtonian Behavior and Rheology

Interplay Between Inertia and Elasticity in Film Casting

[+] Author and Article Information
Radoslav German

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canada

Roger E. Khayat1

Department of Mechanical and Materials Engineering, The University of Western Ontario, London, ON, N6A 5B9, Canadarkhayat@eng.uwo.ca

1

Corresponding author.

J. Fluids Eng 130(8), 081501 (Jul 23, 2008) (12 pages) doi:10.1115/1.2956592 History: Received February 19, 2007; Revised August 24, 2007; Published July 23, 2008

The influence of inertia and boundary conditions on the steady state and stability of isothermal film casting of viscoelastic fluids is examined using a Phan-Thien–Tanner rheological model. The elongational flow between the die exit and the take-up point is investigated. In general, the steady-state film tends to contract for low-inertia flow; this contraction, however, is significantly diminished by inertia. The polymeric normal stresses and primary normal stress difference decrease in the most of the air gap as inertia increases. In contrast, the stress and stress difference increase considerably near the take-up point due to a dramatic increase in the elongation rate. The linear stability analysis for two-dimensional disturbances is carried out. For a polymer with no degradation, and in the absence of inertia (Re=0), the analysis predicts critical draw ratios that form an envelope to an unstable region. This region of unstable conditions reduces as inertia increases. Two branches of neutral stability curve are observed for higher-inertia flow as opposed to a single curve for Re=0. The unstable region expands as α increases, where α is a measure of polymer degradation. When α becomes sufficiently large, the elasticity tends to destabilize the flow. It is also found that boundary conditions have an important influence on the steady-state profiles and stability region, particularly for high-elasticity fluids.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 6

Dependence of the elongational viscosity on the rate of elongation for the range α∊[0,0.2] at De=0.09 and Rv=0.1. Homogeneous elongational flow is considered.

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Figure 5

Dependence of the primary normal stress difference at x=1 on Reynolds number for the range De∊[0.001,0.1] at Rv=0.1, (a) α=0, and (b) α=0.1

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Figure 4

Influence of parameter α on (a) the film thickness hs, (b) the polymeric stress in the streamwise direction τxxs, (c) the polymeric stress in the depthwise direction τzzs, and (d) the primary normal stress difference τxxs−τzzs, for the range α∊[0,0.2] at Dr=10, Re=0, Rv=0.1, and De=0.05

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Figure 3

Influence of elasticity on (a) the film thickness hs, (b) the polymeric stress in the streamwise direction τxxs, (c) the polymeric stress in the depthwise direction τzzs, and (d) the primary normal stress difference τxxs−τzzs, for the range De∊[0,0.1] at Dr=10, Re=0, Rv=0.1, and α=0.1

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Figure 2

Influence of inertia on (a) the film thickness hs, (b) the polymeric stress in the streamwise direction τxxs, (c) the polymeric stress in the depthwise direction τzzs, and (d) the primary normal stress difference τxxs−τzzs, for the range Re∊[0,1] at Dr=10, De=0.05,Rv=0.1, and α=0.1

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Figure 1

Schematic of film-casting flow and coordinates used

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Figure 7

Effect of inertia on the critical draw ratio Drc, for the range Re∊[0,0.2] at α=0 and Rv=0.1

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Figure 8

Effect of parameter α on the critical draw ratio Drc, for the range α∊[0,0.2] at Rv=0.1. Inertia is neglected.

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Figure 9

Influence of inertia and elasticity on the critical draw ratio Drc, over the range Re∊[0,0.15] and De∊[0.0001,1], at α=0.1 and Rv=0.1

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Figure 10

Influence of inertia and elasticity on the critical draw ratio Drc, over the range Re∊0.1,0.3 and De∊[0.0001,1] at α=0.1 and Rv=0.1

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Figure 11

Effect of parameter α on the critical draw ratio Drc, over the range α∊[0,0.1] at Re=0.1 and Rv=0.1

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Figure 12

Effect of elasticity on normal stresses at x=0 for HBCs, NBCs, and ABCs

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Figure 13

Effect of the stress boundary conditions on (a) the film thickness hs, (b) the polymeric stress in the streamwise direction τxxs, (c) the polymeric stress in the depthwise direction τzzs, and (d) the primary normal stress difference τxxs−τzzs, at α=0.1, Dr=10, De=0.09, Rv=0.1, and Re=0

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Figure 14

Effect of the stress boundary conditions on the critical draw ratio Drc, at Re=0, Rv=0.1, and α=0.1

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