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RESEARCH PAPERS: Non-Newtonian Behavior and Rheology

Drop Formation in Non-Newtonian Jets at Low Reynolds Numbers

[+] Author and Article Information
V. Dravid1

Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, 500 Allison Road, West Lafayette, IN 47907-2014

P. B. Loke

Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, 500 Allison Road, West Lafayette, IN 47907-2014

C. M. Corvalan2

Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, 500 Allison Road, West Lafayette, IN 47907-2014

P. E. Sojka2 n3

Maurice J. Zucrow Laboratories, School of Mechanical Engineering, Purdue University, 500 Allison Road, West Lafayette, IN 47907-2014Sojka@ecn.purdue.edu

1

Present address: COMSOL, Inc., Waltham, MA 01803.

2

Present address: Food Science Department, 745 Agriculture Mall Drive, West Lafayette, IN 47907.

3

Corresponding author.

J. Fluids Eng 130(8), 081504 (Jul 29, 2008) (8 pages) doi:10.1115/1.2956612 History: Received May 31, 2007; Revised April 16, 2008; Published July 29, 2008

The objective of this study was to develop an experimentally verified computational model that accurately predicts evolution of shear-thinning liquid jets. A secondary objective was to investigate the formation of satellite drops and to determine conditions under which their diameter can be controlled. The model employs the Galerkin finite/element approach to solve the complete two-dimensional set of axisymmetric governing equations and the corresponding kinematic and dynamic boundary conditions at the free surface. The effect of shear-thinning behavior on breakup was studied in detail for the case of an infinitely long non-Newtonian jet. It was found that shear-thinning behavior may be useful in controlling satellite drop sizes. (We observe that increasing the shear-thinning behavior at Re5 leads to an initial increase in the satellite drop size, followed by a subsequent decrease.) Comparison of model predictions with experimental data is presented for the case of a shear-thinning non-Newtonian jet. The experimental liquid was pumped through a capillary and drop shapes obtained using a high speed camera. The experimentally obtained shapes were compared to those predicted by the model and found to be in good agreement.

Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

Streamlines for a Newtonian jet with Re=5 at three dimensionless times before pinch-off: (a) t=86.05, (b) t=90.05, and (c) t=92.00.

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Figure 5

Axial variation in the surface pressure (a) and surface tangential velocity (b) for a Newtonian jet of Re=5 at t=86.05

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Figure 6

Axial variation in the surface pressure (a) and tangential velocity (b) for a Newtonian jet of Re=5 at t=92.0

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Figure 3

Satellite drop radius versus power-law index n for Re=5, α=10, and β=0.002

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Figure 2

Comparison of model predictions (symbols) with the similarity solution results of Doshi (6) (solid line). Re=0, ε0=0.5, α=1, β=0.02; n=0.8 (squares), n=0.9 (diamonds).

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Figure 1

System geometry with basic dimensions

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Figure 7

Pinch-off time (solid line) and stagnation time (dashed line) versus power-law index for Re=5

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Figure 8

Streamlines for a shear-thinning jet (n=0.3) at Re=5: (a) t=74.3 and (b) t=85.5

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Figure 9

Axial variation in the surface pressure (a) and surface tangential velocity (b) for n=0.3 and Re=5 at t=85.5

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Figure 10

Capillary pressure at the liquid interface for two times. The dashed line denotes a Newtonian jet and the solid lines denote a shear-thinning jet (n=0.7)

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Figure 11

Capillary pressure at the liquid interface for two times. Here the dashed line denotes a shear-thinning jet with n=0.7 while the solid line indicates a shear-thinning jet with n=0.3.

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Figure 12

Typical experimental droplet streams

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Figure 13

Typical extracted images of postprocessed droplets

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Figure 14

Comparison of model predictions (solid line) with experimental data (square symbols) for 0.1% water-XG solution at Re=0.46, n=0.55, and t=9.61±0.09ms. The dashed lines indicate the uncertainty in model predictions.

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Figure 15

Comparison of model predictions (solid line) with experimental data (square symbols) for 0.1% water-XG solution at Re=0.67, n=0.55, and t=9.09±0.08ms. The dashed lines indicate the uncertainty in model predictions.

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Figure 16

Comparison of model predictions (solid line) with experimental data (squares) for 0.2% water-XG solution at Re=0.22, n=0.40, and t=12.48±0.05ms. The dashed lines depict the uncertainty in model predictions.

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Figure 17

Comparison of model predictions (solid line) with experimental data (square symbols) for 0.2% water-XG solution at Re=0.33, n=0.40, and t=10.88±0.07ms. The dashed lines depict the uncertainty in model predictions.

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Figure 18

Comparison of model predictions (solid line) with experimental data (square symbols) for 0.3% XG-water solution at Re=0.19, n=0.30, and t=12.80±0.09ms. The dashed lines indicate the uncertainty in model predictions.

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Figure 19

Comparison of model predictions (solid line) with experimental data (square symbols) for 0.3% XG-water solution at Re=0.28, n=0.30, and t=10.63±0.08ms. The dashed lines indicate the uncertainty in model predictions.

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