The major objective of this work is to develop accurate computational models to predict evolution of shear thinning liquid jets. A secondary objective is to investigate the formation of satellite drops, and to determine the conditions under which their diameter can be controlled. The theoretical approach of Galerkin-finite element analysis is used solve the complete two-dimensional set of axisymmetric governing equations and the kinematic and dynamic boundary conditions at the free surface. The effect of shear thinning behavior on break-up is studied in detail, in the case of an infinitely long non-Newtonian jet. It is found that the shear thinning behavior may be useful in controlling satellite drop sizes. (We observe that increasing the shear thinning behavior at moderate Reynolds number (Re = 5) leads to an initial increase in the satellite drop size, followed by a subsequent decrease.) Experimental validation for the theory is then presented for the case of a shear thinning non-Newtonian jet. The experimental fluid is pumped through a capillary and drop shapes are obtained using a high speed camera. The experimentally obtained shapes are compared to those predicted by theory with results found to be in good agreement.

1.
Rayleigh
L.
,
On the instability of jets
,
Proc. London Mathematical Society.
,
10
(
1879
),
4
13
.
2.
Eggers
J.
,
Nonlinear dynamics and breakup of freesurface flows
,
Reviews of Modern Physics
,
69
(
3)
(
1997
),
865
930
.
3.
Renardy
M.
,
Self-similar jet breakup for a generalized PTT model
,
J. Non-Newtonian Fluid Mech.
,
103
(
2–3)
(
2002
),
261
269
.
4.
Bousfield
D. W.
,
Keunings
R.
, and
Marucci
G.
,
Nonlinear analysis of the surface-tension driven breakup of viscoelastic liquid filaments
,
J. Non-Newtonian Fluid Mech.
,
21
(
1)
(
1986
),
79
97
.
5.
Yildirim
O. E.
and
Basaran
O. A.
,
Deformation and breakup of stretching bridges of Newtonian and sheer-thinning liquids: comparison of one- and two-dimensional models
,
Chem. Engg. Sci.
,
56
(
1)
(
1999
),
211
233
.
6.
Doshi
P.
,
Suryo
R.
,
Yildirim
O. E.
,
McKinley
G. H.
and
Basaran
O. A.
,
Scaling in pinch-off of generalized Newtonian fluids
.
J. Non-Newtonian Fluid Mech.
,
113
(
1)
(
2004
),
1
27
.
7.
Renardy
M.
and
Renardy
Y.
,
Similarity solutions for breakup of jets of power law fluids
,
J. Non-Newtonian Fluid Mech.
,
122
(
1–3)
(
2004
),
303
312
.
8.
Campana
D.
,
Paolo
J. D.
,
Saita
F. A.
,
A 2-D model of Rayleigh instability in capillary tubes-surfactant effects
,
Int J. of Multiphase Flow
,
30
,
431
454
.
9.
S. Ubal, C. Corvalan, M.D. Giavedoni, F.A. Saita, A numerical study on two-dimensional Faraday waves, Computational Fluid and Solid Mech., K. J. Bathe ed., Springer (2001), 1000–1005.
10.
S.F. Kistler and L.E. Scriven, Coating flows. Computational analysis of polymer processing, J. R. A. Pearson and S. M. Richardson Ed. New York, Applied Science Publishers, 1983.
11.
G. Strang and G.L. Fix, An analysis of the finite element method. Englewood Cliffs, New Jersey, Prentice Hall, 1973.
12.
P.M. Gresho, R.L. Lee, R.L. Sani, Recent Advances in Numerical Methods in Fluids, Vol. 1, Chapter on “The time-dependent solution of incompressible Navier-Stokes equations in two or three dimensions.” Pineridge Press Ltd., Swansea, UK, 1980.
13.
Crisfield
M. A.
,
A fast incremental-iterative solution procedure that handles snap-through
.
Computers & Structures
,
13
(
1–3)
(
1981
),
55
62
.
14.
Timmermans
M. -L. E.
and
Lister
J. R.
,
The effect of surfactant on the stability of a liquid thread
.
J. Fluid Mech.
,
459
(
2002
),
289
306
.
15.
Gaster
M.
,
1962
.
A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability
.
J. Fluid Mech.
,
14
,
222
224
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