Jens Eggers Polymer threads: formation and instability.
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Transcript of Jens Eggers Polymer threads: formation and instability.
Jens Eggers
Polymer threads: formationand instability
Drop breakup
…createsextensional flow
and produces multiplesingularities
water drop
Flexible polymers
characteristic time λ
extension rate
stress ~ extension
maximal extension
50 ppm PEO in water
Y. Amarouchene et al. PRL 86, 3558 (2001)
water
1.2mm, T = 0,1 sec
PolymersWagner +
Sattler
64 10WM amu
polymer (Ch. Clasen)
beads on a string
Polymer breakup: overview
blistering
water jet
2 k ( , ) cos( )th z t R e kz
kR
0
3 1/ 20 ( /( ))R
surface tension-inertial balance:
W. Strutt(1873)fastest growing mode: max 9.01R
Newtonian breakup: linear stability
0 198t t s
glyceroldrop center0 350t t s
1mm
experiment byTomasz Kowalewski
0 46t t s
1( , ) ' ( '/ ' )h z t t z t
0' ( ) /z z z 0' ( ) /t t t t
Newtonian breakup: similarity solution
Eggers, PRL `93
3
0.12R
R
1R
Bead formationWagner et al.,
PRL ‘05pure waterPEO in water
One-dimensional approximationEntov et al. `80
Renardy `82
2 2( v) 0zh ht
2
2
3 v+v v v
hz s z z
z z
hpt
z zv 2 v zz z zt
stretching
z
Thread formation Ch. Clasen and G. McKinley
v=2z / zh p
p
0 exp( / 3 )z t
0 0( ) ?h
0 exp( / 3 )threadh h t
Bazilevskii et al, `81:thinning dominated by end effects!
Corner region
thread drop
0 exp( / 3 )h t ( , ) cz zh z t H
Clasen et al.,
JFM ‘06
H
similarity
solution
string tension: 2 ( )T th h
Experiment: rescale drop
thread
Clasen et al. JFM ‘06
( , ) exp( / 3 ) / exp( / 3 )h z t t H z t similarity form:
…but experimental curvature greater x 2
Boger fluid
Blistering instability
30 m
min
zzE h
increases by 5
orders of magnitude!
full strech
Fontelos + Li:
Rayleigh instability
with effective E
Sattler et al.,
PRL ‘08
PEO in water, 2000 ppm
Rayleigh instability?
tamp e
9.3ms
9eff Pas
600E Pas time (ms)
sub-pixel
resolution!
Nonlinear instabilities
1) Iterated thread instability
(bulk)
2) Breathing instability
(end)
Weird instabilities
PEO, 4Mio MW, 2kppm, overall duration 0.016s
Does it ever break?
drops do not wet the fiber!
A solid fiber!
Mayonnaise, ketchup, yoghurt
movies by D. Bonn
Remarks, open problems
• No predictive model for flow at high deformations!
FENE-P: have to be treated as adjustable, , ,s p b
• thinning rate of filament depends significantly
on concentration (factor 10), and even on nozzle
radius!
• no significant quantitative statement about saturation!
• filament thinning still open (stability, full 3D model)
• mechanism for demixing ???!
• extensional behavior of suspensions; is there
extensional thinning?
Wagner, Amarouchene,Bonn, Eggers:PRL (`05)
1-D simulation
Polymeric fluid (100 ppm of PEO)
experiment