Fluids Breakup Dynamics

1
Fluids Breakup Dynamics
Vladimir M. Entov, Aleksey N. Rozhkov Laboratory
of Mechanics of Complex Fluids Institute for
Problems in Mechanics of the Russian Academy of
Sciences, Moscow, RUSSIA DCF-10 Isaac Newton
Institute for Mathematical Science Cambridge, UK,
Oct.4, 2006
2
Disclaimer

• It is a deliberately provocative and
  controversial talk intended to draw attention to
  an important and poorly understood branch of
  physical fluid dynamics in which an interplay
  between rheology and fluid dynamics is crucial

3
Outlay

• What is fracture?
• Applications of fluid breakup and breakup
  control
• Scenarios of fluid breakup
• Filament thinning as a key mechanism of fracture
• Breakup control by additives
• Liquid fracture criteria?
• Open problems

4
What is fracture?

• Fracture of a liquid volume is its separation
  into two or more disconnected parts it is a
  process rather than event
• Strain and strain rate of a material element
  necessarily tend to infinity in finite time

5
What is fracture?-2

• A mathematician viewpoint
• A catastrophe a topology change in finite time
  and/or upon reaching a limiting value of a
  controlling parameter.
• The solution describing the system ceases to
  exist upon reaching the limiting value of the
  parameter or time.

6
What is fracture-3

• Strain and strain rate of a material element
  necessarily tend to infinity in finite time
• Local stress should become infinite in finite
  time
• Rheology properties at extreme regimes become
  crucial

7
Elementary Example a Detaching Drop

• No surface tension viscous fluid

Breakup
Fracture
V
6? dr -W/(?r) dt r2r20 -Wt/(3 ? ?) tbr 3 ?
? r20/W.
L Vt r const/ t1/2 tbr ?
W
Forced fracture by external force
Inertial breakup is impossible Surface tension
is crucial!?
8
Applications of fluid breakup and breakup control

• Atomization (fuels, paint and perfume sprays etc
  )
• Ink-jet printing
• Dosage of pharmaceutical products
• Antimisting additives to aircraft fuel
• Jet stabilization
• Fiber and nano-fiber drawing

9
Scenarios of fluid breakup

• (Liquid Breakup Zoo)

Splash - Water
http//www.rit.edu/andpph/photofile-b/splash_4765
web.jpg
Jet - Water
Fountain (Petergof)
10
Breakup Zoo Drop Impact
Inertia-capillary breakup and effect of elastic
stress on the late stage
Spreading drop breakup (Aziz Chandra, 2000)
11
Swirl Atomization

• Features
• Multistage process
• Air drag and dynamic pressure
• are important
• Additives may affect late stage
• of breakup

12
Liquid Sheet Breakup (G.I.Taylor)
Development and instability of rim
jet Change-of-type (hyperbolic-elliptic) and
catastrophic instability
13
Observations

• Development of a jet or neck with large curvature
  is an essential stage in breakup
• Surface tension is essential for dynamic breakup
  as different from fracture by external force
• Jet breakup provides a generic scenario of
  breakup
• Question Is there a dynamic breakup scenario
  for a liquid without surface tension?

14
Breakup of a Jet of Water

• Features
• Fast development of necking due to capillary
  instability and then breakup
• Once started, necking proceeds without restrain
• Inertia/capillarity dominated

15
Hyperstable Jets and Beads-on-String Breakup
16
Hyperstable Jets and Beads-on-String Breakup

• Prototype experiments
• Living liquid filament a fluid-dynamical miracle
• Filament is hyperstable! --gt Limiting stage of
  breakup!
• Rayleigh-Weber theory

Predicts breakup in lt 10-4s
Elasto-capillary equilibrium
?el gt ? / (2r)
Thinning filament a stand-alone breakup
device
17
Capillary Rheometer

• PEO c1

ex-(2/a)da/dt ?z 0 ?r - ?/a

• ? 10?? ?

18
Breakup Time

• Finite time (Tbr6?a/?) for a viscous fluid
• Infinite time for an elastic fluid
• Polymer molecules should be extended up to limit
  or should be ruptured before filament breakup

19
Bridge breakup

• Bazilevsky et al, 1997

20
Bridge breakup

• Bazilevsky et al, 1997
• Breakup time relaxation time

21
Breakup event

• Limiting extension of polymeric molecules
• Finite extensibility is essential
• Quasi-viscous behavior at the terminal stage
• Time to breakup relaxation time
• In the case of multiple relaxation times the
  longest one controls the later stage (Entov
  Hinch, 1997)

22
Gelled Fluids wormlike micellar solutions

• J.Bico, V.M.Entov, Ch.Clasen, G.H.McKinley
• (MIT, Microfluidics Hatsopoulos Microfluids Lab)
• Polymer-like systems with labile macromolecules
• Macroscopic experiments High-speed camera

23
Fast Extension Ductile Breakup and Recoil
24
Thinning and Breakup of a Surfactant Filament
25
Secondary Beads-on-String Structure prior to
Breakup
26
Features

• Slow capillary thinning
• Small elongation prior to breakup (small
  extensibility or strength of wormlike micelles
  (?))
• Combination of elasto-viscous and visco-plastic
  behavior
• Secondary beads-on-string breakup --
  manifestation of polydispersity?

27
Drop Detachment Dilute Solution Thin Nozzle

• Capillary forces prevail. Elastic stress is
  insufficient to prevent fast necking up to breakup

28
Falling Drops of Surfactant Solution Large
Nozzle
29
Recoil after Drop Detachment
30
Analogy with brittle/viscous fracture transition
in solids

• Liquid is a very imperfect solid (Ya.Frenkel)

Fast loading high rigidity small elongation --
brittle fracture Slow loading low
rigidity large elongation -- viscous
fracture NB Smiths envelope for rubbers!
31
Jets of a Surfactant Solution

• Long jet
• Beads-on-String Structure
• Necking between beads is hindered by elastic
  stress, as in polymer solutions.
• Capillary/elastic instantaneous equilibrium in
  necks
• Long- periodic dynamics

32
Short Jets of Surfactant Solution

• Why the last drop is much larger?

33
Key Features

• Gobbling phenomenon is primarily controlled and
  can be quantitatively desribed by mass and
  momentum balances for inviscid flow with
  capillary forces included
• Role of polymer is to delay breakup of necks
  between drops
• Approximately constant axial tension prevails in
  the jet
• Interdrop filaments thinning occurs not
  autonomously but under persisting axial tension
• Breakup occurs upon reaching limiting extension
  of polymer molecules

34
Filament Thinning Model

Spatially Periodic Breakup, ?z ? 0, axial Force
F ??? R (t)
F
Breaking Jet Axial Force F?? R0 , ?z ??
35
Impulse jet generated by printer head
??????? ?????
HP Think Jet Printhead Dh100 ?m, a0100
?m, v010 m/s, m0300 nG
HP standard ink, t140 ?s
2.2 mm
A.Bazilevsky, J.Meyer, A. Rozhkov Study of effect
of polymer additives
36
Impulse jet breakup
???????????? ??????? ?????
t020 ???
t040 ???
t060 ???
t080 ???
t100 ???
t120 ???
t140 ???
t160 ???
t180 ???
t200 ???
t220 ???
t240 ???
t260 ???
t280 ???
t300 ?s
2.2 mm
37
Shock Disintegration of Liquid

• (A.Rozhkov et al)

38
Copper Wire and Kevlar-like Polymer Filaments
v670 ?/?
?
t50 ?s
t15.1 ???
t29.0 ???
t53.1 ???
t64.7 ?s
?????? ?????????, d1.1 ??
??????? ???
39
Shock Disintegration Liquids
Glycerol d0.46 mm ??
t27.7 ?s
t11.0 ?s
PEO-4 d0.50 mm
t72.0 ?s
t28.1 ?s
t11.7 ?s
40
Thinning Filament PEO-2
t7.8 ?s
d0.20??
t38.6 ?s
t69.7 ?s
41
Annular Liquid Sheet Breakup

• Water PAA
  sol-n, c100 ppm

? v4 m/s/?
--- 1 cm
42
Drop/obstacle Collision No Wall, No Friction
(Rozhkov, Vignes-Adler)
View from above
?
Side view
43
Water Drop
dt4.0 mm, di2.67 mm, vi3.87 m/s, Wei?vi2di/? 550 dt7.4 mm, di3.89 mm vi3.84 m/s, Wei?vi2di/? 792
t 09 ?s
t 01 ??
t 02 ??
t 03 ??
t 04 ??
t 05 ??
t 06 ??
t 07 ??
t 08 ??
t 00 ??
44
Rim Jet as an Essential Element of Breakup
????????? ???????
G.I. Taylor, 1959
?
???? ? ????????? ??????
vr
h
vr (2? / ? h) 1/2
v

• rm?vq/(4??),
• v vi3.5 m/s, q (?di3/6)/(di/vi)13.87 mm3/ms
• rm?vq/(4??)52.14 mm.
• Experiment rm 7 mm!

??????????? ????? ?????????? ? ????????????
?????? ?????????? ??? v vr
45
Collision of a drop with an obstacle water and
PEO sol-ns (Rozhkov, Vignes-Adler)
PEO, c1 ppm
Water

• dt4.0 mm di2.7 mm,
• vi3.87 m/s

t1 ??
t4 ??
t5 ??
t6 ??
t8 ??
t12 ??
t15 ??
t30 ??
t3 ??
t2 ms
PEO c10 ppm
PEO c100 ppm
46
Collision of drops of surfactant solutions with
an obstacle   (A.N.Rozhkov, M.Vignes-Adler,
....)

• Fluids water solutions of DOS, DDAB, Silwett
  L77
• Features multistage process,
• Web-like and spider-like structures, holes

47
Collision of drop with a disc - 1
dt4.0 mm, di2.7 mm, vi3.87 m/s
t, ms Water DDAB 100?CMC Silwett L77 1000?CMC
1
2
 
48
Collision of drop with a disc - 2
dt4.0 mm, di2.7 mm, vi3.87 m/s
t, ms Water DDAB 100?CMC Silwett L77 1000?CMC
3
4
 
49
Collision of drop with a disc - 3
dt4.0 mm, di2.7 mm, vi3.87 m/s
t, ms Water DDAB 100?CMC Silwett L77 1000?CMC
5
6
 
50
Collision of drop with a disc 4
dt4.0 mm, di2.7 mm, vi3.87 m/s
t, ms Water DDAB 100?CMC Silwett L77 1000?CMC
7
8
 
51
Collision of drop with a disc - 5
dt4.0 mm, di2.7 mm, vi3.87 m/s
t, ms Water DDAB 100?CMC Silwett L77 1000?CMC
9
10
 
52
Holes in Liquid Sheets
Silwett L77, c10?CMC, di2.515 mm, vi3.288 m/s
DDAB, c100?CMC, di2.70 mm, vi3.408 m/s
t3.474 ms ?4.899
t2.896 ms ?3.656
t3.101 ?? ?3.915
t3.952 ?? ?5.115
53
Fracture of Liquids

• A multistage process, a hierarchy of
  instabilities.
• At low viscosity the surface tension is
  crucially important
• Rayleighs jet breakup is a generic and best
  understood fracture scenarios
• Taylors liquid sheet breakup provides another
  scenario of blowup due to change of the type of
  governing equations.
• Ductile fracture may develop in tough highly
  viscous and/or filled fluids.

54
Open Mathematical Problems

• Global dynamics can we suggest breakup
  scenarios without capillarity?
• Numerical modelling of multistage breakup
  process in Newtonian and non-Newtonian liquids.
• Steady-state breaking jets and sheets and
  change-of-type phenomena. Boundary conditions at
  the free end of the breaking jet.

55
Some References
Hyperstable Jets and Beads-on-String
Breakup A.V.Bazilevskii, S.I.Voronkov,
V.M.Entov, and A.N.Rozhkov. Orientational effects
in the decomposition of streams and strands of
diluted polymer solutions. Soviet Phys. Doklady,
1981, vol.26, No 3, pp.333-335. A.V.Bazilevskii,
V.M.Entov, and A.N.Rozhkov. Elastic stresses in
capillary jets of dilute polymer solutions. Fluid
Dynamics, 1985, vol.20, No 2, pp.169-175. Capilla
ry Rheometer Bazilevsky A.V., Entov V.M.,
Rozhkov A.N. Liquid filament microrheometer and
some of its applications. Proceedings of the
Golden Jubilee Meeting of the British Society of
Rheology and Third European Rheology Conference.
1990, Edinburgh, UK. London and N.Y. Elsevier
Applied Science, 1990. P. 41-43. Bazilevskii
A.V., Entov V.M., Rozhkov A.N. Breakup of an
Oldroyd liquid bridge as a method for testing the
rheological properties of polymer solutions.
Polymer Science, Ser. A, 2001, Vol. 43, No. 7,
pp. 716-726.

56
Some References (cont)
Impulse jet breakup A. V. Bazilevskii, J. D.
Meyer, A. N. Rozhkov, Dynamics and Breakup of
Pulse Microjets of Polymeric Liquids, Fluid
Dynamics, Volume 40, Issue 3, May 2005, Pages 376
- 392 Shock Disintegration of Liquid I.A.Dukhovski
i, P.I.Kovalev, and A.N.Rozhkov. Disintegration
of Polymer Liquids at High-Speed Impact //
Polymer Science. Ser. A. 2004. V. 46. No 1. P.
31-44. Drops Rozhkov A., Prunet-Foch B.
Vignes-Adler M. Dynamics of a liquid lamella
resulting from the impact of a water drop on a
small target // Proceedings of The Royal Society.
London. Series A. 2004. V. 460. No 2049. P.
2681-2704. A. Rozhkov, B. Prunet-Foch, M.
Vignes-Adler. Dynamics and disintegration of
drops of polymeric liquids // Journal of
Non-Newtonian Fluid Mechanics. 2006. V. 134. No
1-3. P. 44-55. A.Rozhkov, B.Prunet-Foch,
M.Vignes-Adler. Impact of drops of surfactant
solutions on small targets // 7th World Congress
of Chemical Engineering.2005. CD-ROM Proceedings.
Glasgow. Great Britain, 2005 July 10-14.

57
Thank you!