Cambridge Nov 2018

1. 1
Cambridge, November 2018
The effect of Viscosity, Yield Stress, and Surface Tension on the Deformation and
Breakup profiles of fluid filaments stretched at very high velocities.
by,
Malcolm Mackley and Simon Butler
Department of Chemical Engineering and Biotechnology, University of Cambridge
and
Rudy Valette, Elie Hachem, Mehdi Khalloufi and Anselmo Pereira
Mines ParisTech,
CEMEF - Centre for Material Forming, Sophia-Antipolis, France

2. The People
Malcolm Simon
Rudy Elie Mehdi Anselmo
2
Thierry Coupez

3. The effect of Viscosity, Yield Stress, and Surface Tension on the
Deformation and Breakup profiles of fluid filaments Stretched at very high Velocities
Newtonian Viscosity
10−4
- 103
Pas
Typically, 1- 103
mPas
Bingham Yield Stress
1 - 103 Pa
Surface Tension
20 – 500 mN/m
Extensional
Flows
𝜀 ≈ 1000 𝑠−1
1970 Twin jet PhD Bristol
Rayleigh instability
Extensional viscosity , Trouton
Capillary number, Grace
Hinch, Rallison and Leal
The Title
3

4. 4
Drive
belt
Piston
Linear
traverse
Motor
drive
a b
The Trimaster Family, 2006 - 2018
Tri Tuladhar Damien Vadillo
MPR Mk1 Trimaster MK2 Trimaster Mk3 Trimaster

5. 5
Cambridge HB4 Trimaster, 2010s
Stuart Huxley

6. 6

7. 7
Strain Rate 𝜀 = −2
1
𝐷
𝑑𝐷
𝑑𝑡
Hencky strain 𝜀 = 𝛾𝑑𝑡 = −2
𝑑𝐷
𝐷
= 2 𝑙𝑛
𝐷0
𝐷
0.00ms 0.72ms 1.83ms 2.33ms 3.11ms 4.17ms
Water based buffer solution
Hencky Strain
Normalised centre line diameter
Piston Amplitude / mm
Strain rate / 𝑠−1

8. 8
0.00 ms 1.00 ms 3.00 ms 15 ms 25 ms 45 ms
Silicone oil 492 mPas

9. CIMLIB-CFD finite element library
Parallel environment
Flow solver: Navier-Stokes
(Variational MultiScale technique)
Multiphase: Level-Set method
Surface tension: Continuum Surface
Force
Mesh: anisotropic mesh adaptation
Extended to non-linear constitutive
models
Rudy Valette, Elie Hachem, Anselmo Pererio and Mehdi Khalloufi.
CEMEF Sophia Antipolis

10. 10
Maths Stuff
𝝈𝒄
= −𝑝𝐈 + 𝝉,
𝝉 = 𝟐𝜼 𝒆 𝑫 𝒖 ,
𝜼 𝒆 = 𝜼∞ + 𝜼 𝟎 − 𝜼∞ 𝟏 + 𝝀 𝜸 𝒂
−(𝒏−𝟏)
𝒂 ,
𝜼 𝒆 = 𝒌 +
𝝉 𝟎
𝜸
𝟏 − 𝒆−𝒎 𝜸
,
Carreau-Yasuda (C-Y)
Papanastasiou regularization
𝜌
𝜕𝒖
𝜕𝑡
+ 𝒖. 𝛻𝒖 − 𝒈 = −𝛻𝑝 + 𝛻. 𝝉 + 𝒇 𝑆𝑇,
𝒇 𝑆𝑇 = −𝜎𝐾𝛿𝒏
Momentum Equation
Surface Tension
0
20
40
60
80
100
120
1 21 41 61 81 101
Stress
Strain rate
0
20
40
60
80
100
3 30 300
viscosity
Strain rate

11. 11
Water
𝜎 = 70 mN/mh = 1.0 mPas

12. 12
Silicone oil
h = 492 mPas
𝜎 = 20 mN/m

13. 13

14. 14
Surface Tension (h = 1 mPa s; 𝜏0 = 0 Pa )
𝜎 = 0 mN/m
𝜎 = 35 mN/m

15. 15
Bingham Yield Stress (h = 1.0 mPas, 𝜎 = 70 mN/m).
𝜏0 = 1 Pa
𝜏0 = 100 Pa.
𝜏0 = 1000 Pa

16. 16
(Carreau-Yasuda)
𝜂∞ = 0.3 Pa s, 𝜂0 = 6 105Pa s,
𝜆 = 2104 s, 𝑎 = 0.75, 𝑛 = 1.89,
𝜎 = 0 mN/m).
Carbopol
(ClearGlide)

17. 17
Hellmann’s Mayonnaise
(Carreau-Yasuda)
𝜂∞ = 0.3 Pa s, 𝜂0 = 13500 Pas, 𝜆 = 115 s,
𝑎 = 1, 𝑛 = 1.93, 𝜎 =300mN/m.
Bingham:
k = 0,001 Pa s, 𝜏0 = 140 Pa,
𝜎 = 300 mN/m.

18. 18
C-Y: 𝜂∞ = 0.3 Pas,
𝜂0 = 107
Pas, 𝜆 = 105
s,
𝑎 = 1, 𝑛 = 1.85, 𝜎 = 0 mN/m
Bingham: k = 1 mPa s,
𝜏0 = 500 Pa, 𝜎 = 0 mN/m.
Whipped Cream

19. 19
Conclusions
• The HB4 fast filament stretching apparatus is an apparatus that generates
high precision stretch and breakup data.
• The CEMEF solver is a high precision simulation that can capture
HB4 behaviour for different fluids.
• Solver validated against high and low viscosity Newtonian fluids.
• The effect of surface tension and yield stress has been systematically
explored using the solver.
• The effect of surface tension on droplet formation has been demonstrated.
• Solver matched with experimental behaviour for certain yield stress fluids.

20. “This could be the last time, this could be the last time,
maybe the last time, I don’t know.”
(Is this MRM’s last ever CEB presentation 2018?)