13
13
Honey Coils
13
13 Honey Coils
A thin, downward flow
of viscous liquid, such as
honey, often turns itself
into circular coils.
Study and explain this
phenomenon.
2
13
3
13
Inception Dynamics
liquid with low viscosity
4
13
Inception Dynamics
pressure
liquid with high viscosity
shear stress
5
13
Inception Dynamics
thin stream
+
small disruption
flow bending
pressure
liquid with high viscosity
6
13
Partial Analogy
honey
viscous forces
(inner friction)
elastic rope
elastic
forces
77
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
8
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
9
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
10
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
11
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
12
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 = 0.085 Pa s
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
(100 × that of water)
values at 22o C
non-newtonian liquid newtonian liquid
13
13
High Viscosity is Necessary
glycerine soap
glycerol
shampoo
acacia honey
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
linear
oscillation
𝜂 = 0.085 Pa s
(100 × that of water)
values at 22o C
𝜂 = 1.2 Pa s
non-newtonian liquid newtonian liquid
14
13
High Viscosity is Necessary
glycerine soap
glycerol
linear
oscillation
𝜂 = 0.085 Pa s
(100 × that of water)
values at 22o C
𝜂 = 1.2 Pa s
shampoo
acacia honey
circular spirals
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
non-newtonian liquid newtonian liquid
15
13
High Viscosity is Necessary
glycerine soap
glycerol
linear
oscillation
shampoo
acacia honey
circular spirals
to start the bending
viscosity ≥ 1 Pa s
𝜂 = 0.085 Pa s
(100 × that of water)
values at 22o C
𝜂 = 1.2 Pa s
𝜂 ≤ 19 Pa s
𝜂 = 17.6 Pa s
non-newtonian liquid newtonian liquid
16
13
Why Did the Other Liquids Fail?
• viscosity problem
– low viscosity = low shear stress
water, glycerin soap, olive oil, motor oils, syrup
– could be solved by greater fall height
surface tension issue
(Plateau-Raileygh
instability:
stream turns into
drops)
but
17
13
Why Did the Other Liquids Fail?
• viscosity problem
– low viscosity = low shear stress
water, glycerin soap, olive oil, motor oils, syrup
– could be solved by greater fall height
surface tension issue
(Plateau-Raileygh
instability:
stream turns into
drops)
but
18
13
EXPERIMENTS
19
13
Parameters
height of fall
viscosity
20
13
Height
gravity
flow velocity rises
r0
continuity
𝑆𝑣 = const.
h
flow becomes thinner
r(h )
21
13
max spiral height [cm]
Coil Height vs. Height of Fall
acacia honey
𝜂 = 17.6 Pa s
𝜌 = 1410 kg m−3
2
1,5
1
0,5
0
0
𝑄 = 0.045 ml s −1
𝑟0 = 1 ml
10
20
30
40
50
fall height [cm]
22
13
Coiling Frequency vs. Height of Fall
180
160
frequency [Hz]
140
acacia honey
𝜂 = 17.6 Pa s
𝜌 = 1410 kg m−3
120
100
80
60
40
20
0
0
𝑄 = 0.045 ml s −1
𝑟0 = 1 ml
10
20
30
40
fall height [cm]
23
13
Viscosity
• must be high enough (> 1 Pa s)
• greater viscosity
-
• coiling frequency decreases with increasing
viscosity
24
13
Coiling Frequency vs. Viscosity
35
frequency [Hz]
30
25
insufficient
viscosity
20
15
10
5
0
35
h = 10 cm
30
25
20
←temperature← [ C]
→viscosity→
15
10
25
13
NOT ALL COILING IS THE SAME
different regimes of coiling
26
13
Regimes Results of Ribe et.al.
[Ribe et.al., 2006, Dynamics of liquid rope coiling, Physical
Review E 74]
• different regimes found
• affected by height of fall (velocity)
• determined by relative importance of forces
1. viscous
2. gravitational
• gravitational-inertial (transition)
3. inertial
27
13
dimensionless frequency
Physical Review E 74 (2006) Ribe et.al., Dynamics of liquid rope coiling
dimensionless height of fall
28
13
Viscous Regime
•
•
•
•
very low height of fall
viscous force dominant
coiling driven by fluid extrusion
very hard to observe
29
13
Gravitational Regime
• height of fall up to 9 cm
• gravitational force
dominant
• slow & stable coiling
• very predictable
30
13
Inertial Regime
• heights ≫ 10 cm
• inertial forces
dominant
• highest coiling
frequencies, unstable
31
13
Gravitational-Inertial Regime
• transition - between gravitational and inertial
regime (height 9 to 10 cm in our case)
• both forces are relevant
• frequency: discrete
mathematic pendulum) resonant frequency
• 8-like pattern
• history
(hysteresis)
32
13
stable gravitationalinertial regime
slightly moving down
non-stable state
33
13
Coiling Frequency vs. Height of Fall
180
coiling frequency [Hz]
160
140
acacia honey
𝜂 = 17.6 Pa s
𝜌 = 1410 kg m−3
120
100
80
60
40
20
0
0
𝑄 = 0.045 ml s −1
𝑟0 = 1 ml
10
20
30
40
fall height [cm]
34
13
Coiling Frequency vs. Height of Fall
coiling frequency [Hz]
160
140
acacia honey
𝜂 = 17.6 Pa s
𝜌 = 1410 kg m−3
coiling frequency [Hz]
180
120
100
80
60
40
transition
20
gravitational
15
10
5
0
2,5
20
6,5
8,5
fall height [cm]
0
0
𝑄 = 0.045 ml s −1
𝑟0 = 1 ml
4,5
10
20
30
40
fall height [cm]
35
13
acacia honey
𝜂 = 17.6 Pa s
𝜌 = 1410 kg m−3
1,5
1
0,5
0
0
𝑄 = 0.045 ml s −1
𝑟0 = 1 ml
inertial
transition
2
gravitational
max spiral height [cm]
Coil Height vs. Height of Fall
10
20
30
40
50
fall height [cm]
36
13
Coiling Frequency vs. Viscosity
transition
35
25
gravitational
insufficient
viscosity
20
15
10
inertial
frequency [Hz]
30
5
0
35
h = 10 cm
30
25
20
←temperature← [ C]
→viscosity→
15
10
37
13
FURTHER OBSERVATIONS
38
Inertial Regime:
Stable Position
13
ℎ ≈ 10 cm
honey flowing in
honey flowing out
39
13
Inertial Regime:
ℎ ≈ 10 cm
Spiral height [cm]
Stable Position
1,5
1
0,5
0
0
0,2
0,4
0,6
0,8
1
1,2
Time [s] - 0s = 20 seconds after beginning
40
Inertial Regime:
Buckling
13
ℎ ≈ 12 cm
disturbance
instability
41
13
Inertial Regime:
ℎ ≈ 12 cm
Buckling
low fall heights
bigger fall height
unstable
stable
𝑡 =0s
disruption
o effect
𝑡 = 0.1 s
𝑡 = 0.2 s
𝑡 = 0.3 s
disruption
42
Inertial Regime:
Periodic Falling
13
ℎ > 20 cm
max height
honey flowing in
coil falls
coil height
honey flowing out
43
13
Inertial Regime:
ℎ > 20 cm
Periodic Falling
rise
height of spirals [cm]
2
fall
1,5
1
0,5
0
0
0,5
1
1,5
time [s]
44
13
Inertial Regime:
ℎ > 20 cm
Periodic Falling
5x slower
4,5
fall frequency [Hz]
4
3,5
3
2,5
2
1,5
1
0,5
0
0
2
4
6
time [s]
8
45
10
Inertial Regime:
Coilception
13
ℎ ≫ 20 cm
46
13
Inertial Regime:
ℎ ≫ 20 cm
Coilception
inertial regime
spirals as a
new source
viscous
regime
47
13
Thank
you for your attention!
Conclusion
• dynamics of creation shown
• viscous forces qualitatively equivalent to
elasticity
• influence of relevant parameters:
f
f
h
←T←
– height
– viscosity
• different regimes
1.
2.
•
3.
viscous
gravitational
gravitational-inertial (transition)
inertial
+ additional effects shown
48
13
APPENDICES
13
What does the viscosity look like?
25
Viscosity [Pas]
20
15
Shampoo
Acacia Honey
10
5
0
0
5
10
Shear rate [s-1]
15
13
Viscoelasticity
The fluid can have „memory“
„Die Swell“ effect
Thin tube-contraction
13
Die Swell?
Shampoo
Agate honey
Circular spirals
Glycerol
Just
bending
13
Shampoo
• No observed viscous regime
• Similar behavior
• Without inertial regimes
Kaye effect
13
Bubbles-on the way to the Kaye effect
Air-necessary for the Kaye effect
Ann. Rev. of Fluid Mechanics, N. M. Ribe, M. Habibi, and D.Bonn
Liquid Rope Coiling
13
Tube viscometer
Rabinowitsch–Mooney equation
piston
We change
Q
We observe
p
d
Method from
l
R. Bragg, F. A. Holland; Fluid Flow for Chemical Engineers
Measuring viscosity
13
13
Measuring rheology-theory
Shear stress on the wall– stabilized flow
Q
p
 wall 
d p
( )
4 l
Pressure
change
d
Volumetric flow rate
2
Q   dQ   2xvh dx
d
l
0
Velocity profile
Integrating per partes
x
dQ  2xv
dx
d h
vhorizontal
d
2
d
2
 x 2 vh 
x 2  dvh 
0 2xvh dx  2  2   2 0 2   dx dx
0
2
Velocity gradient
0 – Stabilized flow– No „Slipping“)
Method from
R. Bragg, F. A. Holland; Fluid Flow for Chemical Engineers
13
Measuring rheology
Volumetric flow rate
d
2
Q    x   dx
2
0
Gradually editing
d
2
 wall
For the flow in the tube
 x 2x

 wall d
d

x
flow
Z R. Bragg, F. A. Holland; Fluid Flow for Chemical Engineers
d3
Q   3   2   d
8 wall 0
Differentiating relative to  and editing

 32Q  
d ln 3  

32Q  3 1

d 

wall   3 
d  4 4 d ln  wall 




Rabinowitsch–Mooney equation
 wall
d p
 ( )
4 l
13
Measuring rheology-Agate honey
0,2
Rabinowitsch–Mooney equation
Steady flow
 wall
0,5
1
1,5
2
2,5
3
-0,4
Ln(ζ)

-0,2 0
-0,6
-0,8
-1
-1,2
-1,4
d p
 ( )
4 l
 32Q 
d ln 3 
 d   0,7292
d ln  wall
 wall
1


 17,6 Pas
wall 0,052
-1,6
-1,8
Velocity Gradient[s-1]
wall

 32Q  
d ln 3  

32Q 3 1
 d  
 3  
d  4 4 d ln  wall 




y = 0,7292x - 2,1295
0
1
0,9
y=
0,8
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0
Ln(τwall)
0,052x + 0,0568
0
5
10
Shear Stress[Pa]
15
20
13
Measuring rheology-Shampoo
3
Rabinowitsch–Mooney equation

Ln(ζ)
1,5
1
0,5
0
-0,5 0
0,5
1
1,5
2
2,5
3
3,5
-1
-1,5
Stabilized flow
 wall
d p
 ( )
4 l
 32Q 
d ln 3 
 d   2,39
d ln  wall
Viscosity largest in the beginning
biggest
2
 wall

 19,6 Pas
wall
-2
-2,5
Ln(τwall)
Velocity gradient [s-1]
wall

 32Q  
d ln 3  

32Q 3 1
 d  
 3  
d  4 4 d ln  wall 




y = 2,3949x - 5,222
2,5
16
14
12
10
8
6
4
2
0
0
5
10
15
20
Shear Stress[Pa]
25
30
13
Why is it the shape stable?
View from top
v( x )  x

corotating frame of
reference
M viscous
Fviscous→ longitudal
Fviscous
Due to Rayleigh-Stokes analogy[1]
x
Qualitatively
the same
M inertial
behavior as in
Elastic ropes

dAof(Centrifugal,
0  Fnet
 Torques
Coriolis)
 rdA  0  M
viscous
Proved in L. Mahadevan,
Equlibrium
William
S. Ryuimplies
and
Aravinthan D.T. Samuel Fluid
rope trick investigated.
Nature, Volume 392 Number
6672.1998

M  0
[1] Love. A Treatise on Mathematical Theory of Elasticity. Dover 1944
61