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The Rope Coil Effect
by Jakub Wolf
Table of Contents:
Plagiarism Pledge.....................................................................................i
Abstract.................................................................................................ii
Zusammenfassung..................................................................................iii
Acknowledgements.................................................................................iv
1. Introduction........................................................................................1
2. Problem/Aim.......................................................................................4
3. Hypothesis.........................................................................................4
4. Method..............................................................................................5
5. Results...............................................................................................7
6. Discussion of Results..........................................................................15
7. Discussion – Errors and modifications...................................................18
8. Conclusion........................................................................................19
9. References........................................................................................20
Abstract:
It has been known, that when a viscous liquid such as honey is dropped onto a flat
surface or a pool of the same substance, circular coils form. This experiment investigates
how the coils change, when the height is increased. The range of heights went from
directly above the surface of the honey to 27cm above it. The coils were produced by
dipping a honey dipper into a jar of honey and pulling it out into a stationary position at the
correct height. The results showed four different types of coils at four groups of heights for
this particular substance. Furthermore, the time for the honey stream to be interrupted for
the first time was measured for all heights and the results show, that overall it decreases
steadily. At relatively low heights, coils do not form and the time of flow is rather long.
However, when the coils start forming for the first time, the time of flow decreases
drastically.
Zusammenfassung:
Es ist bekannt, dass eine Viskose (geringe Fließfähigkeit) Flüssigkeit, wie etwa
Honig, Spulen bildet wenn es von einer gewissen Höhe herabgelassen wird. In diesem
Experiment, wird untersucht wie sich die Spulen ändern, wenn die Höhe vergrößert wird.
Außerdem wird gemessen, wie lange es dauert bis der Fluss des Honigs zum ersten Mal
unterbrochen wird. Die Resultate wurden durch eintauchen eines Honiglöffels in ein Glas
Honig und das nachträgliche herausziehen und fixieren dieses Löffels erzielt. Die
Ergebnisse zeigen, dass es an vier verschiedenen Höhegruppen, vier verschiedene Spul
typen gibt. Die Zeitmessungen des Honigflusses zeigen, dass sich die Zeit mit der Höhe
einigermaßen gleichmäßig verringert. Am Anfang dauert dies recht lang, weil sich bei
niedrigen Höhen noch keine Spulen formen, aber wenn diese beginnen, nimmt die Zeit
des Honigflusses drastisch ab.
Acknowledgements:
I would like to thank my father Maciej Wolf, for helping me perform the experiment
(specifically for starting the timer). Furthermore I would like to thank my mother Grazyna
RuminWolf.
1. Introduction:
There are many different types of liquids and they all behave differently. Viscous
liquids are characterized by having a resistance to flow, which means they flow slower than
water or such substances.
Viscous liquids are also categorized into Newtonian and nonNewtonian liquids.
“These are so called Newtonian fluids, named after the famous mathematician and
physicist Sir Isaac Newton. One of the things that make water and air Newtonian fluids is
that, unless the temperature or the pressure changes, they maintain a constant viscosity
the measure of the fluid's resistance to flow. Newtonian fluids, for example, don't change
their viscosity when under stress (when a force is applied to them) (u.A. September 13,
2011).”
“A stream of viscous fluid falling from a sufficient height onto a surface forms a
series of regular coils (N. M. Ribe 2004).”
“Fluid coiling has been studied extensively in the laboratory for nearly 50 years
(Barnes & Woodcock 1958; Barnes & MacKen zie 1959; Cruickshank 1980; Cruickshank
& Munson 1981; Huppert 1986; Griffiths & Turner 1988; Mahadevan et al. 1998). However,
its mechanism remains incom
pletely understood. The first important theoretical advance was Taylor’s recognition that
fluid buckling requires a longitudinal compressive stress, like the buckling of an elastic
column under a load (Taylor 1968). Subsequently, the critical fall height and frequency at
the onset of coiling were determined using linear stability analy
sis (Cruickshank 1988; Tchavdarov et al. 1993). Most recently, Mahadevan et al. (1998,
2000) proposed a scaling law for inertiadominated coiling that agreed well with
experimental measurements in the highfrequency limit.
In summary, current theoretical understanding of fluid coiling is limited to the extremes of
very low (incipient coiling) and very high (inertial coiling) frequencies (N. M. Ribe 2004).”
“If the stream is moving faster than the fluid can enter the pool, the stream begins to
slow down and to widen a short distance above the pool. Each particle of fluid passing
through the narrowest section of the stream must slow down. The force responsible for the
slowing is stress in the part of the stream just below the narrowest section. Stress is the
force per unit area of a cross section through the stream. It is greatest at the narrowest
section because the area is smallest there. If the stream is sufficiently narrow, the stress
causes the stream to buckle to one side.
The deflected stream also further buckles in a direction that will initiate a circular motion
around the central axis of the stream. Coiling begins. More fluid enters the buckled region,
waiting its turn to enter the pool, and the stream moves in a circle around the central axis
(Jearl Walker 1981).”
“There are three regimes in liquid rope coiling. Each regime involves an interplay
between viscous, gravitational, and inertial forces [40]. Viscous coil ing occurs when
gravitational and inertial forces are negligible. [...]
Gravitational coiling occurs when a balance between viscous forces and
gravitational forces exists, and the liquid’s inertia is negligible. [...]
Finally, inertial coiling occurs when a balance between the liquid stream’s inertial
forces are balanced by viscous forces (in the form of shear along the coil), and gravity is
negligible (Matthew Evan Thrasher 2005).”
There is a fourth regime, which occurs in height between the gravitational and the
inertial regimes. “A complex inertiogravitational regime (IG) is observed in which viscous,
gravitational, and inertial forces are all significant (N. M. Ribe et al. 2006).”
The goal of this project is to find out which types of coil form at which heights and
also further explain how these coils come about. This will be achieved, by reproducing the
effect with an experiment. Honey will be dropped from a honey dipper into a pool of the
same substance. This will be done from different heights. From the moment the honey
dipper leaves the pool, the time until the flowing stream of honey is interrupted for the first
time will be measured. The results will be used to explain the different coiling regimes
more precisely.
2. Problem / Aim:
When a viscous liquid (a fluid, which is resistant to flow), such as honey, is dropped
from a certain height into a pool of the same liquid, circular coils form above the surface.
However, when the height is varied, the coils differ. The goal of this experiment, is to
investigate why the liquid produces coils and also explain why they vary when the liquid is
dropped from different heights.
3. Hypothesis:
I think, the coils form, because there are opposing forces acting on each other. The
downward force is gravity. The upward force, is the fact that the honey is so viscous that
the jet flowing into the jar isn't absorbed fast enough and slows down and the honey builds
up. The two forces push against each other and the structure becomes unstable and falls
over and the coils form. This process repeats until a tower of coils emerges. The different
types of coils are due to the height difference. The higher it is dropped from, the faster the
jet is, and the faster the frequency of the coils (which is also affected by the thickness of
the jet of honey – the thicker the slower the coils).
The variables, which affect the type of coil are the height, the honey is being
dropped from, as well as the temperature of the honey. Furthermore the shape of the
stream (whether flat or circular) and the surface it is falling on.
4. Method:
The first thing that was done, was building a structure which would make the coiling
of the honey regular. Had there been no structure, the shaking of the hand would have
made the coils uneven and not fall on one another.
The model was made from a 58 cm long wooden stick standing on a circular
wooden base. Along the stick were marks to exactly show the height, the honey was going
to be dropped from. The instrument used to drop the substance was a wooden honey
dipper attached to a metal hook. The hook was used to connect the wooden stick to the
honey dipper and the round end of the hook was used to slide the dipper up and down the
stick. Under it, was a glass filled almost to the top with honey. (see Fig. 1)
(Figure 1: Structure built, to enhance stability of honey coiling. It's made of a wooden stick, a wooden round
base, a metal hook, a wooden honey dipper and a glass which would later contain the honey.)
At first the coiling was tested a few times without noting any results, to check whether it
worked. Then the experiment was started. The range of the heights, which were going to
be used as results was 127 cm between the surface of the honey and the bottom of the
honey dipper. The results in between were recorded in spaces of 1 cm. From the moment
the honey dipper left the coil, a timer was started and it measured the time until the flow of
viscous honey was interrupted for the first time. This was done for every cm in the range
from 1 to 27 cm above the surface of the honey in the glass.
5. Results:
The results of this experiment are shown in a table as well as in photos for each individual
height.
Table1: 'Height of honey dipper' vs. 'Time of flow': (results ± 5s; ± 0.5 cm)
Chart1: 'Height of honey dipper' vs. 'Time of flow': (results ± 5s; ± 0.5 cm)
Tim
e o
f flo
w [
s]:
Height of honey dipper [cm]:
1 2502 2453 1404 1285 1216 1247 1198 1059 105
10 9211 7912 7313 7114 6915 7016 5817 5618 5219 5120 5221 4922 4823 4524 4525 4026 3927 40
Height of honey dipper [ cm ] : Tim e of f low [ s] :
1 2 3 4 5 6 7 8 9 1011121314151617181920212223242526270
50
100
150
200
250
300
Pictures of coils forming on heights in the range 127 cm above surface of honey:
(Figure 2: Height of honey (Figure 3: Height of honey dipper was 2 cm.)
dipper was 1 cm.)
(Figure 4: Height of honey dipper (Figure 5: Height of honey dipper was 4 cm.)
was 3 cm.)
(Figure 6: Height of honey dipper (Figure 7: Height of honey dipper was
was 5 cm.) 6 cm.)
(Figure 8: Height of honey dipper (Figure 9: Height of honey dipper was 8 cm.)
was 7 cm.)
(Figure 10: Height of honey dipper (Figure 11: Height of honey dipper
was 9 cm.) was 10 cm.)
(Figure 12: Height of honey dipper (Figure 13: Height of honey dipper
was 11 cm.) was 12 cm.)
(Figure 14: Height of honey (Figure 15: Height of honey dipper
dipper was 13 cm.) was 14 cm.)
(Figure 16: Height of honey dipper (Figure 17: Height of honey dipper
was 15 cm.) was 16 cm.)
(Figure 18: Height of honey (Figure 19: Height of honey dipper
dipper was 17 cm.) was 18 cm.)
(Figure 20: Height of honey dipper (Figure 21: Height of honey dipper
was 19 cm.) was 20 cm.)
(Figure 22: Height of honey dipper (Figure 23: Height of honey dipper
was 21 cm.) was 22 cm.)
(Figure 24: Height of honey dipper (Figure 25: Height of honey dipper
was 23 cm.) was 24 cm.)
(Figure 26: Height of honey dipper (Figure 27: Height of honey dipper
was 25 cm.) was 26 cm.)
(Figure 28: Height of honey dipper was
27 cm.)
6. Discussion of Results:
There are four different coiling regimes: viscous coiling, gravitational coiling, inertio
gravitational coiling and inertial coiling.
The first two results (1cm > 250s; 2 cm > 245s), as seen on figures 2 and 3, have
a speed so low, that they don't form coils. The honey flows into the jar slowly, and the rate
of absorption is faster than the incoming jet so the honey doesn't have to get out of the way
of itself and is absorbed easily.
The next four results (3 cm > 140s; 4cm > 128s; 5cm > 121s; 6cm > 124s), as
seen in Figures 47, form a thick jet. Here the production of coils begins. The coiling of the
honey is very slow and the jet stays very thick, even in the coils. This regime is called
'viscous coiling'. It occurs only in very low heights. “The simplest case (‘viscous’ coiling)
occurs when gravity and inertia are both negligible and the net viscous force acting on any
element of fluid is zero. Coiling is here driven entirely by the injection of the fluid, like
toothpaste squeezed from a tube. Because the jet deforms by bending and twisting with
negligible stretching, its radius is nearly constant (N. M. Ribe 2004).” This also means, that
the coiling frequency will be very low, because there is very little acceleration, since gravity
all the forces acting on the jet are very small. Compared to the first two results, the time of
flow decreases drastically. This is because at this specific height, the balance of the three
forces shifts.
The following ten results (7cm > 119s; 8cm > 105s; 9cm > 105s; 10cm > 92s;
11cm > 79s; 12cm > 73s; 13cm > 71s; 14cm > 69s; 15cm > 70s; 16cm > 58s), as seen
in figures 817, form a thinner and faster jet. This regime is called gravitational coiling. Here
the force of gravity is stronger and the tail of honey begins stretching and the coiling occurs
faster but not as high. “A second mode, ‘gravitational’ coiling, occurs when viscous forces
are balanced by gravity. The jet now comprises a long tapering tail and a coil that occupies
only a small portion of the total height H (N. M. Ribe).” One can see in chart 1, that the time
of flow of the honey, decreases the most (the gradient is the highest of all the regimes)
during this coiling regime.
In theory, the next regime which should occur in the following heights, would be the
inertial coiling regime. However there is an occurrence in between the last two regimes. It
is called inertiogravitational regime. In the “complex inertiogravitational regime (IG) [...]
viscous, gravitational, and inertial forces are all significant (N. M. Ribe et al. 2006).” This
phenomenon occurred during the next six results (17cm > 56s; 18cm > 52s; 19cm > 51s;
20cm > 52s; 21cm > 49s; 22cm > 48s), as seen in Figures 1823. The shapes which
result in this regime are not the regular circular coils, which occur in the other regimes, but
rather a series of uneven patterns with various frequencies. This phenomenon cannot be
explained as of right now.
The final five results (23cm > 45s; 24 cm > 45cm; 25cm > 40s;
26cm > 39s; 27cm > 40s), as seen in Figures 2428, is the inertial coiling regime. “A third
mode, ‘inertial’ coiling, occurs when viscous forces in the coil are balanced by inertia [...]
The scaling laws for inertial coiling [...] were first proposed by Mahadevan et al. (2000).
The physical reason for the larger role of inertia in the coil is that, for a given strain rate,
the viscous forces within a thin filament deformed by bending are much smaller than in one
deformed by stretching (N. M. Ribe 2004).” In this type, the frequency of the coils is very
fast and the coils are also very small because of the height and hence the increase in
gravity.
7. Discussion – Errors and Modifications:
This experiment, like every other experiment, had its faults, some of which could
have been resolved had there been more time.
The first error, which might have altered the results slightly, was the lamp shining
onto the honey while the experiment was being performed. It might have increased the
temperature of the honey, which would have made it less viscous and therefore prone to
flow more freely and faster.
Another modification, which could have been included, had there been better
equipment, was to let the honey fall out of a container with a hole at the bottom so that the
flow rate was controlled. In this experiment, the flow rate was at times faster and at times
slower, because the honey dipper 'stored' some honey and released it at certain times,
when the honey was flowing.
8. Conclusion:
In conclusion, the honey coiling effect is yet to be fully understood. From the
experiment, one can observe, that the coiling of honey starts at a height of 3cm. This type
of coiling is called viscous coiling. The range of this regime is 3cm – 6cm in height. The
next type is the gravitational coiling regime, which occurs here in a range from 7 cm – 16
cm in height and is the most commonly observed type of coiling. The following type, is the
inertiogravitational regime which occurs in this experiment in a range from 17 cm – 22 cm
in height.
The last regime is the inertial coiling and it occurs in a range from 23 cm – 27cm in height
in this experiment.
The coils themselves form, because the viscosity of the honey doesn't allow the jar of
honey to absorb it fast enough and it builds up. At the same time more honey keeps
flowing onto that build up and the structure loses balance. It falls over and the first coils
form.
9. References:
http://iypt.org/Tournaments/Taipei#Problems (08.01.13)
N. M. Ribe. 2004. Coiling of viscous jets. Proceedings of the Royal Society London A
460. 3223 – 3239. (http://rspa.royalsocietypublishing.org/content/460/2051/3223.full.pdf
(08.01.13))
N. M. Ribe, M. Habibi and Daniel Bonn. July 18, 2006. Physics of fluids 18. 268279.
(http://hal.archivesouvertes.fr/docs/00/12/93/93/PDF/ribeetal_text.pdf (08.01.13))
N. M. Ribe, H. E. Huppert, M. A. Hallworth, M. Habibi and Daniel Bonn. 2006. Multiple
coexisting states of liquid rope coiling. J. Fluid Mech, vol. 555, p. 275279.
(http://www.itg.cam.ac.uk/people/heh/Paper194.pdf (08.01.13))
Carmel Dudley. May 2, 2010. Viscous coiling. (http://web.mit.edu/rnk/Public/carmel.pdf
(08.01.13))
Brendan Fry, Luke McGuire and Aalok Shah. December 10, 2008. An experimental study
of frequency regimes of honey coiling. (http://math.arizona.edu/~bfry/2008%20Honey
%20Coiling%20Team%20-%20Final%20Draft.pdf (08.01.13))
Stephen W. Morris, Jonathan H. P. Dawes, Neil M. Ribe and John R. Lister. May 21,
2008. The meandering instability of a viscous thread.
(http://www.physics.utoronto.ca/~nonlin/preprints/MDRL_07.pdf (08.01.13))
Tao Han, Darrel H. Reneker and Alexander L. Yarin. August 8, 2007. Buckling of jets in
electrospinning. Polymer 48. 60646076. (http://144.206.159.178/ft/862/592273/12186788.pdf
(08.01.13))
http://physics.info/viscosity/ (18.12.12)
http://www2.stetson.edu/~wgrubbs/datadriven/viscosity/viscositywtg.html (18.12.12)
http://www.diracdelta.co.uk/science/source/k/i/kinematic%20viscosity/source.html
(18.12.12)
http://www.doobybrain.com/2012/06/05/liquidropecoileffectmadewithhoney/ (video)
(08.01.13)
http://www.researchequipment.com/viscosity%20chart.html (08.01.13)
– http://www.mathscareers.org.uk/viewItem.cfm?cit_id=383223 (08.01.13)
