Central to physical
experiments is the ability of scientists to scale natural processes
to laboratory environement. Robust scaling implies that characteristic
dimensionless ratios are the same for the model and its prototype. An analogue model is
said to be similar to its natural prototype if it is at once Geometrically,
Dynamically, and Rheologically similar.
implies that ratios between characteristic lengths in the model
and its original are the same.
means that all the forces involved remain in the same relative proportions
to each other in the model and its prototype.
is achieved when analogue materials respond to relatively low stress
(at low temperature) in the same way that rocks respond to much
higher stresses (at higher temperature).
In tectonic modelling, perfect scaling can usually not be achieved simply because our knowledge of many physical variables and therefore dimensionless ratios are within one order of magnitude. Beside scaling can be restricted to the properties relevant to a particular problem. For instance when thermally activated processes or temperature sensitive properties are of little importance scaling for temperature can be disregarded.
Scaling for Plastic flow.
Scaling for Forced (Tectonic Driven) Viscous Flow.
Scaling for Gravity Driven Viscous Flow.
Scaling for Thermal Convection.
Go to Top
range of analogue material is used in our experiments. We provides
all the details concerning our experimental procedure. In
the following, you will find information about some of the analogue
material we use.
O' Sphere (Erinbrook, Australia)
The density of this granular material is in the range 0.4 to 0.44 g.cm-3. It is a sand of hollow ceramic spheres. The sphere diametre varies from 10 to 300 mm. It is quite cheap: AU$ 40 for a bag of 25 kg. We mix it with PlasStrip and Garnet sand to obtain a granular material of suitable density. The particles are near perfect spheres which explain the rather low angle of internal friction in the range of 27º-29º.
PlasStrip also known as JetPlast (used in the building industry as sand blasting)
Its a sand of plastic particles. The density of this granular material is about .72 g.cm-3. The grain size is in the range 50 to 350 mm, the particle are rather angular. It is quite cheap: AU$ 50 for a bag of 25 kg. The angle of internal friction varies in the range of 33-40º probably due to electrostatic force.
Garnet sand (used in the building industry as sand blasting)
Its a sand of garnets. The density of this granular material is about 2.354 g.cm-3. The grain size is in the range 300 to 600 mm, the particle are rather angular. It is also cheap: AU$ 50 for a bag of 25 kg. The angle of internal friction varies in a narrow range 37º+-1.
2000 (BP Chemical)
Hyvis is a polybutene manfactured by B.P. It was provided by Honeywill
& Stein (UK) at a cost of AU$ 5800 for a 170 kg drum. This
polybutene was introduced in Uppsala by Sandy Cruden in the late eighties
and used for the first time by Koyi (1991) and then by Cruden et al.
(1995). Due to its excessive tackiness, this product is not easy
to use (actually it is bloody messy!). Our rheological tests show that
Hyvis 2000 is Newtonian and has a large variation in viscosity from
55 Pa.s at 95ºC up to 104 Pa.s at 20ºC. Its
density is 0.94 g.cm-3.
H. 1991. Mushroom diapirs penetrating overvburdens with high effective
viscosities. Geology, v. 19, p. 1229-1232. Cruden,
A., Koyi, H. & Schmeling, H. 1995. Diapiric basal entrainment of
mafic into felsic magma. Earth and Planetary Science Letters,
Go to Top
Gum (Filled PolyDiMethylSiloxane, Dow Corning)
This compound (better known as Silly Putty or Silastic compound 3179)
has a very high viscosity and a density of 1.14 g.cm-3.
It can be an interesting analogue for the stronger but ductile parts
of the lithosphere.
Gum FB (Rhodia Silicone)
This PDMS which was found by Wouter Schellart (Epsilon, Melbourne). It is easily available in Australia (via Barnett Chemical, cost AU$ 13 per kg) and it is imported from the UK. It is clear like water and its density is0.972 g.cm-3. It flows easily under its own weight (the three pictures below were taken over ~30mn), and can be easily cut with a knife.
Supplier in France: Rhodia Silicone s.a.s., 19 avenue Pompidou, F-69486 Lyon Cedex 03. Tel: (33) 04 72 13 19 00, Fax (33) 04 72 13 19 88
Manufacturing site: Rhodia Silicones s.s., 1 rue des frères Perret, F-69191 Saint Fons Cedex, Tel: (33) 04 72 73 74 75, Fax (33) 04 72 73 75 99
Go to Top
The following rheological
test shows that this PDMS is Newtonian, its viscosity varying slightly
Go to Top
Gum rosin is a by product that derives from the
distillation of natural resin extracted from several varieties of pine
tree. Cobbold and Jackson (1992) were the first to recognise that the
thermal and mechanical properties of gum rosin make it a suitable analogue
material for thermomechanical models.
Cobbold and Jackson, 1992: Gum rosin (colophony):
A suitable material for thermomechanical modelling of the lithosphere.
Tectonophysics, 210, pp. 255-271.
rosin (R3755 ) used in our experiments is supplied by Sigma-Aldricht.
The cost is approximately AU$ 2800 per 100 kg.
temperature gum rosin has a density of 1.1 g.cm-3. The density
is a strong function of temperature with a coefficient of thermal expansion
of about 3.10-4 K-1 (Cobbold and Jackson, 1992).
There is a 7% drop in density as the temperature rises from room temperature
A few rheological tests
were performed to determine the dependence of the viscosity on both
temperature and shear rate. Cobbold and Jackson have already shown
that viscosity of gum rosin varies over 5 orders of magnitude from 100
Pa.s at 80ºC to about 107 Pa.s at 40ºC. Our
results confirm this.
Go to Top
The following graph illustrates
how the viscosity of Hyvis 2000 and gum rosin varies with temperature.
At room temperature (~19ºC) the viscosity of Hyvis is 6 orders
of magnitude weaker than that of gum rosin. At 55ºC the difference
drops to 3 orders of magnitude. For a T>80ºC, Hyvis is more
viscous than gum rosin. This provides us with
an ideal couple of analogue materials to study the impact of viscosity
inversion on fabric development.
Paraffins are growingly popular amongst experimentalists. Paraffins have density in the range 0.82 - 0.86 g.cm-3 and a viscosity that decreases over 5 to 6 order of magnitude from room temperature to ~60ºC. If the conclusion of Rossetti et al., paper on the rheology of wax with Tm of 53ºC can be generalized then waxes have Newtonian viscosity for T/Tm>0.7 (Rossetti et al., 1999). The melting temperature Tm and the density can be controlled by adding mineral oil. Waxes can be easily dyed. Waxes are good analogue for both the ductile crust and the lithospheric mantle. Stay tuned we are in the process of determining the viscosity-temperature-strain rate of wax/mineral oil mixtures.
Rossetti F., Ranalli G., and Faccenna C, 1999: Rheological properties of paraffin as an analogue material for viscous crustal deformation. Journal of Structural Geology, 21, pp. 413-417.
Gel Waxes/Mineral Oil (Versagel C, Penreco US)
Contrarily to waxes that go through melting at specific temperatures, gel waxes have their viscosity that decreases as temperature increases to over 100ºC, see the example below. Gel waxes have visco-elastic rheology, they are crystal clear and can easily by dyed. Their density is about 0.86 g.cm-3 , 26180 KJ are required to rise 360 pound of gel from 15 to 100ºC, that should give a specific heat of 1710 kJ.ºC-1.kg-1)-ºF, thermal conductivity, 100ºC BTU/(hr)(sq ft)(ºF/in).
For the asthenosphere we use a mixture of water and glycerol.
Glycerol is relatively cheap and easily available. Mixed with
water it gives a fluid, the density of which can be finely tuned.
The addition of a few weight% of Natrosol (hydroxyethylcellulose) will
increase the viscosity of the water/glycerol mixture by about 7 orders
of magnitude without altering its density. Check the following
references for the use of Natrosol.
S., and C. Jaupart, 1989: Compositional convection in viscous melt.
Nature, 338, pp. 571-574.
Davaille, A., 1999: Two-layer thermal convection
in miscible viscous fluids. J. Fluid Mechanics, 379, pp. 223-253.
Go to Top