INTRODUCTION
ANALOGUE MODELS
Scaling Principle
Analogue Material
Cobbold's Information Sheets on Silicone
Deformation Rigs
NUMERICAL MODELS
Fastflo
Ellipsis


Last Update 11-06-04

INTRODUCTION


Although often technically challenging physical modelling offers a very elegant way to investigate 3D physical processes.   In many respects it is complementary to 2D numerical modelling.
Physical modelling is visually appealing, being able to see in a few minutes a process that may take millions of year makes a real difference when it comes to teaching and communicating sciences to the public.

is an experimental laboratory designed to explore, via physical modelling, lithospheric processes.  It is partly funded from Australian Research Council through a Large Grant research project on the role of gravity in lithospheric deformation.  It was established early 2001 at The University of Sydney.

The laboratory is located in rooms 102A and 102B on the ground floor of the Edgeworth Building (F05).  Requests, questions and comments can be directed addressed to Patrice Rey.

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ANALOGUE MODELS

Scaling Principle

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.

  • Geometrical similarity implies that ratios between characteristic lengths in the model and its original are the same.
  • Dynamical similarity means that all the forces involved remain in the same relative proportions to each other in the model and its prototype.
  • Rheological similarity 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.

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    Analogue Material

    A 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.
     

    POZ 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. 

     

    Hyvis 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.

    Koyi, 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, 131, 321-340.

     

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    Silastic 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.

     

    Rhodorsil 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


     

     

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    The following rheological test shows that this PDMS is Newtonian, its viscosity varying slightly with temperature.

     


     

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    Gum Rosin
    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.

    The gum rosin (R3755 ) used in our experiments is supplied by Sigma-Aldricht.  The cost is approximately AU$ 2800 per 100 kg.

    At room 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 to 100C.

    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.

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    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.

    Wax/Mineral Oil
    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).


    Water/Glycerol
    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.

    Tait, 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.


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    Deformation Rigs

     
    Side push
    Basal traction (front view)
    Basal traction (side view)

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