“Thermal convection in complex fluids: from laboratory to mantle dynamics”
– Orsay, 12-16 Sepetember 2016 –
The last CREEP short course took place at FAST lab ((Fluides, Automatique et Systèmes Thermiques, CNRS/Univ.P-Sud) in Orsay (FR). For 4 days A. Davaille and N. Ribe (from FAST) and F. Funiciello and V. Acocella (together with different members of the LET lab of the University Roma Tre) led us deep in the earth’s mantle, sketching a compelling picture on the complex dynamics of it. The course was mostly focused on one question: how can we reproduce geodynamic processes arising from mantle dynamics in the lab?
Fig.1 Professor Ribe is showing the metal bars in a viscous fluid with laminar flow
Setting the scene
As a first step, it is useful to highlight the common characteristics of mantle flows: very low Reynolds number (<<1) and high Péclet number (>>1). The first of these dimensionless parameters states that momentum across the flow is transported only by diffusion (i.e. Stokes approximation for momentum balance), while the second one states that heat transport is mostly accommodated by advection in the mantle, while heat diffusion is always negligible. This is a direct consequence of the low thermal diffusivity which characterizes typical mantle flows (e.g. ).
These assumptions represent the starting point for building a consistent model problem of the geophysical flow we wish to describe with our experiment (e.g. subduction of dense lithosphere, hot plumes rising to the surface etc.). Once such a model is properly derived for the phenomenon of interest, the next step is to understand how to solve it.
The idea we posed at the beginning is to build a physical analog of our model problem in the laboratory and let the nature do the solving. But how can we, on a laboratory scale, simulate the movement of tectonic plates, for example, that are thousands of kilometers long and flow over geological time? The principle of dynamical similarity helps us overcoming this issue.
Such a concept is a direct consequence of the Buckingham π theorem and dimensional analysis. What dynamical similarity states is that two physical systems behave similarly if they have the same values of all the dimensionless groups that describe them. Hence, if a laboratory experiment is properly scaled so that dynamical similarity is fulfilled, we can be sure that our results will resemble what is actually happening in totally different scales as the ones characterizing geodynamic phenomena.
Methods for data collection and analysis
Finding the perfect material
When doing lab experiments, things like geometry and duration of the experiment are properly scaled to the natural case, following the similarity criteria described above. However, we also need to find the right material for doing the experiments; a material which shows similar behaviour as the natural example under the conditions of the experimental setup. The earth’s mantle for example, behaves in a viscous way because the rocks are under specific temperature and pressure conditions. Since these conditions cannot be reproduced in the lab experiments, it is necessary to find a material which has these same viscous properties as the rocks in the mantle. Using a rheometer, one can measure the elastic and viscous components of a material, which basically describes how solid or liquid a material is. In this way the behaviour of various materials can be explored, in the search for a material suitable for the experiments.
These elastic and viscous components can be described by using the storage and loss moduli, respectively. The storage modulus, G’, indicates how much energy can be stored by the material when a certain strain is applied, while the loss modulus, G”, indicates the energy which is lost as heat. The relationship between these moduli at various strains, but also their evolution over time, tells us a lot about the behaviour of a material. Most materials are viscoelastic, which means they have both a viscous and elastic component. Two end-member cases are the Newtonian fluids (e.g. water or olive oil), which behave in a purely viscous way and Hookean Solids (e.g. iron at room temperature), which behave linear-elastic. Within a rheometer, a material can be subjected to very tiny oscillatory movements. The resistance of the material to these movements is measured. Both the amplitude and the frequency of these oscillations can be changed, in order to study the behaviour of the material with different amounts of strain and deformation rates, respectively. Also the effect of temperature and time can be tested using the rheometer. Therefore, measuring the viscous and elastic portion of a material using a rheometer is a very important aspect of finding the right material for your analogue model.
Recording the experiment
Analogue experiments can be really entertaining to watch, but to use them for scientific purpose, it is extremely important to record them properly. Due to all the technological developments of the past decades, it is now possible to record experiments in high detail, using various techniques. Apart of the recording of the images by means the traditional camera and video camera, we explored during the course the ‘Particle Image Velocimetry (PIV)’ technique. This technique consists in comparing the images of the particles obtained in different times in order to get the velocity field. We apply such technique by using the PIVlab Open-source software, that does not only calculate the velocity distribution within images, but can also be used to derive, display and export multiple parameters of the flow pattern, and to do the analysis and post-processing of the data in a fast and efficient way.
Fig. 2 Example of analyzing a series of images by using PIVlab
Let’s get dirty: examples of lab experiments
Fig.3 Experimental model of plumes
Fig.4 Experimental model of convection
Fig.5 Experimental model of dike propagation
Fig.6 Experimental model of subduction
In summary, we received excellent lectures by the experts during the CREEP short course 4. From a mathematical explanation about dimensional and scaling analysis, and how to apply it to the Stokes Equations governing the creeping motion, we understood the theory of how to translate a real model to laboratory. From lectures about rheology and the rheometer we learned how to study the properties of materials and how to choose the appropriate ones to do the experiments. In addition, lessons about thermal convection, subduction processes and volcano tectonics, together with learning different tools to control and analyse the experimental results (camera, video, PIVlab, …), made us able to start working with the analogue experiments. Laboratory FAST, in collaboration with the people from the LET Roma Tre, appeared right away as an active and stimulating working environment where we had the opportunity to apply the new knowledge acquired during the theoretical lessons and carry out a broad range of geodynamic simulations taking advantage of state-of-the-art experimental and analytical facilities of the lab.
Written by Gianluca, Elenora, Giacomo, Beatriz and Linfeng
