“What is the essence of magma rheology?

In search for a suitable analog material for magma”

In order to investigate the role of non-Newtonian rheology in the generation of volcanic tremor, the RHEOVOLC Project (PRC CNRS-JSPS 2014) proposes to combine the physics of complex fluids and the analysis of field data. This two-year franco-japanese project (2014-2016) proposes its first meeting in Chamonix, France, from December 1^st to 4^th, 2014.

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SCIENTIFIC OBJECTIVES ------------------------------------------------------------------------------------------------------------------------

1) Volcanic tremor: which mechanism?

Volcanic tremor is a remarkably consistent feature of explosive volcanism observed around the world. It consists in continuous low-frequency ground vibration that can last for minutes to weeks and is characterized by a narrow band of frequencies (0.1 to a few Hz) [Jellinek & Bercovici, 2011]. In-between tremor episodes, long-period (LP) events, which range in the same frequency band, are also important indicators of the volcano activity. Tremor and LP events frequently precedes – and almost always accompanies – volcanic eruptions, which makes them critical for predicting and characterizing natural hazards.

Even if it is commonly accepted that the source of these low-frequency events is the resonance and/or interaction of fluid flow in cracks or pipes inside the volcano [e.g. Chouet, 1996; Rust et al., 2008], the precise mechanism for tremor generation – and, in particular, harmonic tremor – is still under debate. A physical model of volcanic tremor which is, up to now, still lacking, should explain the following points: (1) the existence of a dominant frequency of 0.1~1 Hz in the signal; (2) the time-variable nature of the frequency spectrum, which evolves with the eruption sequence; and (3) the nature of the non-linear oscillations required to generate the tremor.

2) Non-Newtonian rheology: an open question 

One of the key parameters of the volcano dynamics is the non-Newtonian magma rheology. The magma is a multiphase complex fluid, suspension of randomly shaped crystals (solid phase) and bubbles (gas phase) in a silicate melt (viscous liquid phase). The volume fraction of each phase changes with the temperature, pressure and eruption sequence. The rheology strongly depends on the volume fractions of each phase, so that the magma rheology should be characterized by a strong non-linearity – for example, the existence of a yield stress and of a multivalued relationship between the pressure (stress) and flow-rate (shear-rate). The existence of a yield stress has, indeed, been pointed out by several works [e.g. Webb & Dingwell, 1990; Saar et al., 2001; Caricchi et al., 2007; Gonnermann & Manga, 2007; Lavallée et al., 2007].

The effect of yielding and the kinetic character of this phenomenon is important because it leads to the possibility of different states of a material under flow and multivalued flow curves, i.e. to instability and self-organization of a medium [Coussot et al., 2002]. The existence of multivalued flow curves has been reported for polymers and colloidal systems under shear [Malkin et al., 2010a; 2010b]. In polymer science, the so-called spurt phenomenon is known to be associated with flow instability and the emergence of a self-excited oscillatory behavior [e.g. Malkin et al., 2010a]. In associative polymer networks, rheochaos has been reported as an instability and spatiotemporal fluctuations in the shear flow [Sprakel et al., 2008]. These previous works indicate that if the magmatic suspension exhibits the same nature, then a self-excited behavior should be expected, and could be a physical mechanism for the generation of volcanic tremor. In a recent work, Costa et al. [2012] suggested this mechanism to explain cyclic extrusions of lava domes. However, most of the previous models are based on an unrealistic magma rheology.

3) Objectives of the proposal

In this project, we propose to investigate if the non-linear characteristics of magma rheology can be a potential mechanism for tremor generation – in particular, if they are responsible for spontaneous oscillations of the fluid column. Based on the characterization in the laboratory of the rheology of suspension systems (colloidal, soft gel and hard sphere suspensions analogous to the magmatic system) we will clarify (a) how and when the yielding nature emerges, and (b) how and why the multivalued nature emerges. The main novelty will be to characterize the local structure of the flow – in particular, to get informations on the dynamics of the yielding transition – through ultrasonic imaging. Finally, we will compare these results with field data, and propose a physical interpretation for the volcanic tremor.  

This interdisciplinary project joins the Physics Laboratory of ENS de Lyon, with participants specialized in soft matter, complex fluids and rheology measurements (including local measurements with ultrasonic imaging), the Volcanology Team of the Earthquake Research Institute (University of Tokyo), with specialists of volcano seismics and acoustics as well as experimental acoustics and rheology, and three additional partners from Tohoku University, Shizuoka University and Shimane University (Japan), working on the rheology of magma – including the emergence of yield stress in crystal bearing magma – and on the properties of granular matter and suspensions close to the jamming point. It should be a unique opportunity to join skills from different disciplines to focus on the same topic.