Hello,

This relationship is pretty complex, and it is not straightforward that your lava will actually present a yield strength. This depends on the shape and concentration of the crystals and bubbles...

To estimate that, you need to estimate the effects of crystals and bubbles on the viscosity of the magma, depending on crystal shape, size as well as the effects of the bubbles on magma viscosity, which changes depending if you consider a magma very viscous (viscosity > ~ 10^8 Pa s) or quite fluid (viscosity < 10^6 Pa s).

The problem is that, despite some models have been proposed, a general model making a global consensus in the community still remains to be published...

To help you, I will advise reading the paper of Mader et al. (2013) as well as the other papers I included in the references below. This will give you an idea of how to proceed to solve your problem.

Back in 2015 we published in EPSL an example of the estimation of the viscosity of the lava of the Mt Erebus volcano:

Le Losq, C., Neuville, D.R., Moretti, R., Kyle, P.R., Oppenheimer, C., 2015. Rheology of phonolitic magmas – the case of the Erebus lava lake. Earth and Planetary Science Letters 411, 53–61. doi:10.1016/j.epsl.2014.11.042

This may also help you as it is a practical example.

Best regards,

Charles LL.

A few references for the effect of crystals:

Costa, A., Caricchi, L., Bagdassarov, N., 2009. A model for the rheology of particle-bearing suspensions and partially molten rocks. Geochemistry Geophysics Geosystems 10, 1–13.

Del Gaudio, P., Ventura, G., Taddeucci, J., 2013. The effect of particle size on the rheology of liquid-solid mixtures with application to lava flows: Results from analogue experiments: Rheology of Liquid-Solid Mixtures. Geochemistry, Geophysics, Geosystems 14, 2661–2669. doi:10.1002/ggge.20172

Gaudio, P.D., 2014. Rheology of bimodal crystals suspensions: Results from analogue experiments and implications for magma ascent: Rheology of Bimodal Crystals Suspensions. Geochemistry, Geophysics, Geosystems 15, 284–291. doi:10.1002/2013GC005078

Mader, H.M., Llewellin, E.W., Mueller, S.P., 2013. The rheology of two-phase magmas: A review and analysis. Journal of Volcanology and Geothermal Research 257, 135–158. doi:10.1016/j.jvolgeores.2013.02.014

Mueller, S., Llewellin, E.W., Mader, H.M., 2011. The effect of particle shape on suspension viscosity and implications for magmatic flows: PARTICLE SHAPE AND SUSPENSION VISCOSITY. Geophysical Research Letters 38, n/a-n/a. doi:10.1029/2011GL047167

Mueller, S., Llewellin, E.W., Mader, H.M., 2010. The rheology of suspensions of solid particles. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 466, 1201–1228. doi:10.1098/rspa.2009.0445

Villeneuve, N., Neuville, D.R., Boivin, P., Bachèlery, P., Richet, P., 2008. Magma crystallization and viscosity: A study of molten basalts from the Piton de la Fournaise volcano (La Réunion island). Chemical Geology 256, 242–251. doi:10.1016/j.chemgeo.2008.06.039

Vona, A., Romano, C., Dingwell, D.B., Giordano, D., 2011. The rheology of crystal-bearing basaltic magmas from Stromboli and Etna. Geochimica et Cosmochimica Acta 75, 3214–3236.

Some other references for the effect of bubbles:

Lejeune, A.-M., Bottinga, Y., Trull, T.W., Richet, P., 1999. Rheology of bubble-bearing magmas. Earth and Planetary Science Letters 166, 71–84.

Lensky, N.G., Lyakhovsky, V., Navon, O., 2001. Radial variations of melt viscosity around growing bubbles and gas overpressure in vesiculating magmas. Earth and Planetary Science Letters 186, 1–6.

Manga, M., Castro, J., Cashman, K.V., Loewenberg, M., 1998. Rheology of bubble-bearing magmas. Journal of Volcanology and Geothermal Research 87, 15–28.

Manga, M., Loewenberg, M., 2001. Viscosity of magmas containing highly deformable bubbles. Journal of Volcanology and Geothermal Research 105, 19–24.

Pal, R., 2003. Rheological behavior of bubble-bearing magmas. Earth and Planetary Science Letters 207, 165–179. doi:10.1016/S0012-821X(02)01104-4

Pistone, M., Caricchi, L., Ulmer, P., Burlini, L., Ardia, P., Reusser, E., Marone, F., Arbaret, L., 2012. Deformation experiments of bubble- and crystal-bearing magmas: Rheological and microstructural analysis: RHEOLOGY OF THREE-PHASE MAGMAS. Journal of Geophysical Research: Solid Earth 117, n/a-n/a. doi:10.1029/2011JB008986

Pistone, M., Caricchi, L., Ulmer, P., Reusser, E., Ardia, P., 2013. Rheology of volatile-bearing crystal mushes: Mobilization vs. viscous death. Chemical Geology 345, 16–39. doi:10.1016/j.chemgeo.2013.02.007

Article The rheology of two-phase magmas: A review and analysis

Article Rheology of phonolitic magmas – the case of the Erebus lava lake

Charles has provided a great overview and I agree with him...

I only would suggest keep in mind the following:

1. In a closed system, the magma and its rheological behaviour is relatively easy to model. What is difficult is to model the rheology after it 'erupts'.... The vapour-loss rates, chilling induced crystallisation rates and rapid loss of heat need to be modelled for the lavas before attempting to quantify their rheology.

2. As a lava moves, depending upon the loss of vapour and temperature, its viscosity changes laterally and temporally. These changes (with more and more studies in the Hawaii and Icelandic systems) are now better understood than before. They should be brought into the discussion of the rheological behaviour of the lava.

Often, the magma - lava change is not taken into discussion on these studies... One is a closed system, while the latter is an open system.