The Influence of Viscosity on Fountains in Magma Chambers

Geological observations suggest that basaltic magmas mix readily but that rhyolites and basalts can erupt through the same volcanic vent without mixing. The implication is that viscosity may have an important influence on the mixing of magmas. This paper examines the influence of viscosity on magma mixing when a magma of low viscosity is injected as a turbulent fountain into a chamber containing a magma of higher viscosity. Three series of experiments were carried out. In the first, the low viscosity fluid was injected into the tank at a Reynolds number (Re1) of about 1000 to ensure that flow within the fountain was fully turbulent. Both fluids were maintained at the same temperature and the viscosity of the host fluid was varied systematically. If the viscosities of the two fluids are similar, turbulence in the fountain leads to extensive mixing and to formation of a density-stratified layer which collects at the bottom of the tank. However, if the viscosity ratio of the fluids used is greater than 400, no detectable mixing occurs. Motion within the fountain is again fully turbulent but the high momentum of the input fluid is not transmitted to the more viscous host fluid. Experiments carried out at intermediate viscosity ratios resulted in intermediate amounts of mixing. Theoretical considerations suggest that the criterion for mixing in turbulent fountains, when a fluid of low viscosity v1 is injected into a fluid of much higher viscosity v2 is wd> kv2 where w is the flow velocity through an input pipe of diameter d and k is a constant. This relationship is believed to be a general one, applying equally to jets and plumes, although the values of k may vary with the nature of the flow. The second series of experiments was designed to test this relationship and determine values of k for fountains. The results show that, if wd/v2 > 70, the inflowing fluid mixes with the host fluid as there was no viscosity difference between them. However, if wd/v2 < 7, little or no mixing occurs even if motion within the fountain is fully turbulent. In the third series of experiments the temperature of the input fluid was 70°C above that of the host fluid. This led to heating ofa thin boundary layer of the host fluid, lowering the viscosity of the host fluid adjacent to the fountain and thus allowing additional mixing between the fluids. This effect was most obvious in the experiment with the highest viscosity ratio (1229) where a small amount of mixing was detected, compared with no mixing in the equivalent experiment in the first series. The criterion for mixing, wd> kv2 can be applied to natural magmas. The results show that if a primitive basaltic magma is injected, as a turbulent fountain or plume, into a chamber containing fractionated basaltic magma, the two magmas will mix readily. However, if basaltic magma is injected into a chamber containing granitic melt, little or no mixing occurs.