Turbulent mixing between fluids with different viscosities

Abstract

Fluid dynamic processes associated with the injection of new pulses of magma into magma chambers have received increased attention recently^1–3 especially chambers replenished from below with hotter, denser magma of more primitive composition^3,4. The results of several laboratory analogue experiments^3,4 have shown that the dynamical effects of crystallization following replenishment can be quite different when the two layers have similar, or very different, viscosities. The experiments reported below have examined the effect of viscosity differences on the filling process itself. When a turbulent ‘fountain’ of fluid of low viscosity v₁ is injected upwards into a less dense fluid of higher viscosity (v₂), the two fluids may mix thoroughly or not at all, depending on the relative magnitudes of an input Reynolds number Re₁ = wd/v₁ and the viscosity ratio v₂/v₁ where w is the mean velocity and d is the diameter of the input. The criterion for mixing can be expressed alternatively as wd/v₂ > k, a constant, in agreement with a more general theoretical argument which is also outlined here. When applied to magma chambers, our results imply that basaltic magmas will mix readily, but that a basaltic inflow will mix with a silicic host magma only with great difficulty.