A FLUID-DYNAMICAL STUDY OF CRYSTAL SETTLING IN CONVECTING MAGMAS

Abstract

Thermal convection in magma chambers is believed to be almost always highly time-dependent, or 'turbulent', and predicted convective velocities are commonly orders of magnitude larger than settling velocities for typical crystals calculated from Stokes' Law. To understand crystal settling in magma chambers we have therefore undertaken a theoretical and experimental study of particle settling in a turbulently convecting fluid.The regime of interest is where the ratio, S, of the Stokes' Law settling velocity, v s, to the root mean square vertical component of convective velocity, W, at mid-depth in the fluid is less than unity. Although v s < W, settling is still possible because convective velocities are height-dependent and must decrease to zero at the boundaries of the fluid. Particles immediately adjacent to the bottom boundary settle out with their full Stokes' settling velocities. At the same time, convection is vigorous enough to ensure that the distribution of particles in the fluid is uniform. It follows that the number of particles in suspension decays with time according to an exponential law, and the decay constant is simply the ratio of v s to h, the depth of the fluid. Experiments confirm this relationship, at least for low particle concentrations, provided S < 0.5 and there is no re-entrainment of particles from the floor of the tank.We apply this relationship to crystals in magma chambers and so calculate residence times for typical crystals. We find that for basaltic magmas the predicted residence times are small compared with the many thousands of years that a chamber takes to solidify if cooling is dominated by conduction through the country rock. We therefore conclude that crystal settling may be an efficient differentiation mechanism. Significant magmatic evolution may, however, take place on time-scales that are competitive with these residence times.If the settling of crystals is the rate-limiting step during the crystallization of a magma chamber it is expected that a steady state will be achieved at which the rate of supply of crystals into the convecting magma by crystallization balances the rate at which crystals settle out. We show how this idea can explain both the lack of hydraulic equivalence in cumulate rocks and the commonly observed discrepancy between the relative proportions of phenocrysts of various phases in fractionated basaltic lavas and the calculated relative proportions of these mineral phases in the fractionating assemblage. Finally, an attempt is made to calculate the steady-state crystal content of convecting magma chambers. Comparison of the predicted crystal contents with the observed phenocryst contents of typical basaltic lavas suggests that magma chambers may often cool more rapidly than would be expected for conduction through the country rock alone.