A Fluid-Dynamical Study of Crystal Settling in Convecting Magmas |
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| Authors: | MARTIN DANIEL; NOKES ROGER |
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| Institution: | Research School of Earth Sciences, Australian National University G.P.O. Box 4, Canberra, ACT 2601, Australia |
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| Abstract: | Thermal convection in magma chambers is believed to be almostalways highly time-dependent, or ‘turbulent’, andpredicted convective velocities are commonly orders of magnitudelarger than settling velocities for typical crystals calculatedfrom Stokes' Law. To understand crystal settling in magma chamberswe have therefore undertaken a theoretical and experimentalstudy of particle settling in a turbulently convecting fluid. The regime of interest is where the ratio, S, of the Stokes'Law settling velocity, vs, to the root mean square verticalcomponent of convective velocity, W, at mid-depth in the fluidis less than unity. Although vs < W, settling is still possiblebecause convective velocities are height-dependent and mustdecrease to zero at the boundaries of the fluid. Particles immediatelyadjacent to the bottom boundary settle out with their full Stokes'settling velocities. At the same time, convection is vigorousenough to ensure that the distribution of particles in the fluidis uniform. It follows that the number of particles in suspensiondecays with time according to an exponential law, and the decayconstant is simply the ratio of vs to h, the depth of the fluid.Experiments confirm this relationship, at least for low particleconcentrations, provided S < 0.5 and there is no re-entrainmentof particles from the floor of the tank. We apply this relationship to crystals in magma chambers andso calculate residence times for typical crystals. We find thatfor basaltic magmas the predicted residence times are smallcompared with the many thousands of years that a chamber takesto solidify if cooling is dominated by conduction through thecountry rock. We therefore conclude that crystal settling maybe an efficient differentiation mechanism. Significant magmaticevolution may, however, take place on time-scales that are competitivewith these residence times. If the settling of crystals is the rate-limiting step duringthe crystallization of a magma chamber it is expected that asteady state will be achieved at which the rate of supply ofcrystals into the convecting magma by crystallization balancesthe rate at which crystals settle out. We show how this ideacan explain both the lack of hydraulic equivalence in cumulaterocks and the commonly observed discrepancy between the relativeproportions of phenocrysts of various phases in fractionatedbasaltic lavas and the calculated relative proportions of thesemineral phases in the fractionating assemblage. Finally, anattempt is made to calculate the steady-state crystal contentof convecting magma chambers. Comparison of the predicted crystalcontents with the observed phenocryst contents of typical basalticlavas suggests that magma chambers may often cool more rapidlythan would be expected for conduction through the country rockalone. |
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