The stability of a boundary layer on a horizontal surface is governed by the compositional Rayleigh number, Rac, where;
Rac = gAp c d^/vD.
This value must exceed 1000 for boundary layer instability (Rosenberger, 1979). In the above equation g is the gravitational constant, Apc is the compositional density
difference across the film, d is the film thickness, v is the kinematic viscosity, and D is the chemical diffusion coefficient. Values for v and Apc have been calculated from melt compositions. Values for D are in the range 10"5-10"8 cm^s"! (Hofmann, 1980).
Calculations have been carried out for four scenarios in this study:-
1) A compositional boundary layer forming on the horizontal floor of an alumina crucible by hercynite growth.
2) A compositional boundary layer on the floor of a clay crucible, produced by wall dissolution.
3) A boundary layer forming on a horizontal olivine surface. 4) A boundary layer forming around an olivine crystallite.
The calculations in table 3.06 show the thicknesses of boundary layer necessary to produce melt instability (i.e. Rac exceeds 1000), and the times needed for a boundary
(800-10,000^^) J
layer to reach these thicknesses. The computed widths of boundary layers, and the minimum times necessary for them to be unstable are not consistent with observed boundary layer thicknesses.
The thicknesses of boundary layers produced on the floors of experimental charges do not begin to approach the calculated thicknesses, probably explaining why plumes are not seen rising from the floors of crucibles in this chapter (cf. chapter 4). Even in clay crucibles, boundary layers do not reach the minimum v/iWH needed for convection, but buoyant plumes have been observed. In such cases bubbles could have induced boundary layer instability.
The convection of side-wall melt in alumina crucibles, in relatively short duration runs, can be explained because the calculations here are for horizontal surfaces. On
inclined surfaces boundary layers are instantaneously unstable.
The calculations for boundary layers around the crystallite reveals a very thick boundary layer is needed for convection, with the crystallite being only 500pm in diameter. Even though the calculation is for a horizontal surface, and boundary layer
melt from vertical sides of the crystal may contribute to more rapid boundary layer build up, it is no wonder that compositional convection is not observed around crystallites.
For a horizontal boundary layer above an olivine seed, a minimum thickness of 23 cm is required before it becomes buoyant. No such thickness of boundary layer could be observed in this chapter, although compositional convection has taken place. Again the explanation of this inconsistency lies in the fact that calculations are for horizontal surfaces. Donaldson (1993) discusses evidence for boundary layer melt on inclined surfaces flowing round crystals and increasing boundary layer thickness at the bottom of dissolving crystals. If this situation is turned upside down it can be applied to the growing olivine crystals here, causing rapid thickening of a boundary layer above the crystal seed, and so convection occurs within the duration of these experiments. Also, any horizontal surface on the crystal seeds in these experiments has been almost removed by crystal grinding and careful alignment, so no horizontal sides exist on the seeds.
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3.8 Summary and Conclusions
The following list summarizes the findings of the experiments in this chapter:-
• Compositional variation in experimental charges is produced by olivine crystallization, hercynite crystallization and alumina dissolution.
• Alumina dissolution melt near walls and cement produces a lower density than the original melt.
• Growth of olivine crystallites produces a 20-30pm wide, low-density boundary layer around each crystallite. Conclusive evidence for convection of these boundary layers has not been observed.
• The compositional variations, produced in melts by crystallization, are not sufficient to cause a colour difference in quenched glasses. In higher viscosity silicate systems, colour variation may be observed because a bigger compositional variation across a wider zone is required to produce boundary layer instability.
• Surface-tension driven convection (eg. near bubbles and at the meniscus) causes accelerated side-wall dissolution.
• Compositional variation greatly affects the distribution of nucleating crystallites. • The study of fluid dynamics associated with crystallization requires small
supercoolings so that excessive crystallization does not interfere with observation of glass compositions.
• Air bubbles aid the rise of crystals in melts, even if the crystals have a higher density than the melt.
• Olivine growth produces a 30pm-wide, low-density, boundary layer (depleted in j CoO and MgO, but enriched in SiO2) around the crystal seed. This boundary layer is
detectable by EPMA above the crystal apex.
• Across the boundary layer CoO and MgO are depleted by 25 %. The most depleted part of the boundary layer remains at the crystal-liquid interface and is not seen above the crystal seed.
• With longer run duration, vertical compositional differentiation occurs, producing CoO and MgO depletion and A12O3 enrichment at the top and bottom of crucibles.
This chapter has described the existence of compositionally-discrete plumes of Co- and Mg-depleted melt above growing olivine crystal apexes. However, due to the
unsolved problem of melt contamination the results of this series of experiments are not entirely satisfactory, as crystal growth is not the only process causing
compositional variation in the experimental charges. This means that differentiated end-products are not produced solely by crystallization of Co- and Mg-bearing crystals.
In a body of magma several mechanisms produce compositional and density variations (eg. crystal dissolution, side-wall melting, temperature variations, contamination by another magma injection). This study has shown that crystallization in low-viscosity silicate systems does produce compositional variation in boundary-layer melts, and that the change is large enough to drive melt convection. The quantative evaluation of this process is difficult to assess due to contamination. In a magma chamber the effect of crystallization-driven convection may also be impossible to assess due to the influence of other processes. These include:-
1) Side-wall melting and later magma injection.
2) The crystal assemblage being produced at the margins of chambers. For example, olivine will produce a low density boundary layer if crystallized alone, but if enough plagioclase is crystallized in the assemblage then the density of the boundary layer zone may be greater than the original melt.
3) Other convective processes (eg temperature-driven convection) may wash away boundary layers before they are unstable, accelerating crystal growth by bringing fresh, undepleted melt into contact with the crystals. This would prevent maximum depletion of boundary layer melt being reached, and so the process would have a lesser effect on the composition of the magma which is washed away from the crystals.
In basaltic magma chambers at high temperatures the low viscosity will not inhibit compositional-driven convection, but under such conditions crystal growth rates are small and so boundary layer melt is produced slowly. In lower temperature basaltic chambers, or with a more evolved magma, melt viscosity is higher and bigger
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compositional differences are needed to produce boundary layer instability, however the increase in viscosity will also hinder convective processes.
Composition-driven convection is therefore probably most active in the early evolution of a basaltic magma body, and should decrease in importance with increasing time and decreasing temperature.