A numerical study of the nucleation, growth and settling of crystals from a turbulent convecting fluid
Authors: Patocka Vojtech , Tosi Nicola , Calzavarini Enrico 
Published: March 2021

&lt;p&gt;We evaluate the equilibrium concentration of a thermally convecting suspension that is cooled from above and in which&lt;br&gt;solid crystals are self-consistently generated in the thermal boundary layer near the top. In a previous study (Patoc&amp;#780;ka et&lt;br&gt;al., 2020), we investigated the settling rate of solid particles suspended in a highly vigorous (Ra = 10&lt;sup&gt;8&lt;/sup&gt; , 10&lt;sup&gt;10&lt;/sup&gt;, and 10&lt;sup&gt;12&lt;/sup&gt; ),&lt;br&gt;finite Prandtl number (Pr = 10, 50) convection. In this follow-up study we additionally employ the model of crystal&lt;br&gt;generation and growth of Jarvis and Woods (1994), instead of using particles with a predefined size and density that are&lt;br&gt;uniformly injected into the carrier fluid.&lt;/p&gt;&lt;p&gt;We perform a series of numerical experiments of particle-laden thermal convection in 2D and 3D Cartesian geometry&lt;br&gt;using the freely available code CH4 (Calzavarini, 2019). Starting from a purely liquid phase, the solid fraction gradually&lt;br&gt;grows until an equilibrium is reached in which the generation of the solid phase balances the loss of crystals due to&lt;br&gt;sedimentation at the bottom of the fluid. For a range of predefined density contrasts of the solid phase with respect to&lt;br&gt;the density of the fluid (&amp;#961;&lt;sub&gt;p&lt;/sub&gt; /&amp;#961;&lt;sub&gt;f&lt;/sub&gt; = [0, 2]), we measure the time it takes to reach such equilibrium. Both this time and&lt;br&gt;the equilibrium concentration depend on the average settling rate of the particles and are thus non-trival to compute for&lt;br&gt;particle types that interact with the large-scale circulation of the fluid (see Patoc&amp;#780;ka et al., 2020).&lt;/p&gt;&lt;p&gt;We apply our results to the cooling of a large volume of magma, spanning from a large magma chamber up to a&lt;br&gt;global magma ocean. Preliminary results indicate that, as long as particle re-entrainment is not a dominant process, the&lt;br&gt;separation of crystals from the fluid is an efficient process. Fractional crystallization is thus expected and the suspended&lt;br&gt;solid fraction is typically small, prohibiting phenomena in which the feedback of crystals on the fluid begins to govern the&lt;br&gt;physics of the system (e.g. Sparks et al, 1993).&lt;/p&gt;&lt;p&gt;References&lt;br&gt;Patoc&amp;#780;ka V., Calzavarini E., and Tosi N.(2020). Settling of inertial particles in turbulent Rayleigh-Be&amp;#769;nard convection.&lt;br&gt;Physical Review Fluids, 26(4) 883-889.&lt;/p&gt;&lt;p&gt;Jarvis, R. A. and Woods, A. W.(1994). The nucleation, growth and settling of crystals from a turbulently convecting&lt;br&gt;fluid. J. Fluid. Mech, 273 83-107.&lt;/p&gt;&lt;p&gt;Sparks, R., Huppert, H., Koyaguchi, T. et al (1993). Origin of modal and rhythmic igneous layering by sedimentation in&lt;br&gt;a convecting magma chamber. Nature, 361, 246-249.&lt;/p&gt;&lt;p&gt;Calzavarini, E (2019). Eulerian&amp;#8211;Lagrangian fluid dynamics platform: The ch4-project. Software Impacts, 1, 100002.&lt;/p&gt;