EGU2020-12618
https://doi.org/10.5194/egusphere-egu2020-12618
EGU General Assembly 2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Crystal fractionation by crystal-driven convection

Cansu Culha1, Jenny Suckale1, Tobias Keller2, and Zhipeng Qin1
Cansu Culha et al.
  • 1Stanford University, Geophysics , United States of America (cansu.culha@gmail.com)
  • 2University of Glasgow, School of Earth and Geographical Sciences, 8NN University Avenue, Glasgow G12 8QQ, UK.

In the last two decades, improved fine scale analysis in crystalline profiles has improved our understanding of igneous processes, while opening our sight to more complexities. As an example, plagioclase crystal profiles in Holyoke flood-basalt flow revealed that the crystals got exposured to different melt environments as the layer underwent fractional crystallization. Fractional crystallization is an essential process for determining the compositional evolution of magmatic systems. The process requires a reactive segregation process, where crystals precipitate from the melt and segregate from their residual melt. In this study, we are motivated by the subtleties in the crystalline record to model the segregation component of fractional crystallization, or crystal fractionation.

 

We build a numerical model with individually resolved, denser-than-melt crystals in a convective flow. We test the low to intermediate crystallinity regime, where the physical processes leading to efficient fractionation are less clear than at high crystallinity. We simulate the physical segregation of crystals from their residual melt at the scale of individual crystals using a direct numerical method. By resolving each of the crystals, we do not require a priori parameterization of crystal-melt interactions. We use tracers in the melt to track the different melts around the crystals.

 

We find that collective sinking of crystal-rich clusters dominate settling at low particle Reynolds numbers. The relatively rapid motion of this cluster strips away the residual melt around the cluster. Compared to individual settling, the resulting crystal fractionation is efficient but heterogeneous at the crystalline scale. Similar to the Holyoke flood-basalt plagioclase profiles, the crystals in our analysis show exposure to different melt environments as they drive crystal fractionation. Our results suggest that cluster driven fractional crystallization will vary in efficiency. At the system scale, this result would suggest a bell curve compositional abundance distribution in volcanic systems.




 

How to cite: Culha, C., Suckale, J., Keller, T., and Qin, Z.: Crystal fractionation by crystal-driven convection, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-12618, https://doi.org/10.5194/egusphere-egu2020-12618, 2020

Comments on the presentation

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Presentation version 1 – uploaded on 04 May 2020
  • CC1: great presentation !, Oleg Melnik, 04 May 2020

    Please send me the link to your GRL paper

    • AC1: Thanks Oleg! See attached, Cansu Culha, 04 May 2020

      Hi Oleg, Thanks for stopping by! 

      Here is the link: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2019GL086784
      Feel free to reach out to me at cculha@stanford.edu or WhatsApp: +1(240)645-8117

      Happy meetings, Cansu

  • CC2: thermal convection, MELTS, Vojtech Patocka, 04 May 2020

    Indeed, very nice presentation. You mention coupling your model to thermodynamics of crystal generation in the future. What software do you plan to use to compute the crystal properties for a given pressure, temperature, and bulk composition?

    Also, what are the driving forces for your system? Just crystal settling, or do you model thermal convection in the chamber?

    • AC2: Thanks Vojtěch, Cansu Culha, 04 May 2020

      Thanks for seeing the presentation.
      1. You got it! I use the MELTs software to couple to thermodynamics. I've been simulating mafic injections, namely Unzen injection (Browne et al., 2006 series). My results show that the same crystal cluster evolves but it forms a self-feeding instability that even further excellerates the convection. In that system, I look at thermal variability as my observable marker in crystalline profiles. There I see cooling and heating crystals next to one another. Also, some crystals are longer lasting than others depending on their dynamics within the crystal-cluster. I notice that as viscosity increases, crystal driven convection gets hindered so an instability does not form. This is because the thermal front advances and alters magma properties much faster than crystals can advect through the highly viscous system. In terms of fluid dynamics, this is very cool to me. However, as you mentioned, convection can form in other ways like thermal convection, which might lead to similar effects. 

      2. In this contribution, I only model convection through crystal settling, but you can imagine that thermal convection would enhance the speed of convection and not deter from the crystal fractionation process. This is because the thermally convective cell would be large enough for crystals (which are relatively small) can segregate from their residual melt at that reference frame. From my results, I suggest that convection would make the crystal fractionation process more efficient and further lead to crystalline scale heterogeneity.  

      • CC3: Reply to AC2, Tobias Keller, 04 May 2020

        One thing to bear in mind is that density contrasts due to thermal effects tend to be much smaller than due to presence of phases with density contrasts. For example, if your crystal phase is 100 kg/m3 denser than your melt and you locally have 10% more crystals than in surrounding melt, that creates roughly the same density contrast as 400 degrees T-contrast. Crucially, it might only take a few tens of degrees contrast to form 10% more crystals! Therefore, if there's any density contrast between forming crystals and residual melt, that will likely be the dominant driver of convection, not thermal density contrasts.

        • AC3: layer thicknesses , Cansu Culha, 04 May 2020

          Well calculated and put into context Toby! Thanks. 

          There are some observed systems like the Searchlight Pluton that might be thick enough with large enough temperature contrast to sustain thermal convection for a period of time. It is hard to know how ubiquitous they are. Thermal convection is worth considering, but overall crystal driven convection can dominate because of how sensitive unstably stratified crystal formation is to small thermal variability. 

        • CC5: Reply to CC3, Vojtech Patocka, 04 May 2020

          Thank you Cansu and Tobias. Just a quick comment on crystal driven convection: While I agree with what Tobias wrote, at least for the early stages of magma oceans and magma chambers I think thermally driven convection is more likely. The life span of such systems is by orders of magnitude longer than the Stokes settling time of crystals. Thus, existing crystals have plenty of time to settle before the body cools by a few tens of degrees as you say. In other words, the time needed to produce a significant volume of crystals is long relative to settling time and I expect a permanently dillute suspension of a decreasing volume. I know I am not being very quantitative and so far we have run only very preliminary cases in this regard, but I just wanted to bring attention to the time scales: when cooling is very slow relative to the characteristic settling time then you should expect thermally driven convection regardless of Tobias's back of the envelope calculations.

          • AC5: lets test it!, Cansu Culha, 04 May 2020

            Hey Vojtech, thank you for these comments! Lets give it a try. It seems like your bottom left figure in your poster gives the speeds of convection relative to stokes settling speed right? It seems like 2x the speed of stokes speed. Is that right? I might be getting this wrong. 

            I'm going to compare this to the speeds in our 2020 paper (https://agupubs-onlinelibrary-wiley-com.stanford.idm.oclc.org/doi/full/10.1029/2019GL086784) specifically Fig. 1. 
            Magma Oceans (low viscosity):
            At the finite Re, crystals settle slower than a single crystal stokes speed. This does not change when I couple thermodynamics to my simulations. Therefore, from what you suggested Magma Oceans could sustain a thermal convection that is faster than crystal advection! I'll try to attach the simulations here.
            Magma Chambers (high viscosity):
            At low Re, crystals settle collectively as a cluster 12x faster than crystal stokes speed. When I couple to thermodynamics to my simulations, the clusters travel 100x faster than a single crystal stokes speed because of a self feeding instability. I will post this as well. I wonder how this compares to your speeds of thermal convection in magma chambers.
            I should also note that we are unclear how ubiquitous magma chambers are given some of the most recent mental descriptions of magma reservoirs. Thin magma lenses are likely more ubiquitous in magma reservoirs.

          • AC6: Low Re with crystals forming and dissolving with cooling/heating, Cansu Culha, 05 May 2020

            Here are two simulation runs with thermodynamic coupling. I simplified the problem so these results are not with MELTS software results. I only form and disolve crystals and look at that instability. Below a certain temperature I enforce a constant crystallinity. I do not alter melt viscosity or density. This is purely to show the different crystal driven instabilities that form. I present vertical non-dimensional velocity using single crystal stokes speed. My characteristic lengthscale here is crystal radius. 
            Finite Re: Still running simulation, but I confidently suspect speeds to be less than 1 non-dimensional speed. The instability is different from stokes instability because wakes form. 

            Low Re: https://drive.google.com/file/d/1MUUaJM22Fjz-DDAYM9aP8xJtB7XaS0ra/view?usp=sharing

            • CC8: Reply to AC6, Vojtech Patocka, 05 May 2020

              Thank you Cansu for the detailed response and performed tests! In my view, your argumentation based on comparing flow velocities triggered by crystal clusters vs characteristic velocities of thermal convection must be treated with care - I can imagine scenarios in which such comparison fails to provide the correct answer as to what drives the flow. In the case you show it is probably valid because the clusters generate large-scale flow, but generally I would stick to the estimates of relative buoyancy as Tobias outlined. Nevertheless, we all agree that for a given rock type it can go either to crystal- or thermally-driven convection, depending on the cooling rate and viscosity. In any case, I am excited to read your paper and I will stay in touch - our projects seem to partially overlap.

              P.S. Regarding the flow velocities, we get u_rms = 0.15 for Ra=10^12 and Pr=50, with Reynolds number being ca. 28000 for that case, but the value of course depends on the choice of non-dimensionalization (left bottom of our poster). In case you found it useful to have a priori estimates of characteristic flow velocities for any Rayleigh and Prandtl number, I recommend the Grossmann & Lohse theory (e.g. Ahlers, Grossmann and Lohse, 2009).

              • AC11: Reply to CC8, Jenny Suckale, 06 May 2020

                Hi Vojtech, there is no doubt that scaling relationships are useful. However, many assumptions go into these scaling relationships, such as choosing characteristic time scales, length scales etc. In multiphase flows, there always are many scales to choose from and in the type of complex, volcanic systems we are all thinking about there might be many additional processes (e.g., thermodynamics etc) introducing new scales, which might be very consequential for the fluid dynamics, but not represented in some of the classical scalings that are commonly invoked. For this reason, I think it is best to think about scaling relationships as testable hypothesis about the system dynamics and Cansu's work does just that. Interestingly, one key finding is that the Stokes settling speed is not always a meaningful characteristic speed scale for capturing crystalline motion. Not surprising really when keeping in mind that the Stokes settling speed only applies for isolated crystals and neglects all crystal interactions, which become such an important part of the overall dynamics at low Re. 

                Anyhow, it would be interesting to think about overlaps with your research. I've done some work on magma oceans a while back, so feel free to reach out if you're interested.

          • CC7: Reply to CC5, Tobias Keller, 05 May 2020

            Certainly a valid point, Vojtech. We were mostly aiming our work at crustal magma reservoir that might often have more rapid cooling rates than required for a scenario as you describe it. Of course, for large layered intrusions and certainly for magma oceans, the situation might be quite different and I would agree that sustained thermal convection might be relevant there.

          • AC8: Reply to CC5, Jenny Suckale, 05 May 2020

            Hi Vojtech, just to quickly weigh in here: One of Cansu's contribution here (and in her current work which includes thermal processes) is that buoyancy-driven and temperature-drive convection are by no means separate from each other. The crystals not only change the time scale, but also the spatial pattern of convection, creating significant heterogeneity that would otherwise be absent. While small, we find that the crystals are consequential for thermal convection because they break the symmetry of the flow and create new and different convective patterns.

  • AC4: Response to Tom Griffiths' comment in the chat, Cansu Culha, 04 May 2020

    Hey Tom, Thanks for showing interest in the presentation. You asked "As I understood, the “clusters” are not physically attached in Cansu's model. Would there be any effect on the simulation if you allowed some fraction of crystals to physically attach to each other during the settling process (analogous to the process of synneusis)? Would it be feasible to model? Guess it aplies to prev. pres too."

    I think this is a great question, thank you for asking. You are right, I do not model crystals growing and attaching to one another. One interesting thing we did not publish (or present anywhere) is that these crystals do advect closer to one another as "synneusis" would describe. We actually do not need any growth phenomena to actually model synneusis. Growth of crystals that are close to one another is not modeled here, lets think about it. 

    I would hypothesize that letting crystals grow together during syneusis could have a similar effect of changing crystal shape to rectangles. Other research contributions in our group by Zhipeng Qin look at shape (e.g. https://www-sciencedirect-com.stanford.idm.oclc.org/science/article/pii/S0021999119307272). The square crystals form force chains. I suspect that this would alter the flow within the cluster and make the crystals less dynamic within the cluster, as Toby said. When I originally saw our results, I was very impressed by how the cluster looked like one giant crystal. If all of the crystals were stagnant relative to one another (maybe the viscosity is really high in the center of the cluster because of low temperature), the cluster would possibly preserve the residual melt that it would have otherwise lost to shearing within the cluster, but the cluster would still be able to fractionate the residual melt around the cluster. Therefore, I would hypothesize that there would still be zonation variability within the crystal population of neighboring crystals. 

    Our model naturally captures synneusis but it could also model crystal growth allowing crystals to attach to one another. My concern is the community is still uncertain on how to model crystal growth at the consistency we have been modeling the phase dynamics. I'd love to explore some ideas if you or anyone would like to discuss this further. 

     

    • CC4: Reply to AC4, Thomas Griffiths, 04 May 2020

      Hi, thank you for the detailed answer. Fascinating to see numerical models now able to show the synneusis behaviour observed in experiments by e.g. Schwindinger 1999, I hope that in the future it will be possible to answer the question whether the special orientation relationships often found between crystal clustered by synneusis (e.g. Schwindinger 1999, Wieser et al. 2019) are due to shape and fluid dynamics alone or also have something to do with surface/interface energies, though I guess this has to wait for 3d non rectangular shapes to be modellable.

      The idea about there being a difference between melt trapped in the cluster and outside and resulting zoning of crystals is very helpful, perhaps that is something it would be possible to detect in natural clusters as diagnostic of the crystal settling process.

      Unfortunately I am not a detailed crystal growth modeler, but I am interested in studying natural and experimental crystal clusters to work out how and where they formed, e.g synneusis vs. heterogeneous nucleation. Such studies are I think still a long way from quantitative answers (though I would love it if someone proved me wrong!). In the interests of me writing better justifications for my work in paper introductions etc., would it be correct to say that information about the geometry of clusters formed, the relative likelihood of attachment / nucleation in different positions, and the dependency of these on variables like P, T and composition would be helpful/necessary to conduct a simulation which incorporates actual growth and physical attachment of clusters?
      best regards,
      Tom Griffiths

      • AC7: "Shapes, growth, T/P/comp, oh my" -The GeoWizard of Oz, Cansu Culha, 05 May 2020

        I'd love to hear what others think of the topic of synneusis. I think you bring up great points. I think understanding growth processes is useful and would help at least modelers (like me) better understand the crystalline interactions as we model the melt dynamics. I'm looking at your presentation now and see a lot of great connections here. I'll start a discussion there. When I was using Philpott's data, I was intrigued by how these crystals connected at such low crystallinities (<20 vol%). It is really neat that you too can show that the crystals first formed, then connected later in time. 

        • CC6: Reply to AC7, Thomas Griffiths, 05 May 2020

          I would just add that in my opinion synneusis is a definitely real phenomenon (Wieser et al 2019 in combination with Schwindinger 1999 show it very nicely for me, as well as now your work and that of your colleague) but the challenge we face is determining whether a given natural or experimental cluster formed by synneusis or not. As Wieser et al shows and as I am also working on, crystallographic orientation relationships between cluster members looks like it might be a very helpful tool. But for it to work, one needs quite a lot of information about orientation relationships in other, non-synneusis situations as well, especially heterogeneous nucleation. I don't think this exists for plagioclase yet, but hopefully one day it will!

          • AC10: Reply to CC6, Jenny Suckale, 05 May 2020

            Physical models can also help with making that identification. We can compute the path of individual crystals in different flow and can quantify when they swim together and stay together long enough to overgrow.

      • AC9: Reply to CC4, Jenny Suckale, 05 May 2020

        Hi Tom, since you mention the Schwindinger experiments, we recently looked at these in detail in the context of our work on Kilauea Iki. The short answer to your question is that the large misorientation angles observed in the Kilauea Iki glomerocrysts is a consequence of both crystal shape and the ambient flow field. I will be discussing these later today in our contribution:

        EGU2020-22411 Displays   

         

        Jenny Suckale, Michelle diBenedetto, and Zhipeng Qin
        Tue, 05 May, 14:00–15:45  D1552

        Happy to discuss this analysis more if you are interested.