Abstract Core freezing and resultant compositional convection are likely important drivers for dynamo activity in large terrestrial bodies like the Earth. The solidification of compositional mixtures, such as iron and sulfur, generates mush zones of partial melt at the freezing front, which can eject chemically buoyant or heavy liquid that then drives convection. For smaller bodies such as planetesimals in the asteroid belt, conditions for generating a dynamo are harder to achieve. Nevertheless, evidence for magnetization of achondrite meteorites is abundant, suggesting that many planetesimal cores were somehow magnetized. As such small bodies cool rapidly under low gravity they likely spend much of their evolution with a large poorly compacted partial melt mushy zone. The magneto-hydrodynamic behavior of a deformable partial melt zone can induce magnetism via separation of solid and liquid phases, and conversely magnetism can impose extra forces on the phase separation in the mush zone. To this end, we have developed a new two-phase magneto-hydrodynamic theory for deformable mushes and slurries. The model includes the standard effects of Lorentz forces, and the competition between magnetic field stretching and diffusion. There are additional effects at the liquid pore or solid grain scale, which involve the interaction between phases, akin to Darcy or Stokes drag; these include Lorentz drag, as well as pore/grain-scale diffusive exchange of magnetism between solid and fluid phases, and field stretching due to relative motion between phases. Magnetic induction by gravitational phase separation is most significant after extensive mixing of liquid and solid phases, such as induced by vigorous mechanical stirring due to, for example, tidal and elliptic instabilities, or impacts with other bodies, all of which are conceivably common in the asteroid belt, especially in the early solar system. Gravitational phase separation following such events can induce significant magnetism in the liquid and solid phases, and much more rapidly than can magnetization by large-scale circulation. Magnetic field variances can be at first orders of magnitude larger than an imposed background field, during initial gravitational phase separation of the well-mixed slurry. As the phases separate toward the top or bottom, the solid phase compacts, the separation velocity decreases, and the magnetic field variance likewise diminishes. However, solitary waves in the compacting region can cause an additional large magnetic induction in the liquid, taking the form of strongly magnetized wave packets that can be trapped in the solid. Thus, phase separation, segregation and compaction potentially induce large magnetic field anomalies. A linear stability analysis for convection in a porous medium (with a rigid matrix) is also explored. Pore and grain scale effects, such as field stretching due to phase separation, are found to enhance the influence of the magnetic field on convective instability.

中文翻译：

---

两相磁流体动力学：小行星核的理论和应用

摘要 核心冻结和由此产生的成分对流可能是地球等大型陆地天体中发电机活动的重要驱动因素。成分混合物（如铁和硫）的凝固在冻结前沿产生部分熔化的糊状区域，可以喷出化学浮力或重液体，然后驱动对流。对于小行星带中的小行星等较小的天体，产生发电机的条件更难达到。尽管如此，关于无球粒陨石磁化的证据是丰富的，这表明许多星子的核心以某种方式被磁化了。由于这样的小天体在低重力下迅速冷却，它们的大部分进化时间可能都在一个大的、压实的、部分熔化的糊状区域中度过。可变形部分熔融区的磁流体动力学行为可以通过固相和液相的分离产生磁性，相反，磁性可以对糊状区的相分离施加额外的力。为此，我们为可变形的糊状物和泥浆开发了一种新的两相磁流体动力学理论。该模型包括洛伦兹力的标准效应，以及磁场拉伸和扩散之间的竞争。在液体孔隙或固体颗粒尺度上还有其他影响，涉及相之间的相互作用，类似于达西或斯托克斯阻力；这些包括洛伦兹阻力，以及固相和液相之间磁性的孔隙/颗粒尺度扩散交换，以及由于相之间的相对运动引起的场拉伸。由重力相分离引起的磁感应在液相和固相广泛混合后最为显着，例如由于潮汐和椭圆不稳定性或与其他物体的碰撞而引起的剧烈机械搅拌，所有这些在地球上都很常见。小行星带，尤其是在太阳系早期。发生此类事件后的重力相分离会在液相和固相中产生显着的磁性，并且比大规模循环产生的磁化速度快得多。在充分混合的浆液的初始重力相分离期间，磁场变化可能比施加的背景场大一个数量级。随着相向顶部或底部分离，固相压缩，分离速度降低，并且磁场变化同样减小。然而，压实区域中的孤立波会在液体中引起额外的大磁感应，以强磁化波包的形式存在于固体中。因此，相分离、偏析和压实可能会引起大的磁场异常。还探讨了多孔介质（具有刚性基质）中对流的线性稳定性分析。发现孔隙和晶粒尺度效应，例如由于相分离引起的场拉伸，会增强磁场对对流不稳定性的影响。相分离、偏析和压实可能会引起大的磁场异常。还探讨了多孔介质（具有刚性基质）中对流的线性稳定性分析。发现孔隙和晶粒尺度效应，例如由于相分离引起的场拉伸，会增强磁场对对流不稳定性的影响。相分离、偏析和压实可能会引起大的磁场异常。还探讨了多孔介质（具有刚性基质）中对流的线性稳定性分析。发现孔隙和晶粒尺度效应，例如由于相分离引起的场拉伸，会增强磁场对对流不稳定性的影响。