Simultaneous melting and compaction in deformable two-phase media
Simultaneous melting and compaction in deformable two-phase media
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可变形两相介质中的同时熔化和压实
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
D. Bercovici
中科院分区：
文献类型：
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作者：
O. Šrámek;Y. Ricard;D. Bercovici
概述熔体的产生和提取通常使用McKenzie或Scott和Stevenson开发的两相方程来建模。为了简化问题，经常进行各种近似，这可能会导致一些非物理结果(例如，热力学上不一致的熔化条件和不切实际的孔隙率分布)。我们讨论了Bercovici等人介绍的方程组的一个推广版本。这允许单组分系统中两相之间的质量传递，并考虑一组自洽的方程。在我们的描述中，固体和熔体这两个相被提交给单独的压力场，压力场的差异与界面上的表面张力、孔隙率的变化和熔化速度有关。熔化速度的动力学关系式源于热力学第二定律。当基质和熔体不动时，化学平衡的条件对应于各相化学势的通常单变量相等。在最一般的形式中，相平衡受Gibbs-Thomson效应和相的粘性变形的影响，Gibbs-Thomson效应是从热力学角度考虑表面张力而自然产生的。我们将这些新的方程应用于单变量系统中压力释放熔化的稳态问题。我们同时处理熔化和压实，并观察到几个新的效应，包括熔化开始附近的多个区域，这些区域对应于不同的力平衡。基质压实和熔体排出(或基质膨胀和熔体积累)的结果是熔体和固体之间的压差促进(抑制)熔化。对于与大洋中脊岩浆作用相对应的参数，压实作用允许熔融开始，最高可达标准固相线以下2k米的∼。为了确定熔体区域移动的大小，需要数值解。数值结果支持解析得到的边界层解，并表明在大部分熔融区，熔体和基质的运动应接近达西平衡，此时熔体的浮力由两相之间的粘性阻力来平衡。达西平衡遵循的初始阶段是基质粘性应力平衡达西阻力的阶段。在所有情况下，稳态孔隙度剖面仍然是深度的单调函数。在各种早期出版物中所描述的孔隙率最大的熔融区之后，从来没有发现过紧实层的存在。
SUMMARY Melt generation and extraction are typically modelled using the two-phase equations developed by McKenzie or Scott and Stevenson. Various approximations are often made to simplify the problem which may lead to some unphysical results (e.g. thermodynamically inconsistent conditions of melting and unrealistic porosity profiles). We discuss a generalized version of the set of equations introduced by Bercovici et al. that allows for mass transfer between the two phases in a single component system and consider a self-consistent set of equations. In our description the two phases, solid and melt, are submitted to individual pressure fields whose difference is related to the surface tension at the interfaces, changes in porosity and the melting rate. A kinetic relation for the melting rate arises from the second law of thermodynamics. The condition of chemical equilibrium corresponds to the usual univariant equality of the chemical potentials of each phase when the matrix and melt are motionless. In the most general form, phase equilibrium is influenced by both the Gibbs‐Thomson effect that arises naturally from thermodynamic considerations on surface tension and by the viscous deformation of the phases. We apply these new equations to a steady state problem of pressure release melting in a univariant system. We treat melting and compaction simultaneously and observe several new effects including multiple domains near the onset of melting that correspond to various force balances. A consequence of matrix compaction and melt expulsion (or matrix dilation and melt accumulation) is a pressure difference between melt and solid that facilitates (inhibits) melting. For parameters corresponding to mid-oceanic ridge magmatism, compaction permits melting to start as much as ∼ 2k m below the standard solidus. Numerical solutions are necessary to determine the magnitude of the melt zone shift. Numerical results support the boundary layer solutions obtained analytically and suggest that in most of the melting zone the movement of melt and matrix should be close to the Darcy equilibrium where the buoyancy of melt is balanced by the viscous drag between the phases. The Darcy equilibrium follows an initial stage where the matrix viscous stresses balance Darcy drag. In all situations the steady state porosity profile remains a monotonic function of depth. The existence of a compaction layer following a melting zone where the porosity is maximum as described in various earlier publications has never been found.