Abstract We analyze a two-phase porous medium whose permeability and solid viscosity are dependent on porosity. It has been established experimentally and numerically that when such a medium is subjected to shear, the porosity rearranges into stripes of high and low porosity known as melt bands (Holtzman et al., 2003; Katz et al., 2006; Butler, 2009). This study uses linear theory and numerical simulations to analyze the effect of ongoing melting and buoyancy forces on the formation and evolution of melt bands. Previously, the consequences of internal melting have not been quantified and studies including buoyancy forces have conflicting interpretations (Katz, 2010; Butler, 2009). In this study, we show that the inclusion of internal melting significantly decreases the amplitude of these bands if the bulk viscosity is constant, but has a minimal effect on the amplitude when the bulk viscosity decreases with porosity. Most recent studies indicate that bulk viscosity likely strongly decreases with porosity, indicating that ongoing melting does not preclude the existence of significant melt bands in Earth's upper mantle. Buoyancy forces are shown to induce an oscillation of the bands with no effect on amplitude. We also show that isotropic expansion driven by melting and density differences between the solid and liquid can drive a porosity localizing instability.

中文翻译：

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持续熔化和浮力对致密多孔层熔体带演化的影响

摘要 我们分析了渗透率和固体粘度取决于孔隙率的两相多孔介质。已经通过实验和数值确定，当这种介质受到剪切时，孔隙率会重新排列成高孔隙率和低孔隙率的条纹，称为熔体带（Holtzman 等人，2003 年；Katz 等人，2006 年；巴特勒，2009 年） . 本研究使用线性理论和数值模拟来分析持续熔化和浮力对熔体带形成和演化的影响。以前，内部融化的后果尚未量化，包括浮力在内的研究有相互矛盾的解释（卡茨，2010 年；巴特勒，2009 年）。在这项研究中，我们表明，如果体积粘度不变，包含内部熔化会显着降低这些带的幅度，但当体积粘度随孔隙率降低时，对振幅的影响很小。最近的研究表明，体积粘度可能会随着孔隙度的增加而强烈降低，这表明持续的熔化并不排除地球上地幔中存在显着的熔体带。显示浮力会引起带的振荡，而对振幅没有影响。我们还表明，由固体和液体之间的熔化和密度差异驱动的各向同性膨胀可以驱动孔隙率局部不稳定性。显示浮力会引起带的振荡，而对振幅没有影响。我们还表明，由固体和液体之间的熔化和密度差异驱动的各向同性膨胀可以驱动孔隙率局部不稳定性。显示浮力会引起带的振荡，而对振幅没有影响。我们还表明，由固体和液体之间的熔化和密度差异驱动的各向同性膨胀可以驱动孔隙率局部不稳定性。