Coupling Stokes Flow with Inhomogeneous Poroelasticity
Coupling Stokes Flow with Inhomogeneous Poroelasticity
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非均匀孔隙弹性耦合斯托克斯流
DOI：
10.1093/qjmam/hbab014
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Taffetani M
中科院分区：
文献类型：
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作者：
Taffetani M
我们调查的行为通量驱动流通过一个单相流体域耦合到一个两相多孔弹性域。流体域由不可压缩的牛顿粘性流体组成，而多孔弹性域由填充有相同粘性流体的线弹性固体组成。多孔弹性域的材料性质，即渗透率和弹性参数，取决于非均匀的初始孔隙度场。我们确定的无量纲参数的行为的耦合问题：驱动速度和达西流的幅度之间的比率在多孔弹性域，和之间的比率的粘性压力尺度和大小的弹性应力在多孔弹性域。我们考虑一个灌注系统，其中流动被迫从单相流体传递到两相多孔弹性域。我们专注于一个简化的二维几何形状与小的纵横比，并进行渐近分析，推导出解析解。细长的几何形状分为四个区域，两个外部域，描述远离接口的区域和两个内部域，是跨接口的区域。我们的分析提出了定量的理解的作用时，耦合到流体域的多孔弹性域的力学响应的非均质材料的属性。分析表明，在界面区，流体和弹性行为的耦合斯托克斯-多孔弹性问题可以分别处理通过（i）斯托克斯-达西耦合和（ii）固体骨架应力自由。后一个发现是至关重要的，以获得耦合条件跨越外部域的弹性部分的多孔弹性域和流体流动。通过对非均匀材料性质分布的描述，我们揭示了非均匀性和变形性对多孔弹性域力学的影响。
We investigate the behaviour of flux-driven flow through a single-phase fluid domain coupled to a biphasic poroelastic domain. The fluid domain consists of an incompressible Newtonian viscous fluid while the poroelastic domain consists of a linearly elastic solid filled with the same viscous fluid. The material properties of the poroelastic domain, that is permeability and elastic parameters, depend on the inhomogeneous initial porosity field. We identify the dimensionless parameters governing the behaviour of the coupled problem: the ratio between the magnitudes of the driving velocity and the Darcy flows in the poroelastic domain, and the ratio between the viscous pressure scale and the size of the elastic stresses in the poroelastic domain. We consider a perfusion system, where flow is forced to pass from the single-phase fluid to the biphasic poroelastic domain. We focus on a simplified two-dimensional geometry with small aspect ratio and perform an asymptotic analysis to derive analytical solutions. The slender geometry is divided in four regions, two outer domains that describe the regions away from the interface and two inner domains that are the regions across the interface. Our analysis advances the quantitative understanding of the role of heterogeneous material properties of a poroelastic domain on its mechanical response when coupled with a fluid domain. The analysis reveals that, in the interfacial zone, the fluid and the elastic behaviours of this coupled Stokes—poroelastic problem can be treated separately via (i) a Stokes–Darcy coupling and (ii) the solid skeleton being stress free. This latter finding is crucial to derive the coupling condition across the outer domains for both the elastic part of the poroelastic domain and the fluid flow. Via specification of heterogeneous material properties distribution, we reveal the effects of heterogeneity and deformability on the mechanics of the poroelastic domain.