Auton L C, MacMinn C W
Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK.
Proc Math Phys Eng Sci. 2017 May;473(2201):20160753. doi: 10.1098/rspa.2016.0753. Epub 2017 May 31.
The radially outward flow of fluid into a porous medium occurs in many practical problems, from transport across vascular walls to the pressurization of boreholes. As the driving pressure becomes non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid has an increasingly strong impact on the flow. For very large pressures or very soft materials, as is the case for hydraulic fracturing and arterial flows, this coupling can lead to large deformations and, hence, to strong deviations from a classical, linear-poroelastic response. Here, we study this problem by analysing the steady-state response of a poroelastic cylinder to fluid injection. We consider the qualitative and quantitative impacts of kinematic and constitutive nonlinearity, highlighting the strong impact of deformation-dependent permeability. We show that the wall thickness (thick versus thin) and the outer boundary condition (free versus constrained) play a central role in controlling the mechanics.
流体径向向外流入多孔介质的情况出现在许多实际问题中，从血管壁的物质输送到钻孔的增压。当驱动压力相对于固体结构的刚度变得不可忽略时，流体与固体之间的孔隙力学耦合对流动的影响越来越大。对于非常大的压力或非常软的材料，如水力压裂和动脉血流的情况，这种耦合会导致大变形，从而与经典的线性孔隙弹性响应产生强烈偏差。在此，我们通过分析多孔弹性圆柱体对流体注入的稳态响应来研究这个问题。我们考虑运动学和本构非线性的定性和定量影响，突出与变形相关的渗透率的强烈影响。我们表明，壁厚（厚与薄）和外边界条件（自由与约束）在控制力学方面起着核心作用。
