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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Application of Minkowski space to description of anisotropic pore space structure in porous materials
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Application of Minkowski space to description of anisotropic pore space structure in porous materials

机译：Minkowski空间在描述多孔材料各向异性孔隙空间结构中的应用

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The subject of this note is the modelling of an anisotropic pore space structure in rigid porous materials capable of fluid flow through its pores. In this paper, the new macroscopic model of a saturated porous medium is proposed in which a fluid flow through porous skeleton of an anisotropic pore structure is considered as a motion of the material continuum in the plane anisotropic metric space - Minkowski space - immersed in a Euclidean one that is used as the model of the physical space. This model takes into consideration the fundamental fact concerning kinematics of a fluid-saturated porous solid, that the pore space of permeable skeleton forms the real space for a fluid motion and its structure imposes restrictions an that motion. The metrics of Minkowski and Euclidean spaces are applied in the paper to determine the respective measures of any line, surface, and volume elements. The new metric tensors of surface and volume elements in these spaces have been proposed that are directly related to the metric tensors of distance. This enables one to define the geometrical parameters characterising pore structure of such materials: the tortuosity, the volume, and surface porosity. It has been shown that the structure of isotropic pore space of porous materials is described only by two independent scalar parameters. [References: 6]
机译：本说明的主题是能够使流体流过其孔的刚性多孔材料中各向异性孔空间结构的建模。在本文中，提出了一种新的饱和多孔介质宏观模型，其中流体通过各向异性孔结构的多孔骨架流动被认为是物质连续体在平面各向异性度量空间-Minkowski空间-浸没在空气中的运动。欧几里得，用作物理空间的模型。该模型考虑了与流体饱和的多孔固体的运动学有关的基本事实，即可渗透骨架的孔空间形成了流体运动的真实空间，并且其结构强加了对该运动的限制。本文将Minkowski和Euclidean空间的度量应用于确定任何线，面和体积元素的相应度量。已经提出了这些空间中的表面和体积元素的新度量张量，它们与距离度量张量直接相关。这使人们能够定义表征此类材料孔隙结构的几何参数：曲折度，体积和表面孔隙率。已经表明，多孔材料的各向同性孔空间的结构仅由两个独立的标量参数来描述。 [参考：6]

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