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多孔介质中的输运过程,如导热、渗流过程,关注的是热量从高温壁面穿过介质到达低温壁面、流体从多孔介质的边界沿孔隙流到另外一端的过程。此类现象可归结为载流子在多孔介质通道(基质或孔隙)中沿外部势差方向的运动过程。多孔介质通道具有分形特征,可以采用分形维数来描述其通道的通透性。本文基于现象的相似性特征,提出并发展了粒子在多孔介质中的方向随机行走模型,用粒子在基质中的方向随机行走过程来模拟真实的热流传输过程;根据分形统计规律得到粒子方向随机行走分形谱维数,并用其描述基质结构的连通性和方向性。研究结果表明,在孔隙率相同情况下,粒子在基质中的方向随机行走分形谱维数与有效导热系数大小有相同的变化趋势。
The transport process in porous media, such as heat transfer and seepage process, focuses on the process that heat flows from the high temperature wall to the low temperature wall through the medium and flows from the boundary of the porous medium to the other end. This phenomenon can be attributed to the movement of carriers in the direction of the external potential difference in porous media channels (matrix or voids). Porous media channels have fractal characteristics, and fractal dimensions can be used to describe the permeability of their channels. In this paper, we propose and develop a random walk model of particles in porous media based on the similarities of the phenomena. We simulate the real heat flow process by random walking process of particles in the matrix. According to the fractal statistical rules, Fractal spectrum dimensionality, and use it to describe the connectivity and orientation of the matrix structure. The results show that the fractal dimension of random walk in the direction of particles has the same trend with the effective thermal conductivity at the same porosity.