Abstract: According to the Einstein diffusion equation，the effective diffusion coefficient of nano-fluid in biological tissues is calculated using the Monte Carlo method. The biological tissues are assumed as porous media by observing their anatomical structures. The influences of some key structural factors of porous media on the effective diffusion coefficient of nano-fluid are analyzed. The considered structural factors include shape (i.e. circle，ellipse)，size，and permutation (i.e. parallel permutation and compartmental permutation). The results indicate that the effective diffusion coefficient of nano-fluid in circular porous media are greater than that in ellipsoidal ones and it increases in proportion to the porosity of porous media. Moreover，the increase of inclusion size under the same porosity leads to the decrease of the effective diffusion coefficient. In addition，it is found that a phenomenon of “pocket effect” is existed during the transport process of nano-fluid in porous media when the sizes of pores are comparatively smaller than that of the inclusions. The particles will be trapped in this kind of “pocket shape” without getting out of it，which will drastically decrease the effective diffusion coefficient of nano-fluid. The simulation results are in good agreement with the calculated values obtained from theoretical formula，and the validity of this method is verified by the experimental data from references.

Key words: nano-magnetic fluid, Monte Carlo simulation, porous media, effective diffusion coefficient

摘要： 基于肿瘤热疗研究方向，将生物组织提炼成多孔介质，采用Monte Carlo方法对纳米流体在生物组织内的有效扩散系数进行了数值模拟，并分析了各种不同多孔结构（圆形、椭圆形）、不同大小、不同排列方式等结构因素对有效扩散系数的影响。发现纳米微粒在多孔介质内的扩散过程中存在“口袋效应”。模拟结果与理论公式相符，并通过实验数据验证了该方法的正确性。

关键词: 纳米流体, Monte Carlo方法, 多孔介质, 有效扩散系数