中文摘要：

依据霜层的结构具有典型的分形特征,建立基于分形理论的水蒸气在霜层中的扩散模型,并求解水蒸气在霜层中的有效扩散系数。模型以孔隙分形维数、通道轴线分形维数、孔隙率、最大和最小孔隙尺度以及水分子在通道两端飞行的直线距离等参数来描述霜层的结构。研究结果表明：该模型较好地反映了霜层孔隙率变化时通道弯曲程度的变化,以及这种变化对于水蒸气扩散的影响;当孔隙率较小时,霜层中孔隙直径较小且通道较弯曲;随着孔隙率增加,有效扩散系数增长较为缓慢;当孔隙率较大时,孔隙率增加可能使小孔隙合并为较大孔隙,导致通道弯曲程度变小,故有效扩散系数增加。

英文摘要：

Based on the fact that frost structure is fractal, the fractal model of water vapor diffusion in frost was established and the effective diffusivity of water vapor in frost was deduced. In this model, many parameters were used to describe frost structure, such as pore fractal dimension, channel axes fractal dimension, porosity, maximum and minimum pore dimension, and minimum distance of channel. The results show that this model embodies properly channel curve’s change and its effects on water vapor diffusion. Effective diffusivity increases slowly with the increase of porosity at lower porosity, because the pore is small and the channel is highly curved. However, effective diffusivity increases rapidly at higher porosity, because the increase of porosity may unite little pores, which makes the degree of the channel curving decline.