A homogenization algorithm for randomly distributed microstructures is applied to develop a mass diffusion model for dry snow. Homogenization is a multiscale approach linking constituent behavior at the microscopic level—among ice and air—to the macroscopic material—snow. Principles of continuum mechanics at the microscopic scale describe water vapor diffusion across an ice grain's surface to the air‐filled pore space. Volume averaging and a localization assumption scale up and down, respectively, between microscopic and macroscopic scales. The model yields a mass diffusivity expression at the macroscopic scale that is, in general, a second‐order tensor parameterized by both bulk and microstructural variables. The model predicts a mass diffusivity of water vapor through snow that is less than that through air. Mass diffusivity is expected to decrease linearly with ice volume fraction. Potential anisotropy in snow's mass diffusivity is captured due to the tensor representation. The tensor is built from directional data assigned to specific, idealized microstructural features. Such anisotropy has been observed in the field and laboratories in snow morphologies of interest such as weak layers of depth hoar and near‐surface facets.

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利用织物张量表征各向异性的干雪质量扩散模型

应用随机分布的微观结构的均质化算法来建立干雪的质量扩散模型。均质化是一种多尺度方法，将微观水平（冰和空气）中的成分行为与宏观材料（雪）相关联。微观尺度上的连续力学原理描述了水蒸气通过冰粒表面扩散到空气填充的孔隙空间。体积平均和本地化假设分别在微观和宏观尺度之间增大和减小。该模型在宏观尺度上产生质量扩散率表达式，即通常由体积和微观结构变量参数化的二阶张量。该模型预测水蒸气在雪中的质量扩散率小于在空气中的质量扩散率。预计质量扩散率会随着冰体积分数线性降低。由于张量表示，捕获了雪的质量扩散率中的各向异性。张量是根据分配给特定的理想化微结构特征的方向数据构建的。在野外和实验室中，在感兴趣的雪状形态（如薄弱的深层灰层和近地表小面）中都观察到了这种各向异性。