发表机构
University of Trento（特伦托大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建非饱和土壤水统计力学理论，通过多尺度方法得出孔隙占有率连续场方程，引入孔隙分辨达姆科勒数统一现象学，简化得到理查兹方程等，揭示滞后和优先流特性，输入基于孔隙网络几何属性，无需宏观数据校准。
AI 中文摘要
我们建立了一个非饱和土壤水的统计力学理论，其结果是孔隙占有率\(g(r,x,t)\)的连续场方程，\(g(r,x,t)\)表示在位置\(x\)和时间\(t\)时半径为\(r\)的充满水的孔隙分数。该理论跨越三个尺度构建：微观尺度上，孔隙间转移由哈根 - 泊肃叶速率和驱动势（孔隙类化学势之差，采用毛细 - 重力形式，但可进行吸附、渗透或热细化）设定；中尺度主方程使占有率向平衡步长\(g_{eq}=H(r^*-r)\)松弛；在将平均体积收缩到一点时，得到连续平衡方程\(\partial_t g+\nabla\cdot F = C[g]-E - T\)，其他部分均为极限、矩或边界分辨率。动力学方程是沿着吉布斯自由能下降的昂萨格梯度流，对于等温无外力系统有\(H\)定理且质量守恒为其零阶矩。一个无量纲群，即孔隙分辨达姆科勒数\(Da(r,x)\)，组织了行为并统一了长期以来分别建模的现象学。查普曼 - 恩斯科格简化将理查兹方程确定为准静态（\(Da\to0\)）极限，基质势和水力传导率\(K\)仅在该极限下出现且\(K\)在渗流阈值以下消失；毛细管束和临界路径模型是其对角和谱极限。滞后是强迫束的全同性，是几何相位而非每个孔隙的双稳性，有可证伪的回路面积定律\(H\sim I^2\)。优先流是\(Da>1\)时同一方程的表现，所以理查兹/优先流二分法成为由\(Da\)控制的连续交叉。在准静态极限之外，\(g(r)\)是不可约状态变量。所有输入都是孔隙网络的几何属性，可从微观CT测量且无需宏观数据校准。
英文摘要
We develop a statistical-mechanical theory of water in unsaturated soil whose outcome is a continuum field equation for the pore-occupancy g(r,x,t), the fraction of pores of radius r that are water-filled at position x and time t. The theory is built across three scales: microscopic inter-pore transfers set by Hagen-Poiseuille rates and a driving potential (the difference of pore-class chemical potentials, taken in capillary-gravitational form but open to adsorptive, osmotic, or thermal refinement); a mesoscale master equation relaxing the occupancy toward the equilibrium step g_eq=H(r*-r); and, on contracting the averaging volume to a point, the continuum balance d_t g + div F = C[g] - E - T, of which everything else is a limit, a moment, or a boundary resolution. The kinetic equation is an Onsager gradient flow descending the Gibbs free energy, with an H-theorem for the isothermal unforced system and mass conservation as its zeroth moment. A single dimensionless group, the pore-resolved Damkohler number Da(r,x), organizes the behavior and unifies phenomenologies long modelled separately. A Chapman-Enskog reduction identifies Richards' equation as the quasi-static (Da->0) limit, with matric potential and hydraulic conductivity K emerging only there and K vanishing below the percolation threshold; capillary-bundle and critical-path models are its diagonal and spectral limits. Hysteresis is the holonomy of a forcing bundle, a geometric phase rather than per-pore bistability, with a falsifiable loop-area law H ~ I^2. Preferential flow is what the same equation does where Da>1, so the Richards/preferential-flow dichotomy becomes a continuous Da-controlled crossover. Out of the quasi-static limit g(r) is the irreducible state variable. All inputs are geometric properties of the pore network, measurable from micro-CT and calibrated against no macroscopic data.
CommentsMain paper plus supplemental material
