Similarity Hypothesis for Capillary Hysteresis in Porous Materials
Similarity Hypothesis for Capillary Hysteresis in Porous Materials
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DOI：
10.1029/jz069i008p01553
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发表时间：
1964-04
影响因子：
--
通讯作者：
J. R. Philip
中科院分区：
文献类型：
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作者：
J. R. Philip
通过二元分布密度函数(ƒ(α，β)建立了多孔材料毛细滞后特性的定量描述，其中α和β代表润湿和干燥潜力。这在形式上等同于Poulovassilis的独立域理论。对于Poulovassilis的实验数据，相似性假设(大致上是指干湿弯月面曲率之间的几何关系的分布与孔的大小无关)相当适用。找到相应的h函数并且映射ƒ(α，β)。一般来说，建立ƒ(α，β)是一个费力的过程。然而，对于(A)，可以仅从(常规观察的)干燥和润湿边界曲线中发现(ƒ(α，β)。方程A产生积分方程式，其中j和g是从边界曲线已知的，Ψ0是最小势能，h是未知函数。方程B借助于拉普拉斯变换的Faltung定理求解。由此推论，当(A)成立时，h，从而ƒ(α，β)由边界曲线唯一确定。然而，(B)的解决方案在物理上不一定是可以接受的。通过采用(A)加上h的任意但合理的形式，我们可以从单个边界曲线粗略地估计介质的整个磁滞特性。还需要进一步的实验工作来确定(A)的适用范围。(A)除多孔材料中的吸附作用外，还可适用于滞后过程。
A quantitative description of the capillary hysteresis properties of a porous material is developed through bivariate distribution density function ƒ(α, β), where α and β are wetting and drying potentials. This is formally equivalent to the independent domain theory of Poulovassilis. The similarity hypothesis (implying, loosely, that the distribution of geometrical relationships between wetting and drying meniscus curvatures is independent of ‘pore size’) holds fairly well for Poulovassilis' experimental data. The corresponding h functions are found and the ƒ(α, β) are mapped. In general, the establishment of ƒ(α, β) is a laborious process. However, with (A), ƒ(α, β) may be found from only the (routinely observed) drying and wetting boundary curves. Equation A yields the integral equation where j and g are known from the boundary curves and Ψ0 is the minimum potential, h is the unknown function. Equation B is solved with the aid of the Faltung theorem of the Laplace transformation. It follows that, when (A) holds, h, and hence ƒ(α, β), is uniquely determined by the boundary curves. The solution of (B) is not necessarily physically acceptable, however. By adopting (A) plus an arbitrary, but plausible, form for h, we may roughly estimate the whole hysteresis character of the medium from a single boundary curve. Further experimental work is needed to establish the area of applicability of (A). (A) may apply also to hysteresis processes other than sorption in porous materials.