用分形理论研究粘土的粒度分布特征

AN INVESTIGATION ON CHARACTERISTICS FOR PARTICLE SIZE DISTRIBUTION OF CLAYS IN DRILLING MUDS BY THE WAY OF FRACTAL GEOMETRY

应用当代数学新理论———分形几何学方法研究了几种粘土体系的粒度分布特征，发现粘土的粒度分布具有分形结构，可借分维进行定量表征。

The characteristics of particle size distribution of some clay system, i.e. clay muds, are studied by determining and comparing their values of fractal dimension, D f. There exists a linear relationship between the accumulative content of clay particles in the systems with particle size ≥r and the particle size r in ln ln plots and the value of D f is readily determined from the slop, β, of the linear line according to the equation: D f=3-β. The physical meanings of D f is extensively discussed in terms of a lot of rheologic data of some clay muds published in the literature. The fractal dimension, D f, is recommended as a useful characteristic for describing the particle size distribution of the clay in drilling muds.