THE STRUCTURE OF AGGREGATES AND THE MOLECULAR KINEMATICS OF THE VISCOSITY OF A BERNAL LIQUID

Abstract

The structure of 3-dimensional aggregates is discussed as a set of points on which graphs are constructed. By constructing the Voronoi honeycomb (Dirichlet regions) for the points and applying a small "irregularizing transformation", a "simplicial graph" and a "primitive coordination number" (whose value is close to 14 for all aggregates) can be defined universally for both regular and irregular aggregates. Recent studies of the geometry of irregular aggregates (of steel balls, crystal grains, etc.) are reviewed. The theory of liquids of J. D. Bernal is discussed and the simplicial graph is used to show that the "activation volume" of a Bernal liquid is about one-tenth of the molecular volume. The kinematics of flow of aggregates is discussed in terms of their graphs and in terms of a process of "volume exchange"—the production and destruction of free volume. Using these concepts, an equation is derived for the viscosity of a Bernal liquid as a product of five terms expressing respectively the kinematic, stoichiometric, kinetic, pressure-dependent, and shear-dependent factors.