The method of granular dynamics has been used to study the processes of compaction of nanoscale powder systems. The density-pressure compaction curves have been calculated, the elastic and plastic contributions to the deformation have been highlighted, and the elastic moduli have been determined; the applicability of the isotropy approximation has been analyzed. In the space of stress tensor invariants, a yielding surface of a nanosized powder has been constructed, the applicability limits of the traditional associated rule have been investigated, and an alternative plastic flow rule with a wider applicability region has been proposed. The processes of high-speed compacting have been investigated. The dependence of the pressing pressure on the strain rate has been established in the form of a power law with an index of 1/8. The obtained velocity dependence has been used to interpret experimental data on high-speed magnetic pulse pressing of nanopowders.
The original method of Brownian dynamics for the numerical analysis of the processes of coagulation of nanoscale suspensions is developed. The rate of coagulation is analyzed theoretically and in the framework of computer modeling. Analytical expressions that determine the rate of stationary coagulation of nanoparticles suspended in a solvent (dna /dt where na is the particle concentration) and the characteristic coagulation time θ = -na/(dna /dt) are proposed. In contrast to the traditionally used ratios, the obtained expressions allow us to describe with high accuracy the rate of stationary coagulation not only of weak solutions, when the volume content of nanoparticles ρ ≪1%, but also of sufficiently highly concentrated suspensions, at ρ ≈1% and above (ρ=nava where va is the volume of one particle). Analytical expressions are written for cases of three-dimensional geometry, which is relevant for working with real solutions, and two-dimensional geometry, which is convenient for comparison with the corresponding results of numerical modeling. Computer experiments were performed using the two-dimensional stochastic dynamics method. A satisfactory agreement of the obtained theoretical expressions with the results of numerical calculations is demonstrated. The dependence of the coagulation time on the height of the interparticle energy barrier and on the concentration of the solution is analyzed. It is shown that, in contrast to the theoretical expressions obtained, the traditionally used ratios for highly concentrated suspensions (ρ ≈1%) overestimate the characteristic coagulation times by more than an order of magnitude.
