Dynamics Of Random Packings Of Micro-particles In Presence Of Van Der Waals Force

The random packings of non-Brownian particles ubiquitously exist in our daily life and industrial processes,e.g.,the storage of granular matter in the barn,the dust removal in the electrostatic precipitator,the deposition of fly ash in the boiler,the deposition and adhesion of interstellar dust,etc.Extensive studies have been conducted on the packing of granular materials,which are usually of millimeter-sized and dominated by gravity.However,due to the size effect,the van der Waals forces between small micron-sized particles,which are always three orders of magnitude greater than the gravity,become the most important interaction.So far,very limited investigations have been performed on the packing problems of such micro-particles due to the complex interactions.This work presents a systematic and elaborate investigation on the packings of small micron-sized particles,by the means of discrete element dynamics simulations based on the adhesive contact mechanics.Statistical mechanics ensemble approach,which is applicable to describe the packing structures of micro-particles,is also developed from the framework of statistical mechanics theory of granular system.In addition,packing experiments on the basis of high efficiency filter are conducted to verify the results obtained from both the simulations and theoretical predictions.Firstly,we apply a mesoscopic adhesive discrete element method(Adhesive DEM)to simulate the dynamic process of micro-particle packing.The influences of the particle size distribution,surface energy,velocity,friction coefficient as well as the shape factor are systematically considered and incorporated.A dimensionless adhesion number is employed to lump together the effects of the above factors.By measuring the packing fraction,coordination number,the radial distribution function and the angular distance distribution function,we establish the physical relation between the achieved packing structure and the adhesion number.Furthermore,we perform mechanical equilibrium analysis on the single particle in the packing and obtain the equilibrium phase diagram,which accounts for the mechanical stability of the loose packing structures.Secondly,based on the framework of the statistical mechanics theory of granular system proposed by Edwards,we develop the statistical mechanics ensemble approach to theoretically describe the micro-particle packing structures.With this approach,we derive the equation of state of micro-particle packing with arbitrary friction and adhesion,and thus extend the phase diagram of granular packing to the adhesive branches.By generalizing the Maxwell counting arguments,new isostatic limits for adhesive packings are put forward.Hence,together with the two well-known packing limits RCP and RLP,we expand them to two new packing limits ACP and ALP,and redefine them with respect to the friction coefficient and adhesion number.Finally,we perform experiments by packing micron-sized silicon dioxide particles with lognormal size distribution on a stainless filter and study the effects of particle size and velocity on the packing fraction.Through the normalization with the above adhesion number,we compare the experimental results with both simulations and theories to verify their validity.