Monte Carlo Simulation Of Fractal Aggregation In An Open System

Fractal is an important part of nonlinear science.The structure of fractal object often exhibits self-organization and self-similarity.Fractal aggregation is one of the important research topics of fractal science,which is widely existed in the fields of physics,chemistry and biology.And the research on the structural characteristics of fractal aggregation and the dynamics aggregation process has gradually received peoples' attention.In a closed colloidal suspension system,if the influence of external environment is ignored,the particles in the system will collide with each other and aggregate gradually due to the random Brownian motion,which finally make the system reach some steady state.But most systems in nature are not closed but accompanied by the exchange of matter and energy.For example,the evaporation of water,the infiltration,the addition of the outer edge electrolyte,the influence of gravity field,etc.can affect the structure characteristics of the aggregates,and even affect the dynamics aggregation process.This kind of system in which material and energy exchange with the outside world is often called an open system.In an open system,the aggregation process of particles is affected by various factors,and the previous research is often developed in a closed system which often just consider single factor,it cannot explain the law of particle motion.In this thesis,the conditions of fractal condensation of particles in evaporation,infiltration and gravity systems and their condensation kinetics are studied by Monte Carlo method.Due to the random nature of the aggregation process,it is difficult to observe the regularities underlying random phenomena in conventional test methods.Today,computer simulation has become the third scientific research method after theoretical derivation and experimental research.The Monte Carlo method is a computer simulation method,which is suitable for simulating particle motion with large scales.In this thesis,the Monte Carlo method is used to study the conditions of particle aggregation and the features of its aggregation dynamics in the system under evaporation,infiltration and gravity field.The relevant works are as follows:(1)Based on the lattice simulation system,a unified model of fractal aggregation is constructed and extended to apply to the open system.Firstly,the aggregate process of particles is abstracted into two steps: diffusion and collision.Based on this idea,a unified model of fractal cohesion is constructed.Secondly,a corresponding simulation software is developed in Java language,it provides the function of the visualization of the aggregation process by Java 3D technology,and the function of real-time statistics on the aggregation process.Finally,based on this unified model,the diffusion coefficient and aggregation probability of particles are set as a function of time,then a conceptual model suitable for open systems is constructed.(2)Based on the conceptual model applicable to the open system,a fractal aggregation model suitable for the evaporation system is constructed.In the evaporation system,there are two main factors affecting particle motion: the Brownian motion of the particles and the downward movement of surface particles caused by evaporation of surface water.The results show that the above two motions have competitive relationship,they play a dominant role in different aggregation periods.When system is under slow evaporation rate,there is little difference between the aggregation process compared and the basic model;when system is under fast evaporation rate,evaporation has a significant acceleration effect on the aggregation process.(3)Based on the conceptual model applicable to the open system,a fractal aggregation model suitable for the infiltration system is constructed.In the infiltration system,there are two factors that affect the particle motion: the Brownian motion of the particle and the downward movement of the whole system particle caused by the loss of water,and there is also a competitive relationship between the two motion.The results show that,when the simulation is under fast aggregation conditions,the clusters would have a bigger chance to form large clusters.However,with the infiltration rate increased and the movement of the fluid-driven clusters intensified,the cluster movement would be affected to a greater extent in the vertical direction.The results also show that,when simulation is under slow aggregation conditions,particle motion would be mostly dominated by infiltration,and a dense agglomerate would be formed in the bottom eventually.(4)Based on the conceptual model applicable to the open system,the fractal condensation model under the action of gravity field is constructed.Based on the gravity settlement model of the off-lattice simulation system constructed in previous research,by considering the competition mechanism of aggregation and settlement,a gravity settlement model suitable for describing the lattice simulation system is constructed.The results show that the cluster size and the value of the Peclet are the key factors affecting the gravity sedimentation.The larger the cluster,the more obvious the effect of gravity.The larger the Peclet number,the more obvious the gravity settlement of the whole system.In general,the Monte Carlo simulation model constructed in this study suits for describing fractal aggregation of general colloidal systems,and also suits for describing fractal aggregation in open systems.Its application in evaporation,infiltration and gravity field simulation systems verify the reliability and flexibility of the simulation software.The simulation software provided by this research has a friendly interface and strong interactivity,which can provide technical support for relevant scholars to study the fractal aggregation of nanoparticle systems.