Brownian Motion of Aerosol Particles

Particles suspended in a fluid are continuously bombarded by the surrounding fluid molecules. This constant bombardment results in a random motion of the particles known as Brownian motion. A satisfactory description of this irregular motion ( random walk ) can be obtained ignoring the detailed structure of the particle-fluid molecule interaction if we assume that what happens to the aerosol fluid system at a given time t depends only on the system state at time t. Stochastic processes with this property are known as Markov processes. 

Let us consider a particle that is initially at the origin of our coordinate system. Assuming that the only force acting on the particles is that resulting from molecular 

Equations (9.35) and (9.47) provide a convenient framework for the analysis of forces acting on particles. These equations simply state that the acceleration experienced by the particle is proportional to the sum of forces acting on the particle. We have used this equation so far for deterministic forces, namely, the gravity, drag, and electrical forces. We now need to use the stochastic Brownian force, which is simply the product of the particle mass mp and the random acceleration a caused by the bombardment by the fluid molecules. Then the equation of motion is 

Then ensemble averaging this equation (over many particles) gives 

Since we assume that there is no preferred direction in a (directional isotropy of collisions), (r a) will be equal to zero, giving 

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An important consequence of the Brownian motion of aerosol particles is their collision and subsequent coalescence. This so-called coagulation process can be characterized by the particle loss per unit time (Hidy and Brock, 1970) ... 

Washout by rain greatly reduces the Aitken nuclei mode and the coarse particle mode but has little effect on the accumulation mode in the trimodal size distribution (Whitby, 1975). The origin of each mode of atmospheric aerosol size distribution can be associated with various aerosol formation mechanisms, such as Brownian motion of the particles smaller than 0.1 pm in diameter, which causes the particles to diffuse and by collisions to coagulate to larger sizes. Coagulation generates multimodal distributions and affects the shape and the chemical composition of the particles. 

A model for Brownian coagulation of equal-sized electrically neutral aerosol particles is proposed. The model accounts for the van der Waals attraction and Born repulsion in the calculation of the rate of collisions and subsequent coagulation. In this model, the relative motion between two particles is considered to be free molecular in the neighborhood of the sphere of influence. The thickness of this region is taken to be equal to the correlation length of the relative Brownian motion. The relative motion of the particles outside this region is described... 

As pointed out earlier, the present treatment attempts to clarify the connection between the sticking probability and the mutual forces of interaction between particles. The van der Waals attraction and Bom repulsion forces are included in the analysis of the relative motion between two electrically neutral aerosol particles. The overall interaction potential between two particles is calculated through the integration of the intermolecular potential, modelled as the Lennard-Jones 6-12 potential, under the assumption of pairwise additivity. The expression for the overall interaction potential in terms of the Hamaker constant and the molecular diameter can be found in Appendix I of (1). The Brownian motions of the two particles are no longer independent because of the interaction force between the two. It is, therefore, necessary to describe the relative motion between the two particles in order to predict the rate of collision and of subsequent coagulation. 

A very characteristic property of aerosol particles is their Brownian motion. This random motion is a result of the fluctuations in the impact of gas molecules on the particles. It goes without saying that the speed of this motion increases with decreasing size. Generally, Brownian motion is considered significant if the particle radius is smaller than 0.S pm. 

The concentration distribution of aerosol particles in a stagnant fluid in which the particles are subject to Brownian motion and in which there is a velocity v, in the -z direction is described by... 

The concept of mean free path is an obvious one for gas molecules. In Ihe Brownian motion of an aerosol particle there is not an obvious length that can be identified as a mean free path. This is depicted in Figure 9.11 showing plane projections of the paths followed by an air molecule and an aerosol particle of radius roughly equal to 1 pm. The trajectories... 

As emphasized by HIDY and BROCK [2.6] an important feature of an aerosol is the random motion of the particles known as Brownian motion. The study of Brownian motion has a long history and has played a key role in the development of modern statistical physics. 

The aerosol model In VICTORIA accounts for the following basic mechanisms (1) condensation or evaporation from aerosol particle surfaces (2) deposition onto structural surfaces (3) agglomeration of aerosol particles (4) and transport of aerosols from one cell to another by advection. The deposition mechanisms modeled are gravitational settling, laminar or turbulent deposition. Brownian motion, thermophoresis, diffusiophoresis, and inertial deposition in curved channels (bends). Agglomeration mechanisms include Brownian motion, relative gravitational motion. Interactions In a shear field, and inertia in a turbulent field. 

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