# Two-Parameter Probabilistic Model and Experimental Research on Micron Particle Deposition
## Particle Deposition Model
### Two-Parameter Particle Probability Deposition Model
#### 2.3.2 Determination of Collision Probability of Particle Deposition  
To establish the deposition desorption model of adaptive particle-particle deposition wall and particle-particle deposition layer collision, firstly, the collision process between the particles and deposition layer should be analyzed, and the motion state judgment of particles and deposition layer collision based on the two-parameter particle deposition desorption judgment criterion proposed above can be realized by modifying the characteristic parameters of the particles. Then, by introducing the collision probability coefficient \(P_{P}\) of the particles, the judgment criteria for the collision of particles entering the near-wall region are determined, so that the particle deposition desorption models of adaptive particle-particle deposition wall collision and particle-particle deposition layer collision are established. Collision between the particles and sedimentary layer is similar to the collision process with sedimentary wall surface. As shown in Figure 3, particles actually collide with particles adhered to and deposited on the sedimentary layer. At this time, the collided-with sedimentary particles (with plastic deformation) are difficult to desorb (bounce or move horizontally) due to collision impact of particles, due to the adhesion force of the surrounding sedimentary particles and deposited wall surface. It can be assumed that they are inherent parts of the sedimentary wall surface, as shown in Figure 3a. Therefore, considering only the collision between particles and a single deposited particle, due to the symmetry of particle spherical morphology, the maximum stress of this collision process always exists on the line connecting the spherical centers of two particles. The deposition desorption judgment of this collision can be approximately described by Section 2.2.2. When the discrete particles are spherical particles with a uniform particle size, the parameters such as the curvature radius, elastic modulus, and Poisson's ratio of the contact surface between the particles and deposited particles are the same, which can further simplify the two-parameter particle deposition desorption criterion. As for the collision between particles and deposited particles, it belongs to two-dimensional eccentric collision on an x-y plane, as shown in Figure 3b. In order to simplify the calculation process, the sinking scale of the particle center of the plastic deformation of the deposited particles at this time can be taken as a critical sinking scale (i.e., \(h=h_{el}\)), and the distance between the particles and deposited wall surface is l, so the incident angle \(\theta_{i}\)\({}^{\prime}\) of the particles relative to the deposited particles can be expressed as,  
\[\theta_{i}\)\({}^{\prime}=\theta_{i}-\cos^{-1}\frac{l-d_{P}+h_{el}}{2d_{P}} \tag{33}\]  
Substituting the above parameters into the two-parameter particle deposition judgment criteria, it is not difficult to obtain the conditions of the two-parameter particle deposition judgment criteria suitable for particle-particle deposition collision. When particles collide near the wall, the collision object of the particles should be determined, and the corresponding criteria for determining deposition desorption should be selected. The collision probability coefficient \(P_{P}\) between the particles and deposited particles is introduced to describe the collision situation of the particles, and the collision probability coefficient \(P_{P}\) between the particles and deposited particles can be expressed by calculating the percentage of surface area occupied by the deposited particles in a unit wall, such as:  
\[P_{P}=\left\{ \begin{array}{lcl}\frac{N\pi dp}{A_{sub}}\times 100\%&,&0<P_{P}<100 \%\\ 100\%&,&P_{P}\geq 100\%\end{array} \right. \tag{34}\]  
where \(A_{sub}\) is the unit area of the wall surface of the particulate matter deposition; and \(N\) is the number of deposited particles in the unit area.