# Two-Parameter Probabilistic Model and Experimental Research on Micron Particle Deposition
## Particle Deposition Model
### Two-Parameter Particle Probability Deposition Model
#### 2.3.1 Two-Parameter Determination of Particle Deposition
By combining Formulas (12)-(21) and Formula (11), the adhesion energy \(Q_{ar}\) that the particles need to overcome for being desorbed can be expressed as:  
Figure 2:2  
Therefore, the deformation type of the particles is judged according to the deformation variable in which the particles are located; the corresponding contact load \(F\) and contact radius \(r\) are determined; and the elastic energy \(Q_{e}\) stored when the particles undergo plastic deformation, the critical elastic energy \(Q_{el}\), the surface adhesion energy \(Q_{a}\) of the particle deposition wall facing the particles, and the particle desorbed are required to overcome the adhesion energy \(Q_{ar}\). If the sum of \(Q_{el}\) and \(Q_{e}\) is greater than \(Q_{ar}\), the particles can overcome the adhesion energy of the dust accumulation surface and desorb, and vice versa, they are deposited on the wall. Therefore, based on the above description of the conservation relationship of particle energy, the description of the normal-phase critical deposition velocity \(v_{inl}\) for the solution of particle deposition can be obtained, as shown below:  
Figure 2:3  
The sedimentation determination conditions of the tangential dimension collision process need to be given by analyzing the energy changes of the particles in the tangential direction. In the previous description, during the collision between the particles and the wall, due to the presence of the surface adhesion energy \(Q_{a}\) of the particle deposition wall facing the particles, the plastic deformation loss energy \(Q_{co}\) of the particles, etc., there is a loss of momentum after the particles are desorbed, and this energy loss also causes the direction of particle rebound to change. The tangential critical collision angle \(\theta_{cr}\) of the particles is introduced to characterize the minimum angle between the particles and the wall surface when the particles are desorbed relative to the original direction after the particles collide. When the particle collision angle \(\theta_{i}\) is greater than the tangential critical collision angle \(\theta_{cr}\), the particles desorb and rebound, making it extremely difficult to be captured by the deposited wall. In the literature [39], [PERSON] studied the collision between particles that exceed the tangential critical collision angle and the wall surface, finding that the particles change from oblique incidence to parallel sliding close to the wall surface after the collision and will not be attached to the wall surface. At this time, the calculation of the tangential critical collision angle can be solved by analyzing the tangential kinetic energy of the particles and the minimum energy required to destroy their contact area, according to the principle of conservation of particle energy. Contact failure occurs when the normal contact force is equal to the drag force of the JKR theory, which can be expressed as [39]:  
Figure 2:4  
Figure 2:5  
Figure 2:6  
where \(F_{a}\) is the adhesion of the particles, \(\mu^{*}\) characterizes the effective coefficient of friction of the particles, \(\Gamma\) is the surface energy between the particles, and \(k_{t}\) is the tangential stiffness value of the particles. The failure tangential impact energy \(E_{t}\) can be expressed as:  
Figure 2:7  
The forward adhesion energy \(E_{an}\) that must be overcome can be expressed as [39]:  
Figure 2:8  
where \(a\) is the adhesive contact radius at the moment of contact failure due to sliding.