## 2 Literature Review
### Pulse Dust Collection System  
At present, there are four types of dust collectors such as cyclone, bag, electrostatic, and wet. Among them, the bag type dust collection system based on the cleaning method is divided into three types, which are oscillation type, backwash air type, and pulse-jet type. The pulse dust collection system is commonly used in industrial processes to collect dust. When the fan motor extracts the dust generated in the process, the dirty air will be filtered through the filter and be collected on the surface of the filter. Usually, the action of cleaning the filter element with reverse high-pressure air is used to control the cleaning time of the filter element. Therefore, the pressure drop \(P_{Filter}\) produced by the dust collection filter can be divided into three parts, as shown in Equation (1). The first is the pressure drop of the fresh filter as \(P_{f}\), which has not yet filtered the dust and can be described by [PERSON]'s law. The second is the pressure drop generated by the dust cake formed on the surface of the filter element during filtration, which is called the pressure drop of the temporary cake as \(P_{c}\). This part will change to follow the dust cake cleaned by pulse-jet air. The third is the pressure drop caused by the dust particles penetrating into the filter element and cannot be cleaned and eliminated by the pulse-jet air, which is called the pressure drop of the temporary powder cake as \(P_{r}\). This will gradually increase with the number of cleanings of the filter element. \[P_{Filter}=P_{f}+P_{c}+P_{r} \tag{1}\]  
\(P_{f}\) can be described in accordance with [PERSON]'s law (1856) to present the relationship between flow distance \(L_{0}\) and the pressure \(P_{f}\) in a fixed velocity \(V\) with a Reynolds number less than 2100, as shown in Equation (2), where \(\mu\) is the viscosity of fluid, \(K_{F}\) is the permeability of the filter, and \(L_{0}\) is the thickness of the filter. \[P_{f}=\frac{1}{K_{F}}\times\mu L_{0}V \tag{2}\]  
In a stable flow with a Reynolds number less than 2100, the generation of temporary powder cake is the accumulation of powder on the surface of the filter element after a period of time. The mass will show a linear relationship with the pressure called the pressure drop of the temporary powder cake as \(P_{c}\). The Kozeny-Carman model was first applied to describe the pressure drop of a temporary powder cake and is represented as a series of parallel capillaries or channels [19]. The total volume of powder cake is equal to the void volume of the powder, and the surface area is equal to the surface area of the particles, as in Equation (3), where \(d_{s}\) is the average diameter, \(\kappa_{K-C}\) is the constant, \(\epsilon_{0}\) is the porosity of the filter elements, and \(C_{K-C}\) is the Cunningham slip correction factor. \[P_{c}=\left[\frac{18}{d_{s}^{2}\times C_{K-C}}\times\frac{2\kappa_{K-C}(1- \epsilon_{0})}{\epsilon_{0}^{3}}\right]\times\mu L_{0}V \tag{3}\]  
In addition, the Happel cell model treats the powder cake as a collection of individual particles, and the porosity of the dust cake is equal to the ratio of the volume of the particles to the volume of the spherical shell [20]. Based on the above equations, the powder cake deposition thickness \(L_{0}\) can be converted into the dust mass \(W\) accumulated per unit area, as described in Equation (4), where \(C\) is the dust concentration and \(\rho_{P}\) is the dust density \(P\) is composed of the resistance coefficient of powder cake as \(K_{2}\), mass of the powder cake as \(W\), and the filtration speed \(V\), as shown in Equation (5). \[L_{0}=\frac{C}{\rho_{P}}\times\int V(t)dt=\frac{W}{\rho_{P}} \tag{4}\]  
\[P_{c}=K_{2}\times W\times V \tag{5}\]  
Based on the Kozeny-Carman model, it considers the polydispersity particles of the dust and uses standard deviation \(\sigma_{g}\), mean diameter \(d_{g}\), and dynamic shape factor \(\kappa\) to build a \(K_{2}\) for the pressure drop of the temporary powder cake [2], as in Equation (6).