## 2 Holistic Model of the SLM Process and Main Algorithm
### Powder Removal Models  
Powder removal models remove loose powder particles from the powder bed. One such model aims to support multiple material SLM systems with a point-by-point micro vacuum material removal system [41]. It has been designed to remove a single layer of  
Figure 4: An example of particle deposition obtained by the third variant of the model with parametric (**a**) and discrete (**b**) representations. Figure 5: Results of deposition of free-falling atomized and arbitrary-shaped particles (**a**), re-coating of the second layer (**b**), and after the re-coating of the third layer (**c**). powder selectively and precisely at the specific locations, in combination with several dry powder dispensers that deposit powders according to the designed pattern. After the generation of the powder bed and the completion of the single processing stage of the SLM, some of the untreated powder material should be removed. To simulate this operation and process, two variants of new powder removal models have been developed. The first variant was developed to analyze the effectiveness of the loose particle removal operation. It was developed in a 2D version. The model uses the same principles and algorithms as the other LBM models of the holistic SLM model (e.g., the LBM calculation module presented in Figure 2). The objective of this variant is to simulate the gas flow, allowing for local removal of loose particles. The model contains equations that describe the motion of particles entrained in the gas stream. Particles of different masses and sizes are considered in the simulation, although they are assumed to be small enough to influence the gas flow. Then, [PERSON]'s laws are applied to the linear motion of a particle of constant mass without consideration of particle rotations. Because this variant is not used in the holistic model, the details are omitted and only some simulation results are presented here. The intensity of the color shows the vertical component of the velocity of the gas flow (red--upward, blue--downward). In this case, the trajectories of particles of three different sizes are simulated: the violet trajectories correspond to very small particles, green ones represent medium particles, and blue trajectories are related to the largest particles. Only in the case of a 'vacuum' (Figure 6a) does the gap between a vacuum tube and the surface become a crucial parameter. If the gap is too small, the inflowing gas flow is too weak to entrain the particles in the flow. An increase in the gap is accompanied by an increase in the gas flow, and the removal device becomes more effective. When the gap becomes too large, the turbulences that can appear in the tube can lead to asymmetrical flow and instabilities; the effectiveness of the device drops significantly, even for a highly symmetric case. The observed instabilities are typical for wider tubes and diminish as the diameter of the tube narrows. Considering the simulation results from the technological point of view, it can be concluded that efficient control of particle removal using a device with only a vacuum function is fraught with difficulties. This is due to the high dependence of the device effectiveness on the gap, which is difficult to maintain at an optimal level. As can be seen in Figure 6a, there is some movement in the opposite direction, and turbulences can appear within the tube. It is possible to enforce such movement by applying an additional inflow channel with a much higher gas pressure. Some simulation results are presented in Figure 6b,c. A simple liner shape is less effective due to a strong gas stream in a downward direction (Figure 6b). The device becomes more effective in the presence of a  
Figure 6: Gas streams and trajectories of moving particles predicted by the LBM model. The case of vacuum only with a big gap (**a**). The cases of inflows and outflows for different tube profiles and higher pressure (**b,c**). stream in the horizontal direction.