## 4 Results
### Results of the Study of Particle Interaction
The velocity values (Figure 7f) increased as it approached the surface, and when the maximum normal force and displacement were reached, the velocity had a zero value. Then, the particle changed direction to the opposite one, and the detachment process began. In this case, when the particle changed direction, the velocity had the opposite (positive) sign. Now, the interaction/contact in the tangential direction is considered (Figure 8). It should be noted that contact occurred at a relatively short distance (up to 3.5 nm); therefore, in the simulation, it was assumed that the interaction would occur with a flat surface. As inthe case of normal interaction, an increase in the angle of interaction led to an increase in the value of the normal force, and the duration of the interaction decreased. In contrast to the usual interaction, at a small angle, the achieved particle displacement in the tangential direction (shear slip) increased. Moreover, when moving in the tangential direction during contact, the particle moved both forward and backward (Figure 8c). Particle contact in the tangential direction included slip and elastic deformation (at the end of the contact). By observing the velocity graphs, it could be seen that the velocity values settled at the corresponding value at the end of the contact. After the particle bounced, because the interaction was at an angle, as expected, the particle continued to move in the tangential direction as well. In all cases, at the end of the contact, the value of the tangential force equal to zero was reached. It should also be noted that, when the particle was at a certain distance from the interacting surface, there was no interaction in the tangential direction, because the adhesive force acted only in the normal direction. Figure 7: Normal interaction. Particle impact at various impact angles: 1—\(\varphi_{0,1}=10^{\circ}\); 2—\(\varphi_{0,2}=20^{\circ}\); 3—\(\varphi_{0,3}=30^{\circ}\). Normal force versus displacement (**a–c**); normal force (**d**); normal displacement (**e**); normal velocity history (**f**). Taking into account the presented results (Figures 7 and 8), as mentioned in the formulation of the problem, because the mycelium material itself is relatively soft, the particles tended to penetrate (Figure 7e) into the material as well as stick to the surface at small interaction angles. Therefore, in order to increase the efficiency of the filter, a filter containing smaller diameter pores can be selected. In this case, the circulation of the air flow slows down, and the particles tend to stick to the surface even more. However, the filter clogs faster, so a more efficient filter may become less durable. When developing these filters for specific materials, all requirements for them must be evaluated. The required pore size must be chosen so that the flow rate on the pore wall results not only in good adhesion but also in the durability of the filter. It should be noted that, from the point of view of modeling, because the adhesion during interaction acts in the normal direction, the description of the tangential force becomes more complicated. As the results showed, when considering the interaction in the tangential direction (along the interacting surface), different particle behavior can occur. When a particle moves in a tangential direction at a small distance of nanometers, the particle can slide over the surface (Figure 8a) and even return to the initial interaction position (Figure 8c). In the future, if possible, research should continue in cooperation with the manufacturers of this material. Moreover, additional studies related to the search for an effective filter should be carried out. It should also be noted that mycelium is a material of biological origin. The question of modifying a mycelial filter from a biological point of view remains open regarding its applications, including not only the extraction of particles but also the destruction of viruses in the filter. Figure 8: Tangential interaction.