**5. Conclusions**

28 Will-be-set-by-IN-TECH

1 2 3 4

6

7

9

A

7

8

1 2 3

2 4

<sup>B</sup> 7

6

2

Fig. 21. Exhalation - illustration of a movement of small particles.

The novel approach to the filtering mechanisms of nano-particles through medical masks is presented in this chapter together with the criticism of the classical filtration theory.

The novel view on the filtration problem was enabled by development and usage of the J-method, which is the method for determining the porosity parameters in the flat textiles. The pores' hydraulic diameter distribution is one of the method's results, which considers that the channels are formed from one surface of a flat textile to the other one. The channel cross-section size is defined by the pore hydraulic diameter distribution. We showed that the air flow through channels is laminar and that the problem size is in domain of the continuous mechanics. The laminar air flow through channel forms distinctive velocity profile, which is responsible for driving the spherical virus rotation. The Magnus effect appears due to the self-induced rotation of the virus. The axial force is thus generated that is driving a virus toward the channel boundaries. This is named as J-effect.

The novel view on the filtration problem was enabled by development and usage of the J-method, which is the method for determining the porosity parameters in the flat textiles. The pores' hydraulic diameter distribution is one of the method's results, which considers that the channels are formed from one surface of a flat textile to the other one. The channel cross-section size is defined by the pore hydraulic diameter distribution. We showed that the air flow through channels is laminar and that the problem size is in domain of the continuous mechanics. The laminar air flow through channel forms distinctive velocity profile, which is responsible for driving the spherical virus rotation. The Magnus effect appears due to the self-induced rotation of the virus. The axial force is thus generated that is driving a virus toward the channel boundaries. This is named as J-effect.

The numerical investigation, using the computational fluid dynamics approach and the classical Newtonian mechanics, showed that the J-effect is a phenomenon that appears fast and is therefore an efficient mechanism of filtering spherical or near-spherical viruses even in the straight channel.

On the other hand, the Brownian motion of the particles trapped in the air flow as advocated by the classical filtration theory could be dismissed as unrealistic.

There are some questions that have not been addressed here but are also important for understanding of the complete filtration phenomenon. Some of them could be partially addressed by the classical filtration theory. The questions that arise with this analysis could be summarised as:

