**4.6 Illustration of the mechanisms of filtration of the medical masks**

The virus behaviour of filtration (J-effect) is depicted in figure 18. If a virus is placed at the channel centerline, then the distribution of the fluid velocity and pressure around the virus is symmetrical, no virus rotation and consequently no radial force is present. The virus B stays on the centerline. Such a virus can be filtered at the channels' bends or if it is thrown out by a collision with another particle.

The virus A (or C) does not rotate at first and the radial force drives it toward the centerline, figure 18 (I). When the virus begins to rotate and this happens almost instantly and the direction of the radial force changes toward the channel boundary, figure 18 (II). It has to be stressed here that the velocity profile changes locally at the virus location and the parabolic profile is locally lost.

The process of filtration during and between the inhalation and the exhalation is shown in figures 19 – 21, where denotations are: A - cross-section, B - view along the channel, 1,2,3,4 -

Fig. 18. Illustration of a virus in the fluid flow in a channel.

airflow. This means, that there is no particles larger than 10nm left in the airflow that might be filtered out in the diffusion process. It is clear that the diffusion process does not apply here. The frozen state between the inhalation and exhalation (undisturbed period) is shown in figure 20. There are no streamlines and the channel and cavern form a single space and thus enabling the diffusion exchange of the particles between the channel and cavern and filtering

Novel Theoretical Approach to the Filtration of Nano Particles Through Non-Woven Fabrics 231

In the figure 21 the phenomenology is the same as in figure 19, just the direction of the airflow

1 2 3 4

3

2 4

6

7

9

1 2

2

6

Fig. 20. Undisturbed period between the inhalation and exhalation.

based on the Brownian motion.

A

B

is reversed.

fibre, 5 - particle, that has been captured by a fibre surface, 6 - particle, that has been separated into a cavern, 7 - streamline, 8 - airflow velocity profile, 9 - mouth of the mask user.

The filtration process during inhalation is shown in figure 19. There are five particles shown at the entrance of the channel, one of them is placed at the channel centreline (position at the beginning). This virus travels the fastest in the axial direction due to the airflow velocity profile. The other viruses travels also into the axial directions due to the J-effect, it is clearly visible in the second position, which presents the second time snapshot. In the third snapshot, the viruses, most distant to the centreline, have already travelled to the vicinity of the fibre surface. They are captured by the surface in the next time snapshot. In the last snapshot the other viruses are filtered out to the caverns and only the virus on the centreline stays in the

Fig. 19. Inhalation - illustration of a movement of small particles, which would exhibit Brownian motion in a still air.

26 Will-be-set-by-IN-TECH

fibre, 5 - particle, that has been captured by a fibre surface, 6 - particle, that has been separated

The filtration process during inhalation is shown in figure 19. There are five particles shown at the entrance of the channel, one of them is placed at the channel centreline (position at the beginning). This virus travels the fastest in the axial direction due to the airflow velocity profile. The other viruses travels also into the axial directions due to the J-effect, it is clearly visible in the second position, which presents the second time snapshot. In the third snapshot, the viruses, most distant to the centreline, have already travelled to the vicinity of the fibre surface. They are captured by the surface in the next time snapshot. In the last snapshot the other viruses are filtered out to the caverns and only the virus on the centreline stays in the

into a cavern, 7 - streamline, 8 - airflow velocity profile, 9 - mouth of the mask user.

1 2 3 4

A

Brownian motion in a still air.

1 2 3

2 4

6

7

7

8

9

<sup>B</sup> 7

6

2

Fig. 19. Inhalation - illustration of a movement of small particles, which would exhibit

airflow. This means, that there is no particles larger than 10nm left in the airflow that might be filtered out in the diffusion process. It is clear that the diffusion process does not apply here.

The frozen state between the inhalation and exhalation (undisturbed period) is shown in figure 20. There are no streamlines and the channel and cavern form a single space and thus enabling the diffusion exchange of the particles between the channel and cavern and filtering based on the Brownian motion.

In the figure 21 the phenomenology is the same as in figure 19, just the direction of the airflow is reversed.

Fig. 20. Undisturbed period between the inhalation and exhalation.

**5. Conclusions**

the straight channel.

be summarised as:

**6. References**

1. What is happening at the channel bend? 2. What is happening in the caverns?

*Filters*, Pergamon Press.

3. How is the particle separated into a cavern?

4. What share of the particles is separated into cavern?

5. How the particle interaction is affecting the filtering process?

The novel approach to the filtering mechanisms of nano-particles through medical masks is

Novel Theoretical Approach to the Filtration of Nano Particles Through Non-Woven Fabrics 233

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

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

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

On the other hand, the Brownian motion of the particles trapped in the air flow as advocated

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

Brown, R. (1993). *Air Filtration: An Integrated Approach to the Theory and Applications of Fibrous*

presented in this chapter together with the criticism of the classical filtration theory.

toward the channel boundaries. This is named as J-effect.

toward the channel boundaries. This is named as J-effect.

by the classical filtration theory could be dismissed as unrealistic.

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