**4.4 Criticism of the classical theory of filtration**

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where *Fr* stands for the radial force on virus, *y* for the virus displacement in the radial direction and *a*, *b*, *c* for the approximation parameters. This data is used to compute the virus kinematics

where *m* stands for the virus mass and *A*, *B*, *C* for the approximation parameters divided by *m*. The equation can be solved analytically. Nevertheless, the solution is awkward to use and the numerical integration of the differential equation (18) presented in figure 17 was used.

It is interesting to compare figures 11 and 17. We can conclude for the larger virus that it is captured by the tube wall in 5.1 · <sup>10</sup>−7s and for the smaller virus that its capturing time is approximately 2.7 · <sup>10</sup>−8s. The axial velocity of the larger virus at the capture time is only 0.15m/s, which is about 10% of its maximal axial velocity and its axial displacement is approximately 4.0 · <sup>10</sup>−8m, which is three orders of the magnitude less than its displacement in the radial direction. The picture is somewhat different with the smaller virus. It reaches 0.85m/s, which is already about 57% of its maximal axial velocity. It travels approximately 1.4 · <sup>10</sup>−8m in the axial direction, which is again three orders of the magnitude less than its

The mechanism of filtration presented here, which is based on fluid induced rotation of a round object, is closely tied to the Magnus effect. It is valid also in the case of the curved tube, due to the laminar nature of the fluid flow. Hence it is an efficient way of filtration of viruses

*<sup>m</sup>* <sup>=</sup> *Ay*<sup>2</sup> <sup>+</sup> *By* <sup>+</sup> *<sup>C</sup>* (18)

in the radial direction. The second Newton's law was used again.

Fig. 17. The radial virus path.

displacement in the radial direction.

and microbes.

d2*y*

<sup>d</sup>*t*<sup>2</sup> <sup>=</sup> *Fr*(*y*)

The fluid flow that flows around a single fibre is the base upon the classical filtration theory is built, as presented in figure 6. The flow is divided by the fibre and the steam lines that are curved around the fibre, get together again behind the fibre.

The situation, described by the classical filtration theory, is actually occurring during the air flow through the mask. However, the amount of air experiencing it is much smaller than the amount of air that is flowing through pores; see figures 2, 3 and 4, particularly due to the reason that the porosity measurement takes into account split pores.

The shortcomings of the classical filtration theory can be summarized as follows:


#### **4.5 Mechanisms of filtration of the medical masks**

The main difference between the classical filtration theory and the theory presented here is that the air flowing through the medical mask is supposed to flow through channels. This claim is supported by the theoretical and experimental findings of the J-method for the flat textile porosity assessment. The laminar flow through a channel (or a tube) establishes parabolic fluid flow velocity profile. The velocity profile enables the self-induced rotation of the spherical or near-spherical particles. The angular velocity reaches its limit value almost instantly causing the radial force to point towards the channel boundary due to the Magnus effect. Thus, the effective filtering is enabled and the whole phenomenon is named as the J-effect.

Based on the developed theory, numerical simulations and observations of the filtration of the industry waste gases, where needled flat textile is used, the mechanisms of filtration can be summarized in following points.

1. The particle, which is positioned at the centerline of the channel (tube), stays there until it collides with another particle or until the channel changes the direction.

3. the size distribution of the particles, 4. the different shape of the particle,

6. the thickness of the fibres, 7. the fibres' cross-section,

9. the size of the caverns and

collision with another particle.

profile is locally lost.

5. the different thicknesses of the sub-layers of the mask filtering layer,

8. the maximal hydraulic pore diameter and the pore distribution,

**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

Novel Theoretical Approach to the Filtration of Nano Particles Through Non-Woven Fabrics 229

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

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 -

C

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

A

d

d

A

C

<sup>e</sup> I. II.

B B

e

vc

vc

10. the breathing pattern as a function of a subject condition.


This analysis was limited to a straight channel (tube) and perfectly spherical virus, see figures 7 – 9 and figure 18. We have also established, that the channel length is large enough to support the stationary fluid flow. There are more parameters that affects the complex process of filtration. Some of them are difficult to assess, some are left aside to show the basic mechanism of filtration of the spherical or near-spherical particles in a medical mask. The interesting parameters that influence the filtration process are:


24 Will-be-set-by-IN-TECH

2. When the particle is captured by the fiber surface or is separated from the flow into a cavern, then its kinetic energy is too low for the particle to be sucked into the flow again. 3. The particle, which velocity is lagging from the flow one, does not exhibit Brownian

4. Small particles, which are positioned in the caverns, exhibit Brownian motion and are filtered out by being captured at the fibers' surfaces at the caverns' boundaries in the

5. The volume of the caverns and the channels become an unified space during the undisturbed period between the inhalation and exhalation. Thus the viruses can move

6. The particles having spherical or near-spherical shape starts to rotate, if they are not placed

7. The particle rotation is caused by the velocity-pressure distribution around the particle surface which is the consequence of the parabolic velocity profile (J-effect). The angular velocity of the particle reaches stationary value almost instantly and this triggers the radial force that is driving the particle towards the channel boundary (Magnus effect). The main difference with the normal comprehension of the Magnus effect is that the rotation of the virus is of the endogenous origin (self-induced) and not of the exogenous one (J-effect). 8. The particles that have not been filtered during the inhalation or have migrated from the caverns to the channels during the undisturbed period, will, during the exhalation, behave in the same way as they would during the inhalation. Only the direction of the fluid flow

9. The air flow through a channel is at least partly accelerated and decelerated by breathing of a subject which enhance the fluid induced forces acting on a virus. Only stationary state

10. The channel configuration is complex, changing its direction and diameter many times. The geometry of the channel is not known to us except for its minimal diameter, which is

11. The cylindrical (helical) viruses generally do not rotate. The probability for them to be positioned in the channel just right to enable J-effect is extremely small. Hence, this viruses are difficult to filter in a straight channel (tube). Their size is normally much larger than 10nm and their inertia plays an important role at filtering those viruses at the channel's

12. Except for the criticism expressed in this text, the mechanisms of the classical filtration

This analysis was limited to a straight channel (tube) and perfectly spherical virus, see figures 7 – 9 and figure 18. We have also established, that the channel length is large enough to support the stationary fluid flow. There are more parameters that affects the complex process of filtration. Some of them are difficult to assess, some are left aside to show the basic mechanism of filtration of the spherical or near-spherical particles in a medical mask. The

has been taken into account at the analytical/numerical analyses.

theory still applies and they are not discussed further.

interesting parameters that influence the filtration process are:

motion.

changes.

bends.

process of diffusion.

at the channel centre.

identified by the J-method.

1. the concentration of the particles,

2. the particle interactions,

freely between the caverns and channels.

