**4.2 Determination of the physical domain of the problem**

12 Will-be-set-by-IN-TECH

4. The inertia of the particle may cause the particle to leave the streamline of the flow around the fibre and collide with it. In contrast with the point 2 the inertia of the particle is not

5. The presumption here is that the small particles (smaller than 1.5*μ*m) are moving by diffusion like paths as in the still air (Brownian motion) with one predominant direction in the direction of the fluid flow. We believe that this presumption is unjustified if the fabric

The classic theory of filtration is based on the flow around a single fibre. We argue that air is channelled through pores in the inner layer of the mask and hence, the modelling of filtration as a fluid flowing through a tube is justified. The justification is supported by the measurement of porosity parameters of the mask, which presumes the laminar flow through

*Re* <sup>=</sup> *<sup>ρ</sup>vd*

where *ρ* stands for the fluid density, *v* is the mean velocity of the object relative to the fluid, or vice versa, *d* for the characteristic linear dimension (pore hydraulic diameter or particle

The value of the air density is *<sup>ρ</sup>* <sup>=</sup> 1.2kg/m3 and its dynamic viscosity *<sup>μ</sup>* <sup>=</sup> <sup>18</sup>*μ*Pa·s. The characteristic linear dimension is defined according to the object of interest. If the flow through a pore is studied, the dimension is its hydraulic diameter. On the other hand, if

The velocity of the fluid (air) through a mask can be deduced from mask's porosity parameters and human physiology. The air velocity at inhaling or exhaling depends on breathing intensity. Latter depends on an activity and the intensity of the activity of the mask user. The exhaled air is normally denser than inhaled one due to its increased humidity. Let's suppose that a subject inhales from 12 litres of air per minute at normal pressure and during light activity and 60 l/min during moderate exercise. Further on, suppose that the subject inhales 12 times per minute. The size of the active surface of the mask inner layer is 160cm2, and the open area of the layer is 8.42% of the active surface, table 4. The open area is thus 13.5cm2. The air flow velocity through mask inner layer is thus approximately 0.17m/s during light activity and 0.86m/s during moderate exercise Zuurbier et al. (2009). As a conservative approach the

The maximal pore hydraulic diameter is 30m, table 4. The Reynolds number for fluid flow through the largest pore is *Re* = 2 *<<* 2300, which ensures laminar air flow through the inner

The mask is designed to filter all viruses, which come in different sizes: from 10nm to 300nm. When inhaling (or exhaling) the air starts to flow, but a virus is not following instantaneously. The Reynolds number at the moment when a virus is stationary and the air is already moving

*<sup>μ</sup>* (6)

negligible.

porosity is taken into account.

**4. Novel approach to the filtration**

**4.1 Nature of the air flow through a mask**

a sample Jakši´c & Jakši´c (2007) and Jakši´c & Jakši´c (2010).

value of 1m/s is taken in order to compute *Re* number.

mask layer.

The nature of the fluid flow is described by Reynolds number, equation (6).

diameter or fibre diameter) and *μ* for the dynamic viscosity of the fluid.

the flow around stationary particle is in question, the dimension is its diameter.

The process of filtration that is carrying out in the medical masks is at the micro and nano scale. The size of the pores of the mask inner layer is at the micrometer scale and the size of viruses is at the nanometer scale. The Kundsen number (*Kn*) is used to determine whether the classical mechanics of continuum is still valid approach. Kundsen number is defined as

$$Kn = \frac{k\_B T}{\sqrt{2} \,\pi \sigma^2 pL} \tag{7}$$

where *kB* stands for the Boltzmann constant, *T* for the thermodynamic temperature, *σ* for the particle hard shell diameter and *p* for the total pressure and finally *L* for the representative physical length scale. The value of *Kn* for maximal pore and virus size is *Kn* <sup>≈</sup> <sup>10</sup>−9, which is much less than 1. Hence, the mechanics of continuum is applicable.
