## 1 Introduction
That means that the penetration of particles through this type of filter was four orders of magnitude smaller than the Occupational Safety and Health Standard requirements, by a pressure drop of 255 Pa (26 mm H\({}_{2}\)O) at a flow rate of 85 L/min. The effect of fibrous filter loading on the filtration efficiency, pressure drop, and clogging of nanofibrous filters was studied by many teams, using various filtration models (analytical and numerical) and experimentally [64; 65; 66; 67; 68; 69; 70]. A microchannel design for fine particle filtration was proposed by [PERSON] et al. [71]. The authors determined the filtration efficiency for microparticles considering the dielectrophoretic forces, but did not determine the flow field in such a channel. Various methods of testing of filtration devices, including fibrous filters and electrostatic precipitators, in terms of ISO standards have been reviewed by [PERSON] and [PERSON] [68]. The authors claimed that the filtration velocity of the fibrous filter can be higher for smaller fiber diameters of the filter than for larger ones. Furthermore, the maximum penetration of particles through a filter occurs for smaller particles [65]. When nanofibrous filters are used for the filtration, the Cunningham slip correction factor for gaseous molecules increases, and the drag force of the flowing gas on the fiber becomes smaller for finer fibers that results in a decreased pressure drop [66; 67; 68]. A similar effect was observed by [PERSON] et al. [72; 73] for a pair of cylinders, which can be a model of the nanofibrous filter. The drag force decreased with the increasing Knudsen number. The Knudsen number was defined by the authors as the mean free path of gas molecules to the fiber radius. A decrease in the pressure drop across fibrous filters with micron-sized fibers, caused by gaseous molecules slipping, was presented by [PERSON] et al. [74]. This effect was more significant for filters with fibers of high non-uniformity. The empirical formula derived by [PERSON] et al. [74] was confirmed by experiments carried out by [PERSON] et al. [75], for nanofibrous filters with a large inhomogeneity, and the model was extended for the Knudsen number up to 20. [PERSON] and [PERSON] [65] noticed that nanofibrous filters are more efficient in particle filtration than the microfiber media. This effect was attributed to increased particle interception in such a filter. The authors used nanofibrous filters with thicknesses ranging from 10 to 100 \(\upmu\)m. The advantage of microfiber filters was their higher particle mass loading. The flow resistance decreases with the fiber diameter decreasing [76; 77; 78]. This slipping causes a lower pressured drop across the filter, which is attributed to bypassing the nanofibers by gaseous molecules due to a relatively low Knudsen number (\(Kn\)):  
\[Kn=2\lambda/d \tag{1}\]  
where \(\lambda\) is the mean free path of air molecules and \(d\) is the nanofiber diameter. Assuming the mean free path of gaseous molecules to be 60 nm, and a median fiber diameter of 430 nm, the Knudsen number for the filter used can be estimated to be about \(Kn=0.28\). The PIV method of flow field visualization in gas cleaning devices was formerly used for the measurement of gas flow velocity in electrostatic precipitators or their laboratory models (cf. for example, [79; 80; 81; 82; 83; 84; 85]). The authors determined the dust particles' motion and an effect of the discharge and electrodes' geometry on the collection efficiency. Gas flow through a commercial pleated filter was investigated by [PERSON] et al. [86] using the PIV method. The authors determined the velocity distributions downstream of a rectangular pleat filter. The PIV technique was used by [PERSON] et al. [87] to investigate the process of nanofibers' formation by electrospinning. Recently, the PIV technique was also used for investigations of the filtration efficiency of face masks with respect to the removal of coronavirus SARS-CoV-2 [88].