A Contribution to the Theory of Fibrous Aerosol Filters BY N. A. FUCHS,A. A. KIRSCH and I. B. STECHKINA Karpov-Institute of Physical Chemistry Moscow 120 Obucha 10 Received 7th November 1972 Almost all properties of the “ parallel ” filter model-a system of parallel cylindrical staggered and regularly arranged fibres can be treated theoretically but these properties differ considerably from those of real filters. On the contrary the theoretical treatment of the “ fan ” model obtained by turning in the parallel model all fibre rows in their planes by an arbitrary angle is very difficult but its properties are the same as those of real filters with a perfectly homogeneous structure. The “ degree of inhomogeneity ” of a real filter is the reverse ratio of its resistance and of the particle capture coefficient on its fibres (in absence of inertial deposition) to those in an equivalent fan model.This makes it possible to calculate the filter efficiency from its resistance. In the past 30 years many papers on the theory of fibrous aerosol filters have been published beginning with the fundamental work of Sell Albrecht Kaufmann and Langmuir. However on the basis of these papers it has been impossible to calculate the main characteristics of these filters (i.e. their hydraulic resistance and their efficiency in respect to aerosols with various particle size and at various flow rates) from measurable filter parameters-the fibre width and the shape of their cross-section the volume fraction occupied by the fibres (packing density) their orientation the homogeneity of filter structure etc.-without resorting to a number of empirical equations and coefficients.For several years we have been working on the development of a theory which would make possible such a quantitative calculation of filter efficiency. So far we have been able only to approach this goal but not to reach it. However the results of this work seem to have led to a better understanding of the complex processes of aerosol deposition in fibrous filters. For the development of the theory we have used filter models approaching real filters combining in this work wherever possible theoretical deductions with experi- mental studies. At small flow velocities (not exceeding 10-20cm/s) at which the fibrous filters show a high degree of efficiency it may be assumed that all particles of size not greater than a few pm coming into contact with a fibre adhere to it.Besides at such small flow velocities the flow is automodel i.e. the pressure drop across the filter is proportional to the flow rate. We have excluded from considera- tion the effect of electrical forces i.e. the filtration of aerosols with not very small particle charges as well as filters charged or polarized by an external field. In modern filters in the shape of papers cardboard sheets and pads the fibres are oriented more or less parallel to the same plane and the packing density is usually less than 0.1. THE “PARALLEL” MODEL. RESISTANCE In Langmuir’s model-an isolated cylindrical fibre the effect of neighbouring fibres on the flow field is neglected and this model cannot be used for our purpose.The simplest model approaching real filters called by us the “parallel” model is a system of straight equal cylindrical parallel staggered regularly arranged fibres (fig. l) perpendicular to the flow direction. The flow field near the fibre surface in 143 FIBROUS AEROSOL FILTERS this model was calculated by Kuwabara.' For the flow function he obtained the following expression (in polar coordinates) accurate to the terms of a to the first power where Uois the face value of the flow velocity a the fibre radius and a the packing density. 0 0 Q 0 0 0 0 ____)_ FIG.1.-The " parallel "model. Kuwabara assumed the fibres to be arranged parallel but disorderly.In reality as shown experimentally by us (see below) and theoretically by Golovin and Lopatin,2 formula (1) can be used only for a regular staggered fibre arrangement shown in fig. 1. The accuracy of formula (1) was checked in our model experiments with glycerol flowing in a system of staggered parallel cylinders with diameters of 7 or 14 mm with a velocity 0.06-0.16cm/s (Re= 0.01-0.05). The velocity vector in each point was determined by photographing under intermittent illumination the trajectories of metallised spherical polymer beads suspended in glycerol having the same density as the liquid and therefore moving along the flowlines. The trajectories and velocities of the beads agreed accurately with those calculated by means of (1) at p/a<2 for a = 0.05 and at p/a< 1.5 for a = 0.2.Another question important to the filtration theory was solved in these experi-ments. It is usually assumed that the centre of a spherical inertia-less particle moves exactly along the flow lines. However under the action of the flow velocity gradient existing in the vicinity of a cylindrical obstacle the particle must rotate and we cannot assume apriori that no lateral drag is acting on this particle. In any case the larger the particle whose centre moves along a given flow line i.e. the smaller the minimal gap between the particle and the cylinder the larger must be the lateral drag In our experiments we found that spherical inertialess particles with diameters of 0.1 and 3.0 mm move around 7 to 14 1nm thick cylinders along quite identical trajectories i.e.along the flow lines. As the hydrodynamical forces in liquids are much larger than in gases the validity of this conclusion for aerosols cannot be doubted. N. A. FUCHS A. A. KIRSCH and I. B. STECHKINA From (1) the hydrodynamic drag F,’ acting on the unit fibre length in the parallel model can be calculated. It is more convenient to use the dimensionless drag FP= E’;/pU, where p is the viscosity of the medium. The following expression for FPcan be derived FP = ~x/K;K = -0.5 In a-0.75+a (2) (superscript P stands for the “ parallel ” model). For a single regular row of parallel cylinders Mijagi obtained the formula FP= 4x[-ln(na/h2)+0.5+(na/2h2)’/3+. . .]-I (3) where 2h is the distance between the axes of neighbouring fibres.The pressure drop across the model is related to FPby the formula Ap = FPUopuH/na2 (4) where H is the thickness of the filter (or of the model). For a single row Ap = FPUOp/2h2 (5) Formulae (2)-(5) were verified by model experiments with glycerol at very low Reynolds number. The fibres were modelled by wires and capron filaments with diameters 0.15-0.70 mm. A plot of FPagainst a drawn in accordance with formula (2) is shown in fig. 2 together with the experimental results obtained on models -2 -I I0 10 a FIG.2.-The dependence of FPupon cc in the parallel model. Theoretical curve eqn (2). Experi-mental points v 0 n v a/h2 0.41 0.365 0.21 0.074 with h1 = h2and a/h2= 0.067-0.41.Good agreement with the theory was observed up to a = 0.27. An equally good agreement was obtained for models with It <h,. Formula (3) for single fibre rows was valid up to a/h = 0.7. Approximately at hl/h2 = I the FPvalues for a single row and for a system of cylinders become equal i.e. at h > h the hydrodynamic interaction between the fibre rows vanishes and the resistance of the parallel model is equal to the sum of resistances of separate isolated rows. FIBROUS AEROSOL FILTERS In filters made of ultrafine fibres (a< 1 pm) or in filtration at reduced pressure the Knudsen number Kn = A/a (A is the mean free path of gas molecules) is finite and the gas slip at the fibre surface should be taken account of. In this case the following formulae can be derived for the parallel model,6 (FP)-' = (FE)-' +zKn(l -a)/47t (6) and for a single fibre row (FP)-' = (FOP)-' +zKn[l -+(r~a/2h~>~]/4n (7) where F is the value of Pp at Kn = 0 and z is the ratio of the slip coefficient at the fibre surface to A.Formula (7) was verified on a model with a = 4.45 pm 2h2 = 62 pm 2hl = 1.1 mm in the air and in CO at pressures 10 Torr. As follows from above in such a model the hydrodynamic interaction between fibre rows is absent. The results are shown in fig. 3. Experimental points were obtained at p-l Torr-' air 2 3 Kn c02 I 1 I 2 I 3 FIG.3.-(Fp)-' against p-l (Kn) in a single fibre row in air (1-7) and in CO (8-12).mental points refer to various Re values up to 6 x The experi- Re = 1 x -6 x The lines were drawn in accordance with (7) at z = 1.18 for air and z = 1.12for CO,.According to the latest data,8 in air z = 1.15. Thus formula (7) was valid up to large values of Kn (Kn x 3) but already at Re = 0.15 the relationship between (FP)-' and Kn begins to deviate from linearity (PP)-'increasing faster than Kn.* The absolute value of FPat Kn = 0 found in these measurements agreed exactly with formula (3). Real filters consist of fibres of different width. In order to estimate the effect of fibre polydispersity on the resistance of the parallel model a model consisting of a single row of fibres with alternately larger a and smaller a2radii and with the distance * Later experiments did not confirm this conclusion. N.A. FUCHS A. A. KIRSCH AND I. B. STECHKINA 147 between the fibre axes 2hzwas studied. The flow field in such a model was calculated and the following formulae were obtained for the drags 8' and F,P acting 011 thick and thin fibres respectively which are valid for small values of a,/h and aJh F = 8~51; F,P = 8x52; (8) = s12/(C21i22-K2); K = 2 In 2-(~a~/4h~)~-(na,J4h,)~; Ql = In (na,/4h2)2-1-2(na,/4h,)2/3 (9) and similar formulae for c2 and Q2. If Fp = (8':+F!)/2 is the averaged drag and 6 = (a,+a2)/2the mean fibre radius then as shown by calculations for d/h2G0.4 and a,/a2<5 Ppdiffers little (less than by 5 %) from the drag Ppin a mono-disperse grid with the fibre radius equal to d. This result was corroborated by model experi- ments with a viscous liquid at a2 = 22 pm a = 79 or 160 pm h = 500 pin I 2 Plal FIG.4.-Theoretical (1) and experimental (2) flow velocity profiles along the line joining the fibre axes at a/hz = 0.238 and and alla2 = 52.0 0 0 0 oo0 000 U FIG. 5.-A " perturbed " parallel model. FIBROUS AEROSOL FILTERS Re< 0.05. The values of FPdetermined from these experiments agreed within 1-2 % with those calculated for a monodisperse grid. From these results it follows with high probability that the resistance of not very polydisperse filters can be calculated from the mean fibre width. The validity of the flow field near the fibres calculated for the above model was also corroborated in these experiments. The calculated flow liries coincided with those determined experimentally at n/h2 = 0.133 up to p = 2a near thin fibres and up to p = 1.20~~ near thick ones.Even for a very large difference in fibre diameters the perturbing effect of thin fibres on the flow field is considerable as can be seen from fig. 4 showing the experimental and calculated flow velocity profiles along the line joining the fibre axes at 6/h2 = 0.238 and ul/a2= 52. The effect of the irregularity of the model structure on its resistance was also estimated. For that purpose a “ perturbed ” model (fig.5) with equal but irregularly arranged fibres was investigated by means of a viscous liquid and compared with a regular model with h2 = (hi+4)/2. Such a “ microinhomogeneity ” reduced the model resistance considerably and the more so the larger the degree of inhomo- geneity i.e.the quotient h’;/h;and a. The same result was obtained theoretically. The deviation from parallel orientation of fibres in the rows also lowers appreciably the model resistance. PARALLEL MODEL. EFFICIENCY The aerosol penetration through a filter is given by the formula P = exp { -2aql) = exp (-2qaH/na) (10) in which q is the capture coefficient of aerosol particles on the fibres and I is the total length of fibres contained in 1 cm2 of the filter sheet. In the derivation of this formula it is assumed that in each plane perpendicular to the flow direction the aerosol concentration is constant despite particle deposition on the fibres. In the absence of turbulence in the flow through the filter such equalisation of aerosol concentration in the parallel model is possible only under the influence of Brownian diffusion.When the particles are deposited on the fibres not by diffusion but by other mechanisms the error when using formula (10) can be significant. The capture coefficient for diffusional particle deposition in the parallel model qi can be determined by solving the differential equation of convective particle diffusion towards the fibres in the flow field expressed by formula (1). We assume that a< 1 ; Re<&; Pe = 2aUo/D$ 1 (Dthe particle diffusion coefficient). The second of these conditions means that the flow in the fibre system is automodel the third that the particles are deposited from a layer at the fibre surface whose thickness is very small in comparison to the fibre radius.Under these conditions the following formula lo* can be derived for q; q = [2.30(4~/Pe)* +0.312(4~/Pe)+ .. .]/2~. (11) The hydrodynamic factor K is the same as in formulae (I) and (2). At Pe> 10 formula (1 1) can be approximated with sufficient accuracy by a simpler expression q; = 2.9K-+Pe-*. (12) The experimental verification of these formulae was performed l2 using fairly monodisperse aerosols of NaCl and dioctylsebacate with the mean particle radii from 1.5 to 9 nm. The particle diffusion coefficient was measured by means of diffusion batteries. The relative particle concentration before and after a battery N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA 149 etc. was determined by means of a tyndallimeter after growing the particles by vapour condensation on them.The model filters were made of wires and filaments with a = 0.021-0.25 mm. The experimental results are shown in fig. 6 together with the theoretical lines drawn in accordance with formula (I 1). This formula is valid already at Pe values of the order of a few units and for a as large as 0.27 i.e. in a much wider range than imposed by the conditions of its derivation. 0.1 10 I00 I000 Pe FIG. 6.-The diffusional capture coefficient against Pe in parallel models. Theoretical curves ; I. a = 0.01 ; 11. a = 0.05; 111 a = 0.135; IV a = 0.27. Experimental points (1-4) a = 0.01 ; 1 r = 158,; 2 r = 18A; 3 r = 60A; 4 r = 83A; 5 a = 0.05; r = 70A; (6-8) IX = 0.135; 6 r = 41 A; 7 r = 708,;8 r = 558,; 9 a = 0.27; r = 55A.The diffusional deposition of aerosols in a polydisperse parallel model was studied by the same method as its resistance. In this case the aerosol penetration is expressed (instead of (10)) by the formula P = exp (-2qT,,a,~,-2q;,,a2l21 = exp (-2611 (13) where I = l2 is the length of fibres with radii a and a2 contained in a part of the model with 1 cm2 cross-section I = 1 +12. As shown by calculation based on the flow field in such a model at a,/a2<3.5 and 6/h2G0.2,the value of Zais not more than by 5 % less of that of via,calculated for a model with an averaged fibre radius CS = (a +a2)/2. This conclusion was corroborated by measurements with nionodisperse NaCl aerosols with Y = 1.5 nm at Pe = 10-48 on two models-with a = 0.79mm al/a = 3.59 (3/h2= 0.101 and with a = 0.16 mm ;a,/a2 = 7.27 ;6/h2 = 0.182 respectively.The capture coefficient due to interception in the parallel model qg (the sub- script R stands for '' interception ',) is expressed by Langmuir's formula q = [2(1+R) In (I+R)-(~+R)+(~ +R)-']/~K (14) where R = r/a is the ratio between particle and fibre radii. The deposition due to simultaneous effect of diffusion and interception was calculated by means of a computer l3 for the following conditions R< 1 ; 6 = (4~/Pe)*<1 where 6 is the FIBROUS AEROSOL FILTERS ratio of the thickness of the layer at the fibre surface from which the particles are deposited to the fibre radius. The results of these calculations can be expressed (with accuracy 2-3 %) by an interpolation formula qLR = q +y~ + 1.241c-+Pe-*R3.(15) This means that the total capture coefficient q:R is equal to the sum of the capture coefficients due to diffusion and interception plus a relatively small interferential term. Unfortunately formula (15) could not be verified experimentally due to the great difficulty of preparing filter models with the fibre width of the order of 1 pm necessary for such work. The inertial particle deposition in the parallel model has been also calculated by us but as the results have not yet been verified experimentally they are not included. THE “FAN” MODEL A great advantage of the parallel model is the possibility of theoretical treatment of almost all its properties.However when comparing these properties with those of real filters substantial differences were found. The pressure drop across real filters is much less than in the “ equivalent ” models i.e. with the same parameters. A I ~ I ‘Id- iki+ 0 +. 0 i-0 0 0 FIG.8.-A fan model with very small 8. The diffusional capture coefficient in the model increases considerably with a (see fig. 2) e.g. when the model is compressed but changes very little or not at all on compression of a real filter. After testing a series of models we found that the best agreement with real filters is shown by the “ fan ’’ model obtained from the parallel model by turning each fibre row in its plane by an arbitrary angle 6. The properties of the model proved to be independent of the values of 8 provided they were not zero.In fig. 7 photographs of thin layers of a fan model and of a real filter are given which show a similarity in their structure. From measurements with a viscous liquid the following empirical formula was FIG.7.-A photograph of a fan model (a) and an electron micrograph of a real filter (b). [Toface page 150 N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA obtained for the drag on the fibres in the fan model l2 when the ratio of the distance between the rows to that between neighbouring fibres in a row was less than 0.65 Ff = 471/1c’ K’ = -0.5 In a-0.52+0.64a (16) (f stands for the “ fan ” model). When this ratio exceed 0.65 the hydrodynamical interaction between the rows vanishes and the drag is given by formula (3).1.0 cn F 0.i to 100 1000 Pe FIG.9.-The diffusional capture coefficient in the fan model (1-6) and in real filters corrected for their inhomogeneity (7-1 1). The full curve is plotted according to formula (18). Experimental points 1 2 3 4 5 6 2altmm) 0.25 0.5 0.1 0.052 0.043 0.043 2hzl(mm) 1 .o 2.5 1 .o 2.0 1 .o 2.0 U 0.187 0.157 0.079 0.02 0.034 0.017 7 8 9 10 11 2al(llm) 7.14 18.1 13.4 32 3.6 E 1.05 1.8 1.3 1.1 2.0 A theoretical analysis of the flow field in a fan model is extremely difficuit but we were able to make an approximate theoretical evaluation of Ff making use of the fact that P‘ remains constant even at very small values of 8. We consider several adjoining fibre rows divided into short sections (in fig.8 for clarity only two rows are shown). At very small 8 each section can be approximated by a system of parallel grids shifted with respect to one another by various distances A. Calculation of the drag Ffas a function of A based on superposition of the flow fields generated by each separate grid and averaging this drag for all A values from 0 to hZ leads to the formula Ff = 4n/(-0.5 In ct-O.44) (17) which is similar to (16). Thus we obtained an explanation of the fact that the resi- stance of the fan model is less than that of the parallel model but we could not explain why F is independent of 8. The conclusions made above for the effect of fibre poly-dispersity and gas slip on the model resistance proved to be applicable to the FIBROUS AEROSOL FILTERS fan niodel as well but in the second term of formula (6) a numerical factor 1.22 had to be introduced.6 An especially sharp difference between the two models was observed for diffusional particle deposition.As shown by measurements,’ the diffusional capture coefficient in the fan model at a = 0.01-0.15 and Pe = l-lO00 is expressed by the simple formula (see fig. 9) 46 = 2.7Pe-*. (18) Thus the diffusional capture coefficient in the fan model does not depend on c( (as in real filters). This can be explained qualitatively by the mutual compensation of two effects on the one hand the concentration gradient of the aerosol at the fibre surface increases with rising a (as for the parallel model).On the other hand the aerosol stream flowing around each fibre is inhomogeneous both in respect to its velocity and concentration. Due to non-linear dependence of the diffusional capture on the flow velocity this leads to a decrease of the deposition. Doubts about the validity of formula (10) for aerosol penetration does not apply equally well to the fan model and to real filters as the non-constancy of aerosol concentration in a plane perpendicular to the flow direction is averaged over the fibre length and for deposition by interception has no significance. However for other deposition mechanisms where the capture coefficient depends on the flow velocity the lack of constancy both of concentration and flow velocity (hydro- dynamic screening) seems to affect the validity of formula (10).An accurate theoretical treatment of this question is complex but the experimental evidence tends to the conclusion that the error in the use of this formula is small. The effect F 10 t -3166 16~ I o4 r/cm FIG.10.-The total capture coeficient against particle radius in a fan mode! with a = lO-’cm a w 0.05. 1 uo = 1 cm/s ; 2 uo = 5 m/s ; 3 uo = 10 cmls ;4 uo = 20 cm/s. N. A. FUCHS A. A. KIRSCH AND 1. B. STECHKINA of fibre polydispersity on the diffusional deposition in the fan model is the same as in the parallel model. The capture coefficient by interception in the fan model can be expressed by a formula similar to (14) but because of the pecularity of the flow field in this model it is necessary to introduce the hydrodynamic factor k' (see formula (16)) into it instead of I,-.Thus The last term in (1 5) is small and depends relatively slightly 011 K. We may therefore retain it for the fan modei substituting k' for k in it and obtain the formula for the combined capture coefficient l4 For practical purpose the most important question in the theory of aerosol filtration is the filter efficiency in the range of maximum penetration. The values of qbR plotted against the particle radii calculated by means of formula (20) for the fan model with c1 = 0,05 and a = 10pm at Uo = 5 10 and 20cm/s are given in fig. 10. As shown by our calculations the inertial deposition in the range of particle size corresponding to maximum penetration is relatively small (Langmuir came to this conclusion intuitively 30 years ago) and the minima on the curves are due to increase of qk and decrease of r& with rising particle size at constant flow velocity.However in the curves qLR against Uo the minima are caused by the increase of inertial deposition and decrease of q; with rising Uo. REAL FILTERS. DEGREE OF INHOMOGENEITY For real filters notwithstanding a large number of published experimental data very few ofthese could be used in this work chiefly due to incomplete characterisation of the filters used. In all filters with cylindrical fibres as shown below the resistance is less than in the fan model with the same parameters. This is caused mainly by the inhomogeneity of the structure of real filters.As already pointed out the filter resistance decreases considerably in the presence of structural micro-inhomogeneities (on a scale of the mean distance between the fibres). A similar effect is produced by macro-inhomo- geneities such as fluctuations of the thickness and packing density of the filter by any deviation from the parallel fibre orientation and from the perpendicularity of the fibres to the flow direction. The presence of doubled trebled etc. fibres caused by incomplete dispersion of the fibres in the fabrication of filters must be regarded also as a kind of inhomogeneity. As shown by calculation and by experib ments with fan models when all the fibres in the filter are doubled the resistance decreases almost two-fold. Various types of inhomogeneity affect the values of the drag F in the formula (4) differently.As the determination of the magnitude of fluctuations of H and a in real filters is very difficult it is expedient to assume formally that the effect of inhomo-geneity of any kind on the filter resistance expressed by formula (4) consists in reducing the drag F. In fig. 11 the values of F' (the superscript r stands for " real ") calculated by means of(4) (the mean values of a were used) are plotted against o! for a number of real filters with cylindrical fibres together with the curve (Pya)for the fan model plotted according to (16). For all filters with cylindrical fibres tested by us or described in the literature together with necessary data for calculating F in the function of CI,the Fvalues were lower than in the " equivalent " (i.e.with the 154 FIBROUS AEROSOL FlLTERS r I I I ii I -a-20 m Ip -G -a-I -I-4 -a-5 0-6 8-7 e 21 1 1 I I1 FIG.11.-The hydrodynamic drag against a. Fan model formula (16) (curve I). Real filters according to Chen l5 (curve 11) Davies l6 (curve 111) Langmuir (curve IV). Our data for filters with 2u = 7.14; 18.1 ;32 and 13.4 pm respectively (1-4). Data of First (3,Wong l9 (6) and Blasewitz *O (7). The effect of gas slip on the resistance of real filters was studied on mono- disperse filters with a = 1.5-9 pm a = 0.03-0.14 and E = 1.08-2.2 at pressures 210 Torr. As shown by these measurements (PI-'increases linearly with Kn (as in models) in accordance with the experimentally found formula (Fr)-' = (&)-' +1.2lzQ(l-a)Kn/4n (21) in which z = 1.18 (in air) 1.21 is an empirical coefficient corresponding to the tran- sition from parallel to fan model and B a coefficient related to the inhomogeneity of filter structure.To the first approximation p = 83. In the efficiency of real filters we must take into account that in the expressions for Ff (formula (16)) and for I&(formula (19)) the same hydrodynamical factor IC' is included. It follows that the effect of inhomogeneity of the filters on both these quantities should be the same i.e. in real filters r& should be E times less than in the fan model. By investigating a large number of commercial filters as well as those prepared in our laboratory we found i2 that the diffusional capture coefficient in real filters as in the fan model does not depend on a i.e.does not change during compression of the filter. Moreover qD in real filters as a rule is less than in the fan model with the same parameters. There can be no doubt that the main reason of these differences is the inhomogeneity of real filters because any kind of deviation from homogeneity leads to increase in the aerosol penetration through the filter. We N. A. FUCHS A. A. KIRSCH AND I. B. STECHKINA made the simplest assumption that the effect of the inhomogeneity on the drag F and on the diffusional capture coefficient vD is equal (as for interception) i.e. that qf = ~qf-,. In order to prove this hypothesis the diffusional deposition of an aerosol with Y = 27 nm in the fan model and in the filters prepared in our laboratory from isodisperse glass fibres was measured.12 The values of qb for these filters as well as for filters described by Chen,Is multiplied by E (determined from the filter resistance) together with the values of qh for the fan model are plotted against Pe in fig.9. All experimental points lie on one straight line corresponding to formula (18) in com- pliance with our hypothesis. Due to the smallness of the last term in (20) we can generalize this result and assume that tlLR = EVLR* (22) An experimental check of these deductions was made 21 with monodisperse aerosols and a filter prepared from isodisperse terylene fibres in the laboratory (no. 1-14 in table 1) and on the basis of Whitby's 22 data obtained with glass-fibre filters (no.14-16) in the range of maximum penetration. The change of cx. in our filter was achieved by compression. The table lists the following parameters fibre diameter 2a filter thickness H packing density u degree of inhomogeneity E deter-mined by comparing the drag F' calculated from fiiter resistance (formula 4) with the drag Ff in an equivalent fan model. U,is the face velocity of flow r the particle radius Pt and Pi,aerosol penetration for upward and downward flows respectively. TABLE 1 .-CALCULATED AND EXPERIMENTAL VALUES OF THE CAPTURE COEFFICIENT IN REAL FILTERS no. 2n/pm H/cm U. E Uo/(cm/s) rhrn Pt PJ. ~DRIE VDR 1 23.1 3.7 0.042 1.53 5.2 0.67 0.73 0.65 0.0043 0.0045 2 23.1 3.7 0.042 1.53 3.8 0.72 0.73 0.63 0.0045 0.0047 3 23.1 3.7 0.042 1.53 2.6 0.63 0.73 0.61 0.0047 0.0048 4 23.1 3.7 0.042 1.53 4.1 0.85 0.62 0.53 0.0065 0.0056 5 23.1 3.7 0.042 1.53 5.4 0.88 0.65 0.53 0.0061 0.0057 6 23.1 3.7 0.042 1.53 2.7 0.73 0.65 0.50 0.0065 0.0052 7 23.1 3.7 0.042 1.53 3.8 0.55 0.72 0.65 0.0044 0.0039 8 23.1 2.0 0.077 1.53 1.7 0.70 0.65 0.45 0.0072 0.0065 9 23.1 2.0 0.077 1.53 1.6 0.70 0.62 0.54 0.0063 0.0060 10 23.1 2.0 0.077 1.53 0.53 0.35 0.38 0.26 0.013 0.01 1 11 23.1 2.0 0.077 1.53 0.92 0.35 0.55 0.43 0.0085 0.0082 12 23.1 2.0 0.077 1.53 1.4 0.35 0.55 0.50 0.0072 0.0065 13 23.1 2.0 0.077 1.53 2.3 0.35 0.66 0.60 0.0054 0.0050 14 10.0 2.0 0.03 1.4 2.1 0.04 0.835 0.014 0.01 3 15 10.0 2.0 0.03 1.4 2.1 0.3 0.937 0.0051 0.0054 16 10.0 2.0 0.03 1.4 2.1 0.55 0.855 0.01 3 0.010 The difference between Pf and Pi is caused by gravitational particle deposition.We excluded this effect by taking the mean penetration H = (Pt+PJ)/2. In the next column the values of qLR/&evaluated by means of (20) are given i.e. the theoretical values of the total capture coefficient and in the last column are the experimental values of this coefficient determined from B by means of (10). The fact that the experimental values are somewhat larger than the calculated ones is evidently due to the neglect of inertial deposition. It follows that when the geometrical parameters a a and H of the filter and its resistance are known we can calculate with an accuracy sufficient for practical purposes its efficiency when inertial deposition can be neglected i.e.in the particle size range FIBROUS AEROSOL FILTERS corresponding to maximum penetration and to the left of it i.e. for still smaller particles. We realize that there are still many gaps in our work. The most sigmficant is the lack of model experimental data on the inertial particle deposition and the too-small number of filters on which all conclusions were tested. 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