Jordan 1954 - Bibliotheek T D W Uitsluitend VOOI‘ eigen...

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Unformatted text preview: Bibliotheek T» D W Uitsluitend VOOI‘ eigen gebruik / for own use only /////A Prometheusplein 1 Datum: 1 5—oct— 0 3 Postbus 98 2600 MG DELFT Bonnummer: 7 1 0 6 1 6 Telefoon: 015 - 2784636 Fax: 015 - 2785673 Email: [email protected] Aan; T.N.O. 'I'ECHN. PHYSISCHfi DIfiNSi POSTBUS 155 2600 AD DELFT NfiD *. RTAND Tav; A. van de Runstraat Aantal kopieén: 5 Uw referentie(s): 008 . 05105/01 . 01 Artikelomschrijving bij aanvraagnummer: 7 l 0 6 l 6 Artike]; The adhesion of dust par:icles Auteur: D .W. Jordan Tijdschrift; 3R1 T I SH JOURNAL OF APPLIED PHYS I C S J aar: l 9 5 4 Vol. 5 Aflevering: Pagina(s): S l 9 4 — S l 9 7 Plaatsnr.: 8 0 3 D Met ingang van 1 april 2003 zullen de prijzen v00rf0t0k0pie levering baitenland stijgen met 6‘ 0,05 per pagina From April I 2003, prices for photocopy delivery abroad will increase by 6‘ 0.05 per page Discussion on Paper H.3 automatically becomes a direct micron Sizer. Permanent records may also be taken photographically if desired. Author’sreply: The dispersants ’quoted by Mr. Colwill are in common use and variations on the method of introduction of the powder into them are many. The use of a projected image while, possibly, being less trying to the eyes than monocular Vision is nevertheless accompanied by an overall definition and contrast which is lower than that normally Secured by direct viewing. As ‘a consequence the finer particles, at times, remain undetected. > Paper HA The adhesion of dust particles By D. W. JORDAN, B.Sc., Medical Research Council’s Environmental, Hygiene Research Unit, London School of Hygiene and Tropical Medicine, London, W.C.l An important factor inythe handling of dust is the fact that the particles will adhere to each other and to solid surfaces. The mechanism by which this takes place is discussed and some quantitative results are given. it is shown that the intermolecular force between the surfaces in contact is large enough to account for this phenomenon of adhesion, although in some cases ‘ electrical forces and other processes may operate giving considerably greater attraction. An application to dust sampling problems is also mentioned. A factor of great practical importance in‘the handling of air- borne dust is the adhesion of dust particles to solid surfaces, and their mutual adhesion to form aggregates. The reasons for adhesion are frequently not understood, and it is the purpose of this paper to describe the forces involved and to mention their influence on the efficiency of dust sampling instruments. _ The/“Se forces are not generally electrical in nature—they not between the molecules of the surfaces in contact and are of the same type as those involved in surface tension and the tensile strength of materials. They can be shown to "be sufficient in themselves to account for the retention of particles on smooth, clean surfaces, and for the stability ofaggregates undergoing Brownian motion or rotating due to eddies in ' the air. Lennard-Jones“) describes the way in which forces operate between molecules. The force between two molecules con‘sis ts of an attraction ' F r»: A/r7 r (l) and a repulsion _. Fri/rm ' ' (2) where r is the separation of their centres and A, a, are constants. The attracting force A/r7 is named after van der Waals. The precise form of the repulsion is doubtful, but it accounts for the fact that despite collisions between atoms and molecules and their close proximity in, for example, the liquid state, the nubiei do not in fact fly together and form a dense rigid mass as, they would if the attractive force held right up to the nucleus. The repulsive force is only appreciable when the molecules are very close, and will. not be considered. The attraction also falls off very rapidly with distance but is effective within a few molecular diameters. Two molecules are considered to touch when they are so close that the repulsive force operates, and the separation then is one molecular diameter. ‘_ The forces are like gravitation in that the attraction between two elements of volume is not affected by the presence of the other elements, whereas with charged bodies this does not hold. Hence the attraction between‘two bodies containing a great number of molecules can be obtained by adding the, attractions between the individual molecules. - S 194 Bradleym and Haniakerm calculated the attraction between two solid spheres and obtained the equation (11(12 772qu M24112 imam; (3) where :11, d; are the sphere diameters, It is the separation (supposed to be about 5 A when the spheres are in contact), /\ is the constant involved. in the law of force and q is the number of molecules per cubic centimetre. (wth2 is of the order 10”12 or 10*‘3.) For spheres of varying sizes in contact 'JTZAqZ/Zlih2 == A in C.G.S. units (4) where A is a constant, and for a sphere of diameter d resting on a plane the equation becomes F r: Ad dynes (5) A in fact equals 277 x the total surface energy of the spheres. Bradley tested this formula experimentally. He con- structed a microbalance consisting of a spiral spring whose extension could be observed with a travelling "microscope. F: .011 the lower end he fused quartz spheres of various sizes. Another such sphere was attached to a fine capillary tube and brought up to the first, then drawn away from it until they parted. The attraction between them was obtained from the extension of the spring at the moment separation occurred. Agreement with theory, was very good over the range of siZes 7 tested, which seemed to cover spheres from 04 to 1. mm diameter. The constant A was found to be 212, thus for quartz spheres F 212 (Griz/((11 + (/2) dynes (6) when dis measured in'centimetres. . The apparatus could be evacuated, and special precautions were taken to eliminate possible electric charges and the effects of contaminating materials such as adsorbed water Vapour. The attraction was the same whether the apparatus was evacuated or not, and Bradley concluded that adsorbed gas molecules were squeezed out by the pressure. ‘The admission of water vapour, however, gave an increased attraction. ‘ ‘ BeischerW formed long thread-like aggregates of various chemical substances by allowing the aggregation to take place ' BRITISH JOURNAL or APPLIED” PHYSICS The adhesion of dust particles in an electric field. The threads hung from the electrodes and they could be detached to measure the rupture strength. He found that the forces acting depended greatly on the physical nature of the substance investigated, and upon the shape of the constituent particles. Diffusion may lead to the formation of a welded joint, and a substance such as ammonium chloride, with a low but appreciable vapour pressure, was found to have a fibre strength about ten times as great as iron oxide, which has negligible vapour pres sure. If permanent electric polarization exists, the forces may be many times greater. Beischer’s result with iron oxide particles of diameter about 05 [1, corresponded to a value for A of about 3 c.g.s. Fililts, so it may be that the value for quartz is exceptionally 11g 1. ' Lowe and Lucas“) suggest another method for estimating the attraction by comparing it with'the tensile strength, U, of the material acting over a certain area. If two spheres are in contact, the opposing areas where the molecules are within a distance I; of each other is given by area = 71/1 [lldz/(d, + (12) (7) Assume the force across the area to be of the same order as the tensile strength of the material, and put It = 10“8 cm. Then We obtain F= 10*87rU ding/(r1l + ([2) - (8) which is in the same form as Bradley’s formula. The tensile strength of quartz filaments is 101° dynes/cm2 so the constant corresponding to A has the value 314, compared with Bradley’s value 212. Hence, having found a physically reasonable value for It which gives roughly the right results for quartz, it is at least possible that this value may be carried over to other substances with an appropriate value for the tensile strength, provided. it was determined with the substance in a homogeneous, non-porous condition. These considera— tions again suggest that the value for quartz is too high to be typical, since its tensile strength is very great. It is known that airborne dust is charged,‘ and Kunkel“) has measured the charge on artificially dispersed powders. The net charge on a cloud is zero, and the larger the particle the higher the charge: in one experiment 10 it quartz particles v had an average charge of 600 electron units each. Thus it seems possible that the principal force binding aggregates may be electrical; However, Charges of ,this order would not be large enough to play an appreciable part; The force between two electron units of charge (4'77 X 10‘“) e.s.u.), at a distance of R .11., is 22-75 x lO’lZ/R2 dynes. Comparing this with the van der Waals attraction for two (I H particles, 212 X 10—4 (I dynes, it is seen that the latter is of greater order of magnitude. In the case of two 10 to particles, charge 600 units; if the electrostatic attraction is to equal the mole~ cular attraction, all the charge must be concentrated. within 0-01 ,LL of the point of contact. ' ‘ ‘ We shall now consider some numerical examples of the practical eifects of the van der Waals attraction. The van der Waals force becomes more important as the particles considered become smaller. Forces tending to detach particles from a surface, for example, usually depend on the mass of the particles (as when the surface vibrates and the force is mass X the normal acceleration), or on the surface area (as in the case of the aerodynamic drag due to a wind across it); that is, upon d3 .or d2. The van der Waals force is proportional to d, so this will come to predominate as d gets smaller. ‘ - A practical case worked out by Bradleym, where the argument appears to work in reverse, is the possibility of the SUPPLEMENT No. 3 Paper [1.4 breaking—up of airborne aggregates due to Brownian rotation. Here the centripetal force tends to separate the particles. For the equal particles of diameter (I the centripetal force is wpd4w2/12 (where w is the angular velocity of the rotation and p the density). This is proportional to ([4, so the argument above might seem to apply. However, as the particles become smaller the Brownian rotation becomes more violent, to being proportional to (1—5/2, so that the centripetal force is pro- portional to 1/51. Since the van der Waals force depends- 'on d, the aggregates become unstable as they become smaller. However, when the problem is worked out numeri— cally, it is found that impossibly high temperatures would be required to disrupt aggregates of dust or even of the finest particles occurring in smokes. If a quartz particle is suspended upside down from a plate the force of gravity w is mg: 981 x -};7rptl3 and the van der Waals force F: 212d. The particle will" stick if F is ' greater than W, Le. if 212d is greater than 981 x gonad? or (Z less than 0-46 cm (for p = 2 g/cm3). For any natural particle of this size contact between sphere and plate would be very imperfect due to roughness of the surface, so that in fact such a sphere would undoubtedly fall off. However, as sizes become measurable in microns the irregularities become less important and better adhesion is possible. Some idea of the effect of shaking and concussion in . removing small particles from surfaces can be obtained as follows. If the acceleration perpendicular to the surface is a, the dislodging force is ' (9) Hence the particle leaves the plate when 21ch r: %,—7rpcl3rt or a = ZOO/ti2 (putting p m 2 g/cm3). Thus, if d z: 1 ,u the necessary acceleration is 250000 g and if d 100 it it is 2000 g. It is thus impossible to remove such particles by shaking. A sharp blow may remove them, however. For example, if a plate moving at 10 m/sec is stopped in 1/10 mm the acceleration is about 103 cut/sec2 and such a bang would remove particles above about 10 ,u. When dust is carried on to the sampling plate of an impingement dust [sampling instrument at great speed, it might be expected that it would bounce off and be carried away by the air stream immediately. On the other hand, smaller particles may be held by the plate and either remain fixed to it or slide away (see Fig. l). A rough calculation ma = gnptfla G C Fig. 1. Illustrating the behaviour of particles upon striking the collecting plate of a sampling instrument (a) particle sticks, (1)) particle slides, (a) particle bounces. giving the maximum speed of approach of a spherical particle if it is to stick to the plate after falling upon it might be made as follows. ’ When the particle (Fig. 2) mass m, diameter d (supposed spherical), is at A, some distance from the plate and outside the range of the van der Waals force, we suppose it to be approaching the plate with speed w and at an angle 6 with 3S195‘ . l 'sfi‘ Paper H.4 the horizontal, rotating with angular velocity w. At B it is drawn sharply towards the plate due to the van der Waals force R At the point of contact it receives an impulse from the plate with a horizontal component sufficient to bring the point of contact of the particle to rest and thus to alter its F Fig. 2. Track of a sphere striking a plate spin and the horizontal component of velocity, and a vertical component measured by the coefficient of restitution a of the particle, supposed indepehdent of the other impulse and such that vertical component of velocity after contact _ vertical component of velocity before contact 1 After the collision the particle has reduced kinetic energy, which is further reduced by the action of F. Since F only acts very close to the plate we may say that if, on leaving the field of influence of F, the particle still has any upward velocity, then it bounces. If it has not it probably slides. According to Bradley the potential energy P of a particle _ diameter d at a distance 11 from the surface is nearly _P = -— Wquzd/IZII " (10) We know that the force on the particle is ' ' F: wZAqtd/izhz = 212:1 (for quartz) (11) so therefore » p P = —~ 212/161 (12) and for a particle touching the surface we put 12 = 5 x 10—8 cm. ‘ We may now use the equations of energy and linear and angular momentum to work out the track of the particle, assuming the nature of the collision with the surface to be as mentioned above. This is a simple problem in mechanics and the result is that the particle will bounce when the initial . Vertical component of velocity v is such that 1:2 >777 (13) This is the same resultsas would be obtained if the particle were initially falling vertically and had no spin, a fact which is due to the assumption that the change in the vertical component is independent of the change in the horizontal component when the impact takes place. Ifwe now put a = 08, h = 5 X 10"8 cm and p z: 2 g/cm3 and substitute for P and m, then if d is measured in microns We find that the particle will stick only if ‘ v < (SO/d) cm/sec The critical velocity is proportional to l/cl, so that for two particles of different size approaching the plate, the smaller S 196 D. W. Jordan is more likely to stick. The speed is very small compared with the speeds of impingement used in sampling instruments, therefore most of the particles will not remain on the sampling plate unless an adhesive is used. It seems possible that those particles which are at first retained will roll or slide away owing to drag of ,the air (Fig. 1). Retention will still be better for small particles, firstly because they are subjected to smaller average air speeds owing to the presence of the boundary layer, and secondly because the air drag depends on dz, whereas the retaining force, and hence presumably the friction, depends on at, so for small enough particles the friction will be great enough to resist the air drag. Some experiments will now be described which supplement an investigation on the efficiency of impingement sampling instruments by Davies, Aylward and Leacey.(7) It was found there that unless an adhesive was used on the sampling plate the proportion of particles caught was very low. The loss of particles was evidently due to their being blown, away or bouncing off 011 collision with the sampling plate. These experiments were carried out to see to what extent the blowing away' of particles took place. A model, slit—shaped jet was constructed with slightly tapering sides and chamfered edges to produce a steady streamline flow of air (Fig. 3). Above it was fixed a plate to lcm 3. Experimental arrangement. C airtight chamber, J Jet, SS cover slip. The detail of the jet design is shown on the right which could be attached the dusty cover slip under test. The jet was fed with filtered compressed air and a flow meter was connected in the air circuit. The procedure was to sediment dust upon several cover slips at once in a sedimentation chamber; the deposits being supposed equal. One was kept KOO . 80 E a to 5 . fig 40 20 OOW'T's—To‘j (a) 5'“ W (b) Fig. 4. Percentage of particles removed at various air ' speeds (a) glass dust, (b) quartz dust. Air speeds down the jet are indicated in m/sec .on each curve (the dotted lines represent extrapolations need for constructing Fig. 5). BRITISH JOURNAL OF APPLIED PHYSICS The adhesion of dust particles as a control, the others were fixed in turn above the jet and subjected for about 2 sec to various air speeds, comparable to those speeds used in practical instruments. Afterwards counts were made along the line directly below the jet to see what dust had been blown away. Experiments were done with quartz dust and ground glass, and the results are plotted on Fig. 4. O 2_ 4 b 8 IO l2 Size 0‘) Air speeds required to remove 20 %, 50% and 95 % respectively of particles from the plate OJ. = Owens jet dust counter; 11L; Bausch and Lomb dust counter; K.K. Kotzé Konimeter; CJ. 2, 3, 4 = cascade impactor, jets 2, 3 and 4. Fig. 5. - — O - — glass —— A — quartz Paper H.4 Fig. 5 gives the speeds for which 20"”, 50% and 95% respectively of particles were detached. The speeds of flow down the jets of some sampling instrtimentstay’s cascade impactor, jets 2, 3 and 4; the Kotzé konimeter; the Bausch and Lamb and\the Owens jet dust counters—are indicated for comparison purposes. It will be seen that very few particles above 10 ,u. will remain on a dry sampling plate even for the very moderate speeds of blowing used in the cascade impactor, and for the Owens jet dust counter very little of any size will remain, as in fact was noticed in reference (7). Another question connected with air sampling which may be mentioned here is whether or not thermal precipitator samples may be sent by post without losing a significant proportion of the sample. The acceleration required to detach a 10 ,LL quartz particle from the plate is 108 cm/secz. Such an acceleration would be produced by stopping the package within 1 mm after its having fallen 600 it. It is not expected that it would encounter such violence, so we may suppose that the samples would not be seriously affected in the post, which is in fact confirmed in practice. Lastly it must be stressed that all the calculations in this paper refer to spheres only, and cannot be applied even in order of magnitude to large irregular particles which may make contact at only a few points. REFERENCES (1) LENNARD-JONES. Pr'oc. Phys. Soc; [London], 43, p. 461 (1931). ' . v . \ (2) BRADLEY, R. S. Phil. Mag, 13, p. 853 (1932); Trans Faraday Soc, 32, p. 1088 (1936). (3) HAMAKER, H. C. Physica, 4, p. 1058 (1937). r4) Basel-1m, D. K011 Zens, 89, p. 215 (i939). (5) LOWE, H. J., and LUCAS, D. H. Static: Electrification, Brit. J. Appl. Phys,Supplement No. 2, p. S 40 (1953). (6) KUNKEL, W. B. J. Appl. .l’l7y.t., 21, p. 821 (.1950). (7) DAVIES, AYLWARD and LEACEY. Arc/7.. 1m]. Hygiene (mil Ocmmalional Medicine, 4, p. 354 (1951). DISCUSSION 'Mr. D. H. Lucas: Mr. Jordan has been kindenough to refer to the work I did on particle adhesion some time ago“) on the ideal case of perfect spheres. He has not, however, men—' tioned that I extended the theoretical study to more practical cases. Since the application of ideal results to real situations is sometimes a dangerous cause of error, I would like to point out that the range of action of molecular forces is very small, even compared with the smallest particles we are considering, and it is the “diameter of curvature” in the region of contact rather than the diameter of the particle which should be substituted in the formula. In the case of a perfect sphere the two diameters are equal. In practical cases the radius of curvature at the point of contact is likely to be much less than the radius of the particle, either because of shape factors or because of surface roughness. It is therefore very dangerous to estimate a‘n adhesive force in terms 'of the size of the particle. It is a fact of experience that angular material such as carborundum is much more free running than glass Spheres ‘ of the same size range and this illustrates the point. Mr. W. R. Lane: The calculations of Bradley and Hamaker referred to in Paper H.4 illustrate the role of van der Waals forces in the adhesion of clean, dry, spherical microscopic particles to each other and to smooth, dry,. clean'surfaces. SUPPLEMENT No. 3 In practice, however, it seems likely that moisture has a significant effect in the sense that an adsorbed layer of polar, molecules may give rise to much larger forces of adhesion. This View receives support from the observation that the inter- particle adhesion of many powders can be greatly reduced by coating the particles with a thin hydrophobic layer. - A film of a silicone polymer, for example, of a few molecules in thickness, is remarkably effective in reducing the tendency of ‘the particles of many fine powders and dusts to clump together. Mr. R. P. Abraham: About 25 years ago the late Dr. Owens devised a simple method of holding large particles on to a cover glass. 10% Canada balsam dissolved in xylol givesa thin coat of balsam after evaporation. When particles are in place a vapour of xylol will soften the balsam and hold the particles without altering their position. The vapour can be easily produced by inverting a dish containing blotting paper on to which a few drops of xylol have been placed. Dr. H. Heywood: The classical systems of packing spheres for minimum voidage are Well known, but the work of Mr. S. Melmore in devising geometrical systems of open packings are worth studying“) These systems had porosities of 94 to 96 %, and compared remarkably well with electron S 197 Discussion on Paper H .4 microscope photographs of carbon black and magnesium oxide smoke. Although the latter did not possess geometrical regularity, as did the systems devised by Mr. Melmore, the general similarity of chain structure was remarkable. 1 REFERENCES (I) LOWE and LUCAS. Static Electrification, Brit. J. Appl. Phys, Supplement No. 2, p. S 40 (1953). (2) MELMORE. Nature, 149, pp. 412, 66.9 (1942). Paper 1-1.5 L ‘ The aggregation of aerosols By J. M. DALLAVALLE, Sc.D., CLYDE ORR, In, Ph.D,, and B. L. HINKLE, Ph.D., The Georgia Institute of Technology, ‘ - Engineering Experiment Station, Atlanta, Georgia, U.S.A. Aggregation of the individual particles composing an aerosol is a phenomenon of primary importance in the aging of the aerosol. The influence of electrification and_fore1'gn vapours .on the aggregation proceSS has been investigated. Results indicate that electrification amounting to a few electron charges per particle has little effect on the rate of aggregation, but has a decrded influence on the shapes of the aggregates. In the case of aerosols whose particles have a significant vapour pressure, certain substances which lower this vapour pressure have been found to increase the rate of aggregation, presumably by reducing the vapour cushion surround- ing the particles. When the particles are readily soluble in a substance whose vapour is present, the rate of aggregation also appears to be increased because of reduction of the vapour layer about the particles. ‘ The aggregation of aerosol particles on aging is a complex process governed by mechanisms which sometimes defy prediction. Smoluchowski’s. theory fer the coagulation of monodisperse sols has been extended to the analysis of the behaviour of aerosols, but conditions satisfying the theoretical assumptions are seldom met in practice. For example, most natural aerosols exhibit a high degree of polydispersity and are seldom free from thermal or turbulence effects. In r addition, the eii‘ect of ' an aerosol’s electrification on its aggregation has been a subject of considerable interest and controversy. , g . The recent studies of Kunkel,(1) in agreement with the earlier work of Whytlaw-Graya) and associates, indicate that the electrification of an aerosol does not alter the aggregation rate. Gillespie,(3) however, eXamined aerosols whose particles carried many electron charges and found that the aggregation rate increased as the magnitude of the charges was increased. The conclusions drawn by some investigators concerning the eifect of certain vapours on the aggregation of aerosols _ are often diametrically opposed to the experimental observa- tions Of other investigators. Smirnov and SolntsevaW report the effectiveness of water vapour and butyric acid as aggregants for an ammonium chloride aerosol, but Samokvalov and Kozhukhovam state that water and octyl alcohol in low concentrations act as stabilizers, rather than aggregants, for ammonium chloride. ,SamokvalovW suggests that if the vapour of a substance with a high dipole moment is introduced into a nonpolar medium such as air, the polar substance undergoes oriented adsorption on the dispersed particles and thus stabilizes. the dispersion. Radushkevich and Chugunovam have found that the rate of coagulation of an ammonium chloride aerosol was reduced by phenol, and was unaffected by methyl alcohol, ethyl alcohol and oleic acid. Petryanov and his co-workers,“” however, report that phenol vapours had no effect on the aggregation of a ferric oxide aerosol. Fujitanim found, by measuring the sedimentation velocity, that a fog produced from an aqueous ammonium chloride solution was stabilized by acetone while carbon tetra- chloride acted ,in the opposite way. Although some of the , apparent discrepancies have been traced to differences in ex- perimental technique, it is obi/ions that many of the phenomena 3198 require further-study before clarity of generalized statements on aging can be "realized. ‘ V , ‘ The purpose of the present study was to investigate some of the aspects of aggregatiOn with emphasis devoted to the role of electrification and to the effects of foreign vapours in the aerosol system. Because of the apparent disagree— ment concerning aerosol behaviour as reported in, the literature, many of the results of this work, while serving as confirmation of some studies, also serve as refutation of other studies. Therefore, it is advisable to qualify present results as pertaining only to the materials and conditions employed. ELECTRIFICATION Before any systematic study of the effect of electrification on an aerosol’s aggregation could be made, it was necessary to devise a technique which would. give accurate, reproducible measurements of the nature and magnitude of the electrical charge carried by the particles and a technique with which the charge on the particles could be altered. Apparatus for charge analysis. A variety of apparatus has been used by previous investigators. The apparatus of Wells and Gerkeflo) subjected airborne particles to an alternating electrical field, thereby causing charged-particles to oscillate and to move in zigzag paths when the particles were passed through the field. The results were recorded photographically. White and .l-IilK“) used the method of Wells and Gerke to obtain the charge on each particle from the amplitude of its vibration, but could not distinguish between positively and negatively charged particles. The apparatus of KunkelU) and Kunkel and 1~Iausen,('2’ recorded photographically successive positions of individual particles settling under the influence of gravity through a horizontal, electrical field. The charge on each particle was i then determined from the path taken by theparticle. Apart from being a tedious and time—consuming analysis for obtain— ing statistically precise results, the technique had one serious limitation. Small convection currents resulting from tem- perature differences between the wall or'ends of the settling chamber could easily invalidate the results. Gillespiea) and Gillespie and Langstrothm) used an BRITISH JOURNAL OF APPLIED PHYSICS Fm riv- V‘s «c l ...
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Jordan 1954 - Bibliotheek T D W Uitsluitend VOOI‘ eigen...

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