Oct., 1958
BEHAVIOR OF LIQUIDDROPLETS ON SOLID SURFACES
Presumably, Mme. Ter Minassian-Saraga did not suspect that the quantities b and (a’ - c) in her results are functions of the amount of benzene per molecule of stearic acid delivered to the surface, Le., functions of the concentration of the spreading solution. This functional dependence is indicated by the trend of the data of column 4, Table I. If one subtracts the area per molecule obtained for stearic acid spread from the benzene solution of concentration 7.72 X lo-* M (assuming that c = 0 for this case) from the other values reported in Table I, one obtains values of c ranging from 0 to 1.4 A.’J/molecule, increasing as the concentration of the spreading solution is decreased. We believe Mme. Ter Minassian-Saraga’s conclusion that the total area occupied by benzene in the monolayer is independent of the amount of myristic acid in the surface (p. 91, column 1, paragraph 2) t o be erroneous. Our results, in view of a postulated interaction between benzene and the
1295
fatty acid monolayer, can be interpreted such that the total area occupied by benzene in the monolayer depends not only upon the amount of stearic acid in the surface but also upon the relative amounts of benzene and stearic acid delivered to the sarface. Other studies showing that organic solvent vapors are strongly adsorbed on stearic acid monolayers are those by Dean and McBain ( J . Coll. Sci., 2, 383 (1947)); Dean and Fa Si Li ( J . Am. Chem. Soc., 72,3979 (1950)), and Dean and Hayes (ibid., 73, 5583 (1951), and 73, 5584 (1951)). It seems an obvious corollary of their results that there can be retention of certain solvents by the monolayer during the spreading process. Micheli (Phil. Mag., ( 7 ) 3, 895 (1927)) and Jones, Ottewill and Chater (2nd. International Congress of Surface Activity, Acad. Press, vol. 1, p. 188) have found that organic vapors are strongly adsorbed on clean water surfaces.
ON THE BEHAI7IOROF LIQUID DROPLETS AFTER IMPINGING ON SOLID SURFACES’ BY ISAIAHGALLILY AND VICTOR K. LA’MER Contribution from the Department of Chemistry, Columbia University, New York, N . Y . Received March 8 , 1068
The deposition of particles impinging on solid surfaces was investigated for a s stem composed of a two-dimensional jet of glycerol aerosol and Desicote-coated glass microscope slides inclined to it. J h e patterns of the particles deposited in these experiments were found to change with the velocity ol the jet and the radius of the aerosol contrary to the way usually expected. They indicate that a certain fraction of the particles bounces off from the surface on first contact. A qualitative explanation of the phenomena found is offered.
I. Introduction succeeding the impingement of particles is conUntil recently it has been assumed that an aero- trolled by the opposed action of “removing” and sol particle moving at a low Reynolds number and adhesional forces. They hold that the impacting impacting on some solid surface adheres at its first aerosol particles would fail to adhere whenever the point of contact.2 Thus the capacities of collecting ( L removing’’ force (or energy) exceeds that due to devices such as cylinders, slides and fibrous filters, adhesion. However, these forces are evaluated difto remove aerosols were calculated and checked ferently in the two studies. While Jordan visualizes the adhesional force as experimentally without paying attention to the “sticking probability’’of the impinging particle~.~-7 operating be$ween an impinging solid sphere and a On the other hand, in sampling sprays by impaction plane that have only one point of contact regardless the probability of noli-adherence usually has been of the velocity at impact, Gillespie and Rideal taken into account and in practice the collecting allow for the compression of the particle and the surfaces are coated with suitable materials to affect subsequent generation of elastic strains withln it. adhesion. The problem of the “sticking prob- Whereas the “removing” action is attributed by ability” of aerosol particles impinging on solid sur- Jordan to the kinetic energy of the impacting parfaces was treated lately in a series of studies which ticles, Gillespie and Rideal consider the viscous drag questioned the complete-adherence assumption of the medium flowing past the surface as the prineven for the sub-micron and the low Reynolds cipal operating agent. Thus, according to Gillespie and Rideal, the number ranges of particle sizes and velocities.*-l‘ A. Previous Work.-According t o JordanlO and impinging particle would not adhere when Gillespie and Rideal,9 the sequence of events (1) Thia work was supported in part by Contract AT(30-1)2017 between Columbia University and the U. S. Atomic Energy Commission and in part by the Government of Israel. Isaiah Gallily: P. 0. Box 7057, Hakiryah, Tel-Aviv, Israel. (2) (a) I. Langmuir, O.S.R.D. 865, Sept. 4, 1942, reprinted by De partment of Commerce; (b) C. Y. Chen, Chem. Reus., 5 6 , 5 9 5 (1955). (3) C. N. Davis, Inst. Mech. Engrs. (London) PTOC.( b ) , 1B, 185 (1952). (4) F. Albrecht, Physik. 2..82, 48 (1931). (5) S. IC. Friedlander, A.I.Ch.E., J . , 3, 43 (1957). (6) V. K. La Mer, el aE., Final Report NYO 512, Contract AT(30-1)651, Columbia, University, N. Y., (7) E. A. Ramskill and W. L. Anderson, J . Colloid Sci., 6 , 416 (1951). ( 8 ) T. Gillespie, ibid., 10, 266 (1955). (9) T. Gillespie and E. Ridesl, ibid., 10, 281 (1955). (10) D. W. Jordan, Brit. J . A p p . Phys., 8 , S194 (1954). (11) I. Gallily, J . Colloid Sei., 12, 161 (1957).
1951.
where a is the radius of the particle, R, is the radius of its common circle of contact with the collecting surface, h is its separation (at contact) from the plane, BA is the surface energy of adhesion/cm.21p is the viscosity of the dispersing medium, Va is its velocity parallel to the surface and a t a distance a from it, and y is a dimensionless constant smaller than 1. With respect to the interplay between drag and adhesion one should mention also Rumpf’s paper12 where the forces acting on deposited particles imbedded within a turbulent boundary-layer flow are (12) H. Rumpf, Chem. Ing. Tech., 6 , 317 (1953).
1296
l S A l A H GALLILY AND VICTOR
K.L A M E R
Vol. 62
away. To gain information about the operating mechanism the collecting surface was sparsely covered with sub-micron particles (much smaller than the tested ones) hoping thus that, should sliding occur, each displaced droplet would leave a clear trail after it. The experiments themselves were carried out by impacting a jet of homogeneous aerosol, of constant radius and concentration, on inclined glass slides at several velocities of flow and photographing the collecting surface through the microscope. Since the impinging jet comprised a range of particle sizes, and as these particles struck the solid surface with different velocities, we expected and found the reimpinged particles to be dispersed over the surface rather than concentrated in a narrow strip. Accordingly, the distances of the deposited droplets from the stagnation point of the jet were measured in each case, their cumulative distribution formed, and the Inter Quartile Range (I.Q.R.), viz., the difference between the upper and lower quartiles as a measure of the dispersion in the distribution13 was noted. Fig. 1.-A block diagram of the main experimental appaThe experimental set-up (Fig. 1) consisted of an ratus. aerosol generator (A), a flow conduit (B) terminating in a rectangular nozzle (C), a machined plate AEROSOL AIR I I (D) containing the collecting surface, and intercepting devices for sampling purposes. The Sinclair-La Mer homogeneous aerosol generator14 was used in the present study with its cooling chimney inverted for the production of larger aerosols. l6 The flow conduit, separated from the chimney by the interceptor, was composed of a circular glass tube having a cone of approach of 7.8” and a number of openings for mixing, exhausting and maintaining a constant rate of flow through it. The metallic plate (D), placed on a frame with four levelling screws, could be tilted between 0” and 90” 0 STAINLESS STEEL to the horizontal. Lengthwise it had a groove for microscopic glass slides which formed a practically . . p BRASS infinite plane with respect t o the nozzle. The Fig. 2.-The interceptor. Arrow goes to motor (not interceptor (S) (Fig. 2) sampled a small portion shown). of the aerosol under conditions of steady flow. It analyzed and some consideration is paid to the role was composed of an array of four pipes cut by a thin of the roughness of the surface. recess where a plate with suitably positioned recB. Statement of Aim.-In order to understand tangular slits could be moved by an electric motor and evaluate more correctly the collection of aero- (M) (shown in Fig. 1). sols by impaction, it was considered worthwhile in Instead of the usual “controlled speed shutter” the present state of knowledge to study systemati- type of devices that produce a disturbance in the cally, and obtain more definite information about aerosol on sampling, the volumetric rate of flow the dependence of the particle “sticking prob- through the nozzle was kept constant in our exability” on such variables as its radius, velocity of periments by an accurate and gradual switching flow and the roughness of the collecting surfaces. from a certain flow of pure air t o its equivalent aerosol stream and vice versa. With this arrange11. Method and Apparatus As it was impractical to photograph the actual ment the time of sampling in the experiments could tracks of impinging droplets, a study of the pat- be varied merely by changing the transmission terns of particles deposited on a suitable surface screw attached t o the motor indicated by the arrow. under various conditions of experiments was made. 111. Experimental Parameters and Considerations From these patterns inferences are drayn about Regarding the Jet and Collecting Surfaces the behavior of the aerosol on impact. Our first objective was to experiment with a system where The experimental system, chosen to be as simple non-adherence would most likely occur to a considerable exas possible, comprised liquid particles, a two(13) A. C. Aitken, “Statistical Mathematics,” University Mathedimensional jet, and a plane solid surface inclined Texts, Oliver and Boyd, 1949,p. 35. to it. With this system we anticipated that non- matical (14) V. K. La Mer and P. R. Gendron, ”Chemistry in Canada,” adhering droplets would either slide over the sur- April, 1952. face or bounce off and reimpinge a little further (15) J. H.Burgoyne and L. Cohen, J . Colloid Sci., 8,364 (1953).
Oct., 1958
1297
BEHAVIOR OF LIQUIDDROPLETS ON SOLID SURFACES
tent. Accordingly, wr used a glycerol aerosol (specific gravity 25”/25” 1.250) and a surface coat of Desicote (Beckman 262-B), a water-repellent material, applied to all of the collecting glass slides. Representative samples of the slides were then examined for roughness under an electron microscope. The remainder were sparsely covered by submicron glycerol droplets so that the trails of sliding particles would leave tracks on the surface. As the pattern of the deposited droplets depends on the efficiency of the aerosol impingement, on the cross-section of the jet at the slide and, supposedly, on the “sticking probability” of the particles, care always was taken to ensure constancy of the first two factors. The efficiency of impingement ( T ) of a two-dimensional jet directed normally against a plane surface depends, according (2pe to Ranz and Hofelt,16 on an inertial parameter N D Vo/9pd)’/p X a, a non-Stokesian parameter Npg= and the spacing of the nozzle N , = s / d . Here VOis the exit velocity of the jet, d is the width of the nozzle, s is its distance from the plane, pg is the density of the dispersing medium and pe is the density of the particle material. It is probable, of course, that in the present case is affected also by e, the angle between the collecting surface and the horizontal. However, as this factor acts in opposite directions for the upstream and downstream regions of the inclined plane, it seemed justifiable to use Ranz and Hofelt’s analysis as a first-order estimation of the impingement efficiencies. In the present series of experiments the aerosols used had average radii ranging from 1.48 to 5.14 p and u/ii values of 0.08 to 0.19 (where u is the standard deviation and 8 is the arithmetic mean). The exit velocities of the jets were between 1125 and 1612 cm./sec. The glass nozzle*’ had a width of 0.76 mm., a lengbh of 8.79 mm., and extended about 29 mm. The angle e was 41’ and the spacing parameter N , = 2.0 f 0.2. Thus the values of the inertial parameter ranged from 0.71 to 2.94 and the values of the non-Stokesian parameter were between 5.69 and 8.15 which supposedly ensured the 100% efficiency of impingement. I n respect to the jet, due attention was paid to its spread and change of width near the collecting surface with the variation of N.. The increase of this width downstream is given theoretically’* for the laminar case-corresponding to the present Reynolds numbers (based on the hydraulic mean depth of the nozzle) of 1140 to 1633, by
)
IV. Procedure Each experiment involved four steps: the preparation of slides, impaction of aerosols, microphotography, and counting the number of images of the droplets on the developed films. In the first step, the glass slides (Pittsburgh Nqn-Coorosive, No. 12-550) were bathed in hot sulfo-chromic,acid, rinsed with tap water, a detergent solution, distilled water and finally dried in an oven. After cooling, these slides were again dipped several times in Desicote and dried a t 40”. They were polished thoroughly with a lens paper and flushed by a stream of dust-free nitrogen. The slides exhibited a clean surface under a light microscope. As polishing usually produces electrostatic charges, we tested a representative sample of these slides by a field (16) W. E. Rans and C. Hofelt, I n d . E ~ QChem., . 49, 288 (1957). (17) Drawn over an accurately ground graphite mould. (18) H. W. Liepmann and J. Laufer, NACA TN, No. 1257.
I
I
3.0
6.0
l
e .o
DISTANCE OF DEPOSITED PARTICLE (mm.).
Fig. 3.-A typical cumulative distribution of the distances of the deposited particles from the stagnation point of the jet; VO= 1525cm./sec.; = 3.03~.
1
0
4.0
x
P
f
--- 2.21P l.46n”
e-
\-I
where x is the longitudinal coordinate, v is the kinematic viscosity of the flowing gas and b is half the width. Likewise,. photographs of the issuing jet at the various exit velocities showed that the cross-section near the nozzle increased very little downstream. Comparison of the photographs with the changes found in the patterns of the deposited particles justify disregarding the variations in crosssection factor of the jet. The glass slides themselves, examined under the electron microscope, showed, for distances of up to 7p, a small rugosity as compared with the size of the tested droplets. Thus this factor was also considered to be of a minor influence.
I
0.0
-a4w S.03C 6.14P
3.0
E
I
8.0
a 0
I .o
1200
1400
1600
bVERAGE EXIT VELOCITY OF lMPACTlNO JET (cm/Ed.
Fig. 4.-The Inter Quartile Range of the cumulative distribution of distances us. the average exit velocity of the impacting jet. meter.lQ The charges found were small compared with those generated similarly on less conductive materials (such as ebonite, etc.), and since on theoretical grounds it is believed (19) Electrostatio Voltmeter made by Specialties, Ino., Syorrset,
L. I., N. Y .
ISAIAHGALLILYAND VICTORK. LAMER
1298
0
--
X
-.
I250 CMJSEC. 1375 CMISEC. I525 CM./SEC. 1612 CM./SEC.
D -
3.0-
?’
s
f ” ci
-
a
2.0-
i 1.0
‘I
/
7
X
I.o
/
I I I 2.0 3.0 4.0 AVERAGE RADIUS OF AEROSOL
/
I
5.0
($1.
Fig. 5.-The Inter Quartile Range of the cumulative distribution of distances us. the average radius of the aerosol from the impacting jet.
Vol. 62
In the second step the main aerosol generator (A in Fig. 1) and the one used to produce the sub-micron aerosol were switched on. As the temperature of the operating parts attained a steady state, the coated slides were placed in a sedimentation box into which a sub-micron aerosol of measured radius was led for a time sufficient to produce a sparse deposit. The number concentration of the deposited particles was always checked microscopically. Prior to the impactions, the rate of exhausting in the flow conduit (B) was set a t an appropriate value and a pretreated slide placed under the nozzle in the specially pre ared groove. The impinging operation itself was accompgshed by actuating the electric motor (M), thus working the interceptor (S). This operation was repeated with four exit velocities for a given radius of the aerosol. After completing the impactions three slides of samples, taken at different times during the run, were photographed and the size distribution of the aerosol assessed. The main body of the slides was photographed with a low magnification ( X 2 0 ) and the films were developed for the subsequent determinations of the cumulative distribution of distances. These determinations were carried out by dividing the length of the image of the slide into appropriate class-intervals and counting, through a special viewer, the number of droplet images in each one of them.
V. Results The present series of experiments comprised six runs followed by twenty-three determinations of cumulative distribution of distances. One of these distributions is represented as an example in Fig. 3. The Inter Quartile Range (I.Q.R.) noted for each one of the distributions (see Table I) is graphed in Fig. 4 as a function of the average exit velocity of the jet and in Fig. 5 as a function of the average radius of the aerosol, for otherwise constant conditions of experiments. TABLE I
THE INTER-QUARTILE RANGEOF TRIBUTlON O F
THE CUMULATIVE DISDISTANCES FOR VARIOUS VELOCITIES O F JET AND R A D IOF ~ AEROSOLS 7
-FREE
STRE&MLINES
ISCHEMLTICAL)
....-.-ASSUMED Of
Fig. &-Assumed
PATH PARTICLE
path of a bounced off droplet.
---- ADHESIQN VS.
RADIUS
-
DRAG VS. R A D I U S (v;
AVERAGE RADIUS O f
> vi,
AEROSOL,
Fig. 7.-The adhesional force, and drag, us. the radius of the impinging particles (semi-quantitative). that the adhesion of particles is affected only slightly (see Discussion), their presence was ignored.
a (p) 1.48 2.25 3.03 3.60 3,69 5.14
d a 0.18 .15 .I2 .12 .14 .09
1125
... 0.17
... ... ... ...
I. Q. R. (mm.1 Velocity (cm./sec.) 1250 1375 1525
0.48
.. .
.35 .26 .31 T.67
0.39 .96 .31 .35 .22 3.15
1.27 2.45 2.80 0.31 2.80 2.7G
---.
1612
... 2.41 3.11 3.46 4.34 2.98
VI. Discussion The patterns of droplets deposited an the coated slides when examined microscopically show some unusual features as revealed by their I.Q.R. values (Table I). If the deposition of aerosols is due almost solely to the impaction mechanism it is difficult t o understand why the dispersion of particles over the collecting surface increases with the velocity or the radius of the aerosol. Actually, one might expect the opposite behavior. Likewise, using the same arguments, it is hard to explain why most patterns show two separated groups of droplets. The phenomena observed could be interpreted as resulting from the bouncing off of some glycerol droplets from the Desicote-coated slides and their subsequent reimpingemeat. Moreover, as we have not found on the collecting surface any cleared up trails (which in some preliminary experiments were seen to occur with 30-40 p droplets), it is believed that the sliding mechanism does not operate here and that the non-adhering droplets
Oct., 1958
BEHAVIOR OF LIQUIDDROPLETS ON SOLID SURFACES
leave the surface very near their point of first contact. We presume, therefore, that in the present case the droplet bounced off is affected by the viscous drag of the air and moves very near the slide along a curved trajectory LO reimpinge on (or miss) the surface (Fig. 6.) The likelihood of leaving the slide after the first contact and the curvature of the path executed in the air subsequently would be determined by the adhesion between the particle and the surface, by the “strain” produced on impingement in the deformed droplet and its release; also by the viscous drag of the air, and the Brownian motion of the particle in the stream line. It should be emphasized that according to Jordan’O the long-range electrostatic forces affect the particle’s adhesion very slightly as compared with the van der Waals forces of attraction. Assuming a small deformation a t impact the adhesional force is given by the bracketted right-hand side of equation 1. I n this equation the radius of the common circle of contact (R,) for a solid sphere is expressed by Real R2,,maX a u 4 X V12 (3) where VI is the normal component of the particle velocity at the surface. However, as one has to deal here with liquid droplets the adhesional force ( F A ) may be given as
AVERAGE
EXIT VELOCITY OF
1299
JET.
Fig. %--The adhesional force and drag, us. the average exit velocity of the jet (semi-quantitative).
experimentally as an approximate measure for the energy with which the droplets bounce off, one might correlate it with the difference between D and FA, and D itself. Thus, using Rumpf’s scheme of we can draw graphs for each point on the surface strucli by the impinging aerosol. From Figs. 7 and 8 it is seen that the bouncing off of the particles should start only after a certain velocity of impact (see also Fig. 4); below that point and above some higher velocity adherence FA = A ~ X A a(l BaqVF) (4) would be coxpleteZ1and the I.Q.R. curves (servwhere A , B, P and q are constants depending on the ing as a measure of the effect) should show a materials composing the droplets and collecting maximum, or a levelling off tendency, as predicted surface and q, P > 1. The viscous drag (D), in other terms by Gillespie and Rideal.g ‘These constituting supposedly the main factor affecting figures show that by increasing the velocity of the the path of the bounced off particle, might be given impinging jet the maximum of the bouncing off t o a first approximation by Stokes’ law corrected curve would shift toward smaller particle radii, which is believed to be reflected in the shape of the for the “wall effect”20 upper and lower curves of Fig. 5. D =6~paV~ 1 Acknowledgment.-The authors acknowledge the (5) (l-kk) aid given by Mr. Samuel Kamhi for taking the electron microscope photographs, and by Mr. where e is twice the distance from the wall in a Ronald Wacht,el for assisting in calculations conmotion parallel t o it and k is a constant. cerning the cumulative distributions of distances. Taking the Inter Quartile Range (I.Q.R.) found
+
(20) P. G. W. Hawksley, Brit. J . A p p . Phys., 8, S 1 (1954).
(21) Though at the high velocities one has t o consider the possible shattering of the particles.
