r,.
F, EVAXS
Division of Industrial C h p m i s t r y , Commonwealth Scientijic and Industrial Research Organization, Melbourne. Victoria, Australia
1IE flotation piocess, in 1~11ichvarious niinerak nitiy be separated from an ore, depends 011 the ability of ftli air bubble moving through a suppension of finely ground ow t o eollide and adhere to those particles with a hydrophobic surfac~. The process of adhesion may he studied by pressing II captive air bubble against a hydrophobic surfacc submerged in a-ater. .‘I certain time d l elapse between the moment of apparent roiit’;ict (as denoted by distortion of t,hc bubble) and true contact> (the formation of a solid-air interface). This time was termed the induction period by Sren-Silsson ( I S ) , who determined tlic varitibion of induction period \vith bubble size :ind the concentratioii 01 collector, which reagent causcs tile surface to become hydrophobic to varying extents. His theory of the induction period assumed that the hubble rc:ielied an eydibrium distanw h i i i the solid surface and remained there until soiiie process prowecirtl to completion, whereupon the bulshle adhered.
~
__
-
Thc problem is dealt with in three parts. First, the conwpi of ‘,rupture thickness” is introduced, a method is dcseribed for ineasuring its value, and t!ic effect of rupture thicltness on incluction period is discussed. The collision b e b e e n a particle anti n bubble is then examined and an expression for the time avai1:iblt~ for contact is derived. Finally, a study is made of the shapc of ii bubble pressed against a hydrophobic surface, and the possihilitiof c t h d a t i n g the inductiori period is discussed. DETERh1PNATIOS OF HIJPTURE TIIICKNEBS
T o c~:ilculatetne time required for a bubble to establish coiitilrt with a plane hydropliohic surface one must know the thiclinwr: : I t n-hirli t h e film spontaneously ruptures---termed the rupture rhirkness. Alt,hough the films under examination are a few thousand dngstroms thick, interferometric methods can bc used to rncasure the thickness only if sufficient time is available t o make the necessary observations. On a strongly hydrophobic surface the induction period is less than 1 second and illuminat,ion rannot be made sufficiently intense to obtain the necessary high speed photographs of the fringes. K i t h the apparatus describcd, measurements are riiade possihlc by prolonging the induction period indefinitely, the dis-
b
__
~
__ -
-.
Figure 1. Apparatus f o r PIeasuring Rupture 1 hiclilless D.
Disk
M.
Microscope Light source
R. Rublrle I,.
S. 7’.
v.
Slit Bubble holder Vc*srl
In the present paper it is slio.i\-rithat the hubb!e is i i o t 5t:itioi;ary during the induetion period, and that the water film ~r-hicli separat,es the bubble from tlic, solid surface drains rontinuousl~~ through a restrictcd outlet. Tl!e induction period is I I i ~ r r f o r ~ defined as the time required for the disjoining film to drain to suc~li a thickness that rupture takes place. Now Elton ( 2 ) has shon.n that in pure water the approach of a bubble to a plane hydrophilic surface takes several hours t o reach a thickness of 2000 A. However, ii we press t,he same bubble against a plane hydrophobic surface, air-mineral adhesion is achieved in less t,han 1 second. Obviously the mechanisnis are quite different in the two cases. If ttic flow of liquid betn-em bubble and hydrophilic surface is considered to be the nornial case, then flow in the liquid adjacent, to the hydrophobic surface is either abnormally fast or the film must rupture a t some considerable thickness. It was the object of this work to determine which of these processes is iniportant and if possible relate it to the induction period.
’1 To N o s %
Figure 2. .ipparatus f o r Preparing a Small 1Iydrophohlv Spot
joining film being maintained in dynamic equilibrium by balaneing the normal outflox of wat,er against an inflow caused h y lateral motion of the solid surface relative t o the bubble. APP.~RATLTS.A disk of fused silica, 1 inch in diameter and I nun. thick, was rotated in the horizontal plane by means of a vert,ical silica shaft fused t o the center of the disk (Figure 1). The underside of the disk was just immersed in vr.ater and a
2420
November 1954
INDUSTRIAL AND ENGINEERING CHEMISTRY
bubble, blown on the end of a. hydrophobic glass tube, was pressed against the underside of the disk by means of a micromanipulator. By focusing a microscope on the flattened upper surface of the bubble, fringes were observed which represented the thickness contours of the film of water separating the bubble from the disk. The angular velocity of the disk was continuously variable. The total pressure in the bubble was measured directly by a manometer containing dibutyl phthalate, the excess bubble pressure being the total pressure minus the pressure due to the head of water between the underside of the disk and the water level. These two levels were measured by a cathetometer which enabled the pressure to be determined to an accuracy within =k0.50/0. The whole apparatus was kept in a thermostat maintained a t 20" rt 0.2" C. As most measurements were with the first few fringes, it was convenient, for their identification, to use white light and compare the interference color with a reference fringe projected onto an adjacent part of the microscope field. When the disk was rotated, water was drawn continuously between the disk and bubble, the film thickness increasing with speed of robtion and decreasing with increasing excess pressure. Standard conditions of excess pressure (1100 dynes per sq. cm.) and film thickness (2500 A , ) were arbitrarily chosen and the variation of disk velocity was studied as a function of other variables in the system. The chosen hydrophilic system was that of clean silica in pure water. The chosen hydrophobic surface was the same surface after exposure to the vapor of monoethyl trichlorosilane, the contact angle being controlled by the time of exposure. The use of such reagents for waterproofing glass has been described by Rochoiv (9). The choice of waterproofing reagent is rest,ricted to one which is not soluble in water; otherwise it diffuses to the bubble surface, where it has a marked influence on the film thickness. For instance, the film thickness is doubled by the addition of 10-6M sodium hexadecyl sulfate. This rather unexpected effect is due to the circulation of surface-active material on the bubble surface, such material being carried from C to B (Figure 3) by the motion of the disk, then moving over the lon-er portion of the bubble to C, where it d r a w additional liquid into the film. Such a mechanism has been described by Schulman and Teorell (IO) as surface transport. When only a portion of the surface was t o be made hydrophobic, it was found convenient to expose the whole surface to the vapor, then to dissolve the siloxane film from the unwanted portion with chromic acid. For some experiments where only a small spot about 0.5 mm. in diameter was required to be hydrophobic, the apparatus shown in Figure 2 was used. After the whole disk had been exposed to the silane vapor, it was held face downward in vessel A under water. A small air bubble was attached to the required spot and the water displaced upwards by hot chromic acid. After leaching for a few minutes, the chromic acid was displaced downward by water and the disk washed thoroughly. Only the spot protected by the attached bubble was then hydrophobic. This method had the advantage that, while the whole surface was hydrophobic, the contact angle could br measured by the captive bubble method described by Wark (14). EXPERIMENT 1. To determine the influence of the state of the disk surface on film thickness, one half of the disk was made hydrophobic and the other half hydrophilic. On rotation, the bubble t,hen traversed the two areas alternately. Figure 3 shows the contours of the film as the bubble traversed the hydrophilic surface. As the bubble traversed the hydrophobic half, it made contact a t the two points D. To prevent such contact, the disk ve1ocit)ywas increased until the thickness a t D ~ a fabout i 2000 A,, the thickness a t A increasing simultaneously from 2600 to about 6000 -4. The contours of the film t,hen remained unchanged as the bubble passed from the hydrophilic to the hydrophobic area of thc disk. I t was not possible by this method to estimate the rupture thickness accurat,ely, because of the high curvature a t D
2421
(Figure 3 ) and because of the sensitivity of the thickness at I? to inevitable external vibrations. EXPERIMENT 2. T o measure the rupture thickness accurately the following modification was made. A spot, of diameter equal to about one third of the distance D - D,was made hydrophobic and the bubble positioned in such a may that as the disk rotated the spot traversed the arc C A B (Figure 3). By this means a film, unaffected by vibration and of uniform thickness, momentarily existed between the bubble and the hydrophobic spot. The speed of the disk was slowly reduced until rupture just occurred on the hydrophobic spot. The film thickness a t A was then determined by comparing the intrrference color with the standard colors.
\
/
\
Figure 3.
25MPI'
\\
Flattened Upper Surface of Bubble as Seen through the Microscope Position of fringes hhown diagrammatirally
The rupture thickness increased with contact angle, a value of 1500 =k 100 A. being found for a surface exhibiting the maximum contact angle for the silane (66'). This value was independent of the internal pressure of the bubble over the limited range available for study (500 to 1500 dynes per sq. cm.). DISCUSSION. Although the concept of rupture thickness 1s sufficient to explain qualitatively the rapid adhesion of a bubble to a hydrophobic surface, the possibility remains that thinning prior to rupture is assisted by abnormally fast flow adjacent to the hydrophobic surface. Henniker (6) has demonstrated that water flows faster through a capillary when the walls are hydrophobic and claims that the viscosity of the liquid adjacent to a hydrophobic surface is less than that adjacent to a hydrophilic surface. If this effect were sufficient to influence the rate of approach of an air bubble to these surfaces, one would expect, in Experiment 1,a change in the contours of the bubble as it traversed the boundary between the hydrophobic and hydrophilic surface. S o such change was npparent. Normally, a second factor influences the rate of approach of a bubble to a hydrophilic surface-namely, a repulsive force which is believed to arise from the interaction of the double layers. If this repulsive force should be less between a hydrophobic surface and a bubble surface than between a hydrophilic surface and a bubble surface, then the approach of a bubble to a hydrophobic surface would be abnormally fast. I n Experiment 2 we have a hydrophobic spot on an otherwise hydrophilic area against which a bubble is pressing uniformly. Thus conditions are such that
2422
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
differential repulsion should be made evident by local thinning over the hydrophobic spot during the time that the spot travels from C to B (Figure 3). Such thinning was occasionally observed, the nonreproducibility being possibly due to contamination, which has been shown by Evans ( 3 ) to have a marked influence on the repulsive force between a bubble and a solid surface. Supporting evidence for differential repulsion has been presented by Evans and Ewers (6) for another system where the results were reproducible. Thus it is concluded that the flow of liquid is abnormally fast between a hydrophobic surface and a bubble wrface, but as the difference is appreciable only when the disjoining film is somewhat less than 1000 A, the effect will be of little importance in flotation systems where the rupture thickness 1s in the vicinity of I500 A.
Vol. 46, No. 11
In flotation the bubble is much larger than the particle, so that the rebound may be treated as that from a plane air-water interface deformed to the shape of the particle as in Figure 4. The time available for contact is the time during which the surface is deformed. Let R
= = M = VAT = = = T
h'
radius of bubble radius of particle massofparlicle normal veloyity of particle surface tension depth of penetration
For a depth of penetration h, the increase in surface area a p proximately equals the area of segment of fiphere BDC minu8 area of circle of radius A B : Increase in area = 2 ~ r h- ( 2 w h
- nh2) = xh2
and the work done due to increase in area is
W
= ryh*
(1)
The force due t o the distorted surface, which acts on the particle, is
Figure 4. Sectional View of Spherical Particle Penetrating Air-Water Interface
These experiments indicate that the method could be extended to the study of the vaiiation of rupture thickness with electrolyte concentration or with surface active material ad.orbed a t the bubble surface. In experiments in which air bubbles aere allowed to slide up an inclined hydrophobic plate immersed in 1%-ater,Pryor and Dzienisiewicz ( 8 ) took the distance traversed by the bubble as an index of hydrophobicity, the inference being that adhesion was promoted by the passage of the bubble in close proximity to the plate. Their system of a bubble sliding over a stationary plane surface is equivalent to the present system of a disk surface sliding past a stationary bubble, in which it has been shown that the disk may be rotated indefinitely a t constant speed without causing the bubble to make contact. Similarly, the distance which the bubble slides up the inclined plate can have no direct effect on adhesion and one must look for associated factors to explain Pryor's results-for example, a change in wlocity of the bubble FI: it moves up the plate. CALCULATIOY OF TIME 4V.4ILABLF: FOR C O V T 4 C l
For attachment of a mineral particle to a bubble in a flotation cell, the induction period must be less than the time of apparent contact. While such an initial attachment may not ensure successful flotation, for there may be many reasons why bubble and particle subsequently part company, it is a necessary preliminary to flotation. The problem considered here is that of a spherical bubble rising t,hrough a suspension of spherical mineral particles in water. A particle which lies in the path of the bubble tends to follow the streamline on which it lies and the point a t which it collides with the bubble is defined as that a t which the t\yo spheres just touch. However, because of the greater density of the particle, its inertia will cause the particle to leave the streamline and collide forcibly with the bubble. The particle will then rebound from the bubble surface.
Thus the force accelerating the particle in the direction normal to the bubble surface is proportional to the depth of penetration and the motion in this direction is therefore simple harmonic. The time available for contact, T , is half the period of the simple harmonic motion Therefore
(3)
The simple harmonic motion can be correct in this model only if the particle does not penetrate a distance greater than its own radius. This is found to be so from examination of high speed cine photographs taken by Spedden and Hannan (11). The assumption that the bubble deforms to the shape of the particle is justified only when the radius of the particle is large compared to the thickness of the intervening film. Thus the theory would probably not apply to particles of radius less than 10 microns. From Equation 3 it follows that the time available for contact, is independent both of the normal velocity of the partirk and of the point a t which the particle strikes the bubble. However, the time available for contact is not, in itself, any indication of the probability of the collision being fruitful, but merely sets an upper limit to the time during which rupture of the disjoining film must take place. On thc other hand, the factors which govern the expulsion of water from the disjoining film are by no means independent of the conditions of collision, the expelling pressure being in fact proportional to the velocity normal to the surface (Equation 2). Philippoff ( 7 ) has independently developed a similar theory based on the elastic rebound of a cylindrical particle falling under gravity onto a stationary bubble. The expression thus derived for the time available for contact resembles Equation 3. Sutherland (12) deduced an expression for the time available for contact from a different point of view. He assumed that the particle was without inertia and followed the streamline given by potential flow around a bubble. Collision with the bubble was a t the point where the streamline was separated from the bubble by a distance equal to the radius of the particle. The time available for contact was then taken as the time required for the particle t o move around the bubble to the point where the streamline was again separated from the bubble by a distance equal to the radius of the particle. The relation thus obtained was
T =
4R E - sech-1 ___ 3v d3rR
INDUSTRIAL AND ENGINEERING CHEMISTRY
November 1954
where E = perpendicular distance of the particle a t infiriitv from the path of the center of the huhble T = radius of particle R = radius of bubble V = velocity of bubble relative to the liquid a t rmt T = time available for contact The value of E a t 2’ = 0 was denoted by D. Figure 5 shows how the time available for contact varied with the position of the particle.
01
0 2
0 3
0.4
0 5
Ob
0.7
08
0 9
1.0
90
Figure 5. Relationship between Time of Apparent Contact and Position of Particle Relative to Bubble (Sutherland)
In contrast to this result, the time available for contact found from Equation 3 is independent of E, but dependent on the mass of the particle. The numerical value of the time available for contact for particles of various radii is given in Table I.
2423
used to study the approach of a bubble to a stationary silica surface, the rate of approach being regulated by the micromanipulator. When the silica surface was strongly hydrophobic, the apparatus was modified so that high speed photographs could be taken. The light source was changed to a gas discharge tube operating a t 100 flashes per second, and the angle of incidence arranged so that the light was completely reflected a t the flab tened upper surface of the bubble. The duration of the induction period, the point of rupture, and the ratc of recedence of the disjoining film could all be determined from tile photographs thus obtained. RESULTS AKD DISCCSSION. Derjaguin’s experiments have been confirmed by the present work. By controlling the rate of approach of the bubble, the stages of development of the lens have been shown to be as in Figure 6. While the flattened area of the bubble was still growing radially, the entrapped film was substantially plane (Figure 6,b), but as the bubble came to rest the film thinned abruptly a t the periphery (Figure 6,c), followed by a slon, adjustment of the shape to conform to the requirements of the pressure drop across the Elm and the curvature of the bubble (Figure 6,d). When the same experiment was performed on a slightly hydrophobic surface, for which the induction period wab several seconds, precisely the aame behavior was observed, except that when the film thickness a t the periphery reached the rupture thicliness, contact took place. T o prove that contact was initiated at the periphery even on surfaces exhibiting short induction periods, the high speed photographic method was used. It was fourid that on a surface rendered strongly hydrophobic by treatment in a solution containing 15 mg. of hexadecyl trimethyl ammonium bromide per liter, the Elm ruphred a t the periphery after an induction period of 0.3 second.
TABLE I. THEORETICAL TIME O F APPAREwr CONTACT (Density of particle 5 ) Time dvailable for Radius of Particle. Contact, P Milhsec. 200 1.88 100 0.67 50 0.23 10 0.02
Comparison of Figure 5 and Table I shows that the large majority of particles which strike the bubble will rebound before they have time to negotiate the path pictured by Sutherland. SHAPE O F BUBBLE IN APPARENT CONTACT WITH SOLID SURFACE
I n order to calculate the induction period theoretically, in addition to knowing the rupture thickness, a suitable geometrical model must be chosen to represent the shape of a bubble as it approaches a hydrophobic surface. Derjaguin and Kussakov ( 1) showed, by an interference method similar to that described above, that the shape of the Elm trapped between a bubble and a plane hydrophilic surface is a plano-convex lens which drains slowly through a narrow peripheral outlet. The curvature of the lens being negligible, the force which expels water from the lens is the excess bubble pressure, which is inversely proportional to the radius of the bubble. The shorter induction period exhibited by small bubbles is due to this factor and not, as Prpor ( 8 )suggests, to the fact that, small bubbles have “much free surface energy seeking for satisfaction.” EXPERIMENTAL. The arrangement illustrated in Figure 1 was
a
Figure 6.
b
c
d
Approach of Bubble to Plane Hydrophilic Surface
The geometrical model which approximates to the above s j s ten1 is that of a ring approaching a plate, with the limitation that no inward drainage can take place. Obviously, if the rate of ai)proach of the bubble is sufficiently slow, the rupture thickness is reached before the bubble is appreciably distorted, and the modP1 which best described conditions prior to rupture is probably that of a sphere approaching a flat plate. Because of the difficulty i n deciding which model applies for a given set of conditions, no method can be suggested for calculation of the induction period theoretically. Even if a model is accepted, there is still the problem of choosing the initial separation a t zero time. I n addition to these difficulties, which apply to a bubble approaching a flat surface, there is an additional factor to be considered for the system illustrated in Figure 4, in which a spherical particle a p proaches a relatively large bubble. Here the continually changing area in apparent contact with the bubble must be taken into account in estimating the rate a t which water is expelled from the disjoining film. I n view of these difficulties it is not surprising that Philippoff (Y),who treated the problem as the approach of two rigid disks, obtained a value for the rupture thickness which excc.eds the value given herein by a factor of 10. Furthermore, in calculating the time of recedence of the film, Philippoff assumed that rupture was initiated a t the center of the film, whereas it is
2424
INDUSTRIAL AND ENGINEERING CHEMISTRY
now shown that under the conditions of his experiment rupture would be initiated a t the periphery. Hirnilarly Hassialis and JIyers (G)overlooked the lenslike shape of t,he ent,rapped film. Theae authors actually observed the fringe system corresponding to Figure 6, b u t were unable to intcrpret it. Sven-Nilsson ( I S ) used a method for measuring induction period whereby the bubble holder M-as vibrnted Tyhile the bubble was pressed against a plane hydrophobic surface. By observing thr fringe patt,ern during such i i n esperirnont, it, is seen that the tiisjoining film is of the type shown in Figure 6,d, and each vibration propagates a wave on the bublile surface which carries a siiiall amount of v,-at,er into the lens, thus opposing out,ward drain:ige. Contact occurs when the periph of the lens is able to thin to the rupt,ure thickness in the interval i)et,ween two sucwssive wave^. I’hilippoff has quest,ioncd the rclevancy of Sven-Silssou’P results to practical flotation 011 the grounds that t,he duration of bubble-mineral contart is t,oo short t o Le influenced by such “longterm phenomena.” Sven-Silssoii‘s results are an excellent qualitative index of induction period, the high values obtained beiog simply the result, of using :I plane surface instead of a smnll mineral particle. Such R misunderst,aiiding arises from the vieTv, no longer t,enable, t,hat induction period is an int,rinxic property of the hydrophobic surface, whereas the present work shows t h a t for a given solid in a given liquid, only the rupture t,hickness is an intrinsic property of the interface, the induction period depending in addition on the size and shape of the particle and on the motion of the particle relative t,o the bubble.
Vol. 46, No. 11
ACKNOVI’LEDGM ENT
The author is indebted to IC. L. Sutherland, W. E, Ewerq, anti other members of the Physical Chemistry Section for their hclptu1 discussion and their criticism of the nianuscripi. LITER i’I’URE CITED
(1)
Dci.j:tgnin, 13., anti l., mici Jiyers, C . C . , Mining E,ig., 3 , 961 (t951). er, $1.C., .1. C‘olloid Sci., 7, 443 (1952). (2 f’hilippoff. \T., M i n i n g E?lg., 4, 386 (1952). ti Daiciiisicwics. ,J,, RdZ. Inst. M
