Shorter Communications

= 28*12(V,)Ai -cms/sec

when Pa is expressed in ems.

(3)

Consider now fluidised particles of average diameter 80 p and assume that the minimum bubble size the bed could sustain is 050 cm dia. From (3) above the flow rate to pro- duce these minimum sized bubbles is 2.9 cmYsec. The mini- mum fluidisation velocity for such particles with atmospheric air is about O-3 cm/set or about 15 cma/sec in an 8 cm dia. tube. Thus, in this example, a 20 per cent increase in gas flow rate is necessary to initiate bubbling and this is the kind of increase found necessary with particles of this size.

There are many crude assumptions in the above calcul- ation but it illustrates that a minimum possible bubble size means that a limited increase in gas flow will not necessarily produce bubbles and particles separation must occur to reduce the drag coefficient[7] or particles would be lifted from the bed. Since observable uniform particle separation does not occur with larger particles, it is concluded that the minimum bubble size increases at a slower rate than the

minimum fluidisation velocity does so that Gti becomes a smaller proportion of the minimum fluidisation flow rate as the particle size increases.

Department of Chemical Engineering University College London Torrington Place, London W.C.1

P. N. ROWE

NOTATION

G steady gas flow rate producing bubbles, LYT G ml” minimum steady rate to produce bubbles in a fluid&d

bed, LYT g gravitational acceleration, L/T2

H fluidised bed height, L u m.t (superficial) minimum fluidisation velocity, L/T u m.b. (superlicial) minimum bubbling velocity, L/T

V, bubble volume, Ls (V&n volume of minimum sized bubble in a fluidised bed,

Ls

REFERENCES

[1] RICHARDSON J. F. and ZAKI W. N., Sedimentation and Fluidisation. Trans. Instn them. Engrs 1954 32 35. [2] RICHARDSON J. F., Private communication, August 1968. [3] RICHARDSON J. F. and DAVIES L., Variations of bed height with bubbling in an air/catalyst fluidised bed. Nature

1963 199 898. [4] DAVIDSON J. F. and HARRISON D., Fluidised Particles, p. 50. Cambridge University Press 1963. [5] ROWE P. N., The motion of a bubble rising through a fluidised bed. Chem. Engng Sci. 1964 19 75. [6] GODARD K. and RICHARDSON J. F., Minimum stable bubble volumes and bubble collapse rates in fluidised beds.

Junel968(Tobepublished). [7] ROWE P. N., Drag forces in a hydraulic model of a fluidised bed- II. Trans. Instn them. Engrs 196139 178.

Ghemical Engineering Science, 1969, Vol. 24, pp. 416-4 19. Pergamon Press. Printed in Great Britain.

Drop size in stirred liquid-liquid systems via encapsulation

(First received 16 August 1968; accepted 16 August 1968)

IN AN earlier note[l] an encapsulation technique was pro- posed for determining the drop size distribution in stirred systems of immiscible liquids. The suggested method involves the rapid encapsulation of all individual drops in a dispersion as they exist in the dynamic state in the stirred system. To accomplish this a reactant is suddenly added to the continuous phase which will quickly react with a second component, contained in the dispersed drops, to form an encapsulating polymeric film around each drop. Upon terminating agitation the encapsulated drops settle as discrete entities and are ready for size distribution analysis.

At the time of the original note operational details had not been completely developed nor was it clear as to the most effective method for determining the size distribution of the encapsulated drops. A simple and rather novel technique for solving the latter problem was subsequently devised.

It is the purpose of this paper to elaborate on the encap- sulation and drop classification procedures and to sub- stantiate the practicality of the overall technique by pre- senting some specific results obtained on stirred dispersions of tetrachlorethylene in water.

THE BASIC EXPERIMENTAL METHOD

A ‘series of experiments were performed in which 5 ml of tetrachlorethylene were dispersed in 15OOml of water by stirring at selected, constant impeller speeds in a balIled beaker. The dispersed tetrachlorethylene contained 1% (vol.) sebacvl chloride. At the moment at which droplet en&psulation was desired, a small volume of aqueous hexamethylene diamine (plus NaOH) was quickly added to the continuous water phase. An extremely rapid inter- facial polycondensation reaction[2] occurred at the surface of each drop resulting in the formation of a thin encap-

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Shorter Communications

sulating film of Nylon 6-10. The reaction equation is to effect phase separation and the volume of tetrachlor- given by ethylene in each size traction was measured.

0 0

H,N-(CH,),-NH,+Cl>C-(CH,&Cl m

hexamethylene diamine sebacyl chloride

H H 0 0 I I II II

I-F N - (CH,), - N - C - (CH,), - C -1. Cl + n NaCl Nylon B-10

Upon stopping the agitation the encapsulated drops settled tothe bottom of the beaker.

A simple, rapid method for determining the size dis- tribution of the encapsulated drops was clearly needed to complete the task of analysis. Direct wet screening of en- capsulated drops was unsuccessful, as might be predicted, due to the stickiness of the polymer. The idea arose that if a thin metallic film could be applied to the polymer-coated drops, a more favorable surface would then be exposed to the screens and direct wet screening might then be successful. A considerable body of information exists on the metallizing of plastics[3] and silvering of plastics appeared to be as straight-forward as the time-honored silvering of glass to produce mirrors. Developing this notion, the encapsulated drops were coated with a thin film of metallic silver prior to screeningt and wet sieving then proved to be highly effective. Silver film formation was achieved by con- tacting polymer-coated drops with ammoniacal silver nitrate and chemically reducing the silver by addition of formaldehyde. Further details are given in a-later section. The silvering treatment also improved the mechanical strength of the encapsulated drops, thus minimizing rupture in the sieving process.

The encapsulated drops retained on the sieves were transferred to 3 ml calibrated sedimentation tubes. Con- centrated nitric acid was then added to each tube to destroy the silver and Nylon films thus releasing the tetrachlor- ethylene. Centrifugation of the sedimentation tubes followed

tNote to experimentalists The silvering process preliminary to screening has found

application in another, unrelated study. It was desired to obtain a rather narrow cut of solid polymer beads in the 60/70 mesh range. Interestingly, this was obtained from an alleged 20/50 mesh sample of beads (supplied by an in- .dustrial firm), which was silvered, then dried and screened. Substantially all silvered uarticles were in the 60/70 mesh range. Possibly the silvdring treatment circumvents the difficulty of agglomeration hue to electrostatic effects which could have been responsible for the alleged larger size of the raw sample.

Similar experience was encountered with a glass bead sample (allegedly 60/70 mesh). After silvering and then screening a very substantial quantity was found to be of much smaller size. The silvering-then-screening procedure may be of interest to others faced with the problem of obtaining narrow cuts of non-metallic solids. It would be a simple matter in many cases to strip the silver chemically after screening and thus obtain a very narrow cut of the desired material.

FURTHER EXPERIMENTAL DETAIL

The stirred system The two-phase, tetrachlorethylene-water, system was

housed in a 2-liter glass beaker equipped with four glass baffles (9/ 16 in. wide, 1 / 16 in. thick) arranged symmetrically. Agitation was provided by a 3 in. dia., 6-blade turbine impeller (stainless steel). The impeller shaft was connected through a Bakelite coupling to a gear train driven by a constant speed synchronous motor. Variations in the gear train allowed selection of constant impeller speeds ranging from 150 to 400 rev/mm. The impeller was positioned about 2 mm off the bottom of the beaker.

The continuous phase for each run was 1500 ml of con- ductivity water which had been pre-saturated with tetra- chlorethylene. The dispersed phase was 5 ml of tetrachlor- ethylene (Eastman Spectra grade) to which had been added 0.05 ml of sebacyl chloride (Eastman).

The encapsulation run Water was first charged to the vessel and brought to the

appropriate temperature. Then, the tetrachlorethylene was added by pipette and allowed to settle in a pool at the bottom. This assured the same initial state for the system for all runs. Agitation was then started and continued for the desired period of time at which point 40ml of aqueous hexamethylene diamine solution were quickly added to the water to atfect droplet encapsulation. The diamine solution was prepared by mixing 20 ml of aqueous hexamethylene diamine (70 (vol.) %, Eastman) with 20ml of aqueous sodium hydroxide (ca. 1*3N).

A few seconds after addition of the diamine solution agitation was terminated and the baffle assembly lifted from the beaker. It was found expedient to continue to swirl the suspension gently with a stirring rod for a few minutes to enhance further polymerization, thus imparting added strength to the polymer film. The encapsulated drops were then allowed to settle to the bottom after which the water ‘phase was carefully siphoned off. The next step was to activate the surface of the polymer-coated drops to make the polymer film receptive to a silver coating. This was done by soaking the drops for a few minutes in about 20 ml of aqueous platinic chloride solution (1 g of platinic chloride in l-0 gal of water). After solution removal the drops were silver coated via an oxidation-reduction reaction. 20ml of aqueous formaldehyde were poured onto the drops followed by 30ml of aqueous ammoniacal silver nitrate. The suspension was swirled and the silvering reaction took place quite rapidly. The drops were then ready for screening. The formulation of the silvering and reducing solutions followed the recommendations of Narcus [3 1.

,

EXPERIMENTAL RESULTS

Drop size distribution data were obtained for the tetra- chlorethylene-water system for stirring times of 1, 2, 4, 6, 10, and 15 min at constant impeller speeds of 150, 200, 250, 300, and 400 rev/mm, respectively. System tempera- tures of 25°C (&O.S”C) and 2°C (&O*S”C) were considered. The results were found to be quite reproducible.

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Typical drop size distribution data at 25°C are shown in Figs. 1 and 2. In both plots the drop diameter is plotted against the cumulative volume percentage of drops less than the indicated diameter on arithmetic-probability

60-

30-

IO -

S-

2- I I I I I I I

0 100 200 380 400 500 800 700 DROP DIAMETER ( MICRONS)

Fig. 1. Effect of stirring speed on drop size distribution.

SS-

ss-

so-

SO-

20-

IO-

S- Stirring speed ,200 R.I

2-

0 00 200 300 400 boo 800 DROP DIAMETER (MICRONS)

Fig. 2. Effect of stirring time on drop size distribution,

paper. Figure 1 shows the manner in which the size dis- tribution was altered as the stirring speed increased from 150 to 400 rev/mm. The stirring time was 6 mitt in each case. Figure 2 indicates the shift in drop size distribution as the stirring time varied from 2 to 15 min at a constant stirring speed of 200 rev/mm. The general effect of both increased stirring speed and ‘stirring time is to produce smaller drops.

DROP SIZE DISTRIBUTION NARROW

A striking feature of the results obtained was the rather narrow spread of drop sizes found for each set of experi- mental conditions. Shinnar[4] has suggested examination of the ratio ~,,,Ju&~ as an index of drop size spread, where 90 cumulative vol. per cent of drops is of a diameter less than d,, and 10 per cent is smaller than a&,.. For the present study this ratio was always of the order of 2.0. Thus, 80 per cent of the dispersed phase volume is within an approximate diameter range of a factor of 2.0. It is interesting to observe that similar results were obtained by Shinnar who made drop size distribution measurements on stirred dispersions of molten wax in hot water. Shinnar’s study differed, however, in that the dispersions were stabi- lized by the addition of protective colloids to the aqueous phase. The technique for determining size distribution also differed in that small samples of the dispersion were siphoned off, frozen rapidly and subjected to microscopic examination. How sensitive the nature of the drop size distribution is to system geometry remains to be seen. The present results, as were Shinnar’s, were obtained with turbine-type agitators and where the agitator was quite large in comparison with the mixing vessel.

It should be mentioned that no corrections were made on the observed drop sizes in this work for the thickness of either the polymer film or the silver coating. The latter was shown to be negligible. Determinations were made of the amount of silver coating for six size fractions by dissolving the silver and titrating using the Mohr method. Calculated silver thicknesses ranged from 802 to 0.25~. No direct determination of the polymer coating thickness was made. However, it is to be noted that the amount of polymer formed was limited by the relatively low sebacyl chloride content (1% (vol.)) of the dispersed phase. An estimate of maximum possible polymer formation indicates that the thickness of the polymer coating should not exceed 1 per cent of the drop diameter.

DISCUSSION OF RESULTS

We feel that the results obtained demonstrate the practi- cality of the encapsulation technique as a procedure for ob- taining drop size distribution data. It is felt, however, that broad quantitative generalizations at this point would be premature. Further study of the technique is needed since a number of questions need to be resolved. A case in point is whether the observed results on drop size ‘variation with stirring time and stirring speed truly reflect changes in these variables alone. It is to be noted that the experi- mental system, up to the moment of encapsulation, is a three component system- tetrachlorethylene, sebacyl chloride and water. Any interaction which would alter the chemistry of the system might have an effect on the observed drop

418

size. For example, a change in interfacial tension could Nylon-type (polyamide) interfacial polymer. Whether easily result. Sebacyl chloride does hydrolyze to some encapsulation would be satisfactory or not would depend extent, so the possibility of a secondary influence does exist. upon the physical properties of the resulting polymer film.

Some evidence suggesting a possible influence of hydrolysis was found in carrying out a series of encapsulation experi- ments at the lower temperature of 2°C. where hydrolysis is considerably diminished. The latter point was demon- strated by Wasley et al.[S] and conlirmed in our work by monitoring the pH of the continuous water phase while stirring a dispersed sebacyl chloride-tetrachlorethylene solution in water. While the change in the drop size dis- tribution with time at 250 revlmin was substantially the same at 2°C and 25”C, the response to a change in stirring speed was slightly different. For a stirring time of 6 mitt, when the stirring speed was increased to 400 rev/mm the size distri- bution tended to shift toward somewhat larger drops at 2°C (cornoared with 25°C). The difference appeared to be larger than the variance expected in experimental reproduci- bility leaving the annoying feeling that hydrolysis could be a responsible factor.

Another approach is to examine other possible inter- facial polycondensation reactions which may be better suited to meeting the overall requirements. Particularly promising in this connection is polyurea formation involving a diisocyanate and a diamine. Morgan and Kwolek [2] made the interesting observation that a benzene solution of hexamethylene diisocyanate did not show. any hydrolysis after many hours of contact with a water phase. With hexa- methylene diamine in the water phase-an interfacial film forms rapidly. If the physical properties of the polyurea film lead to successful encapsulation,_this __system would be of considerable interest. This is being investigated.

While a number of issues remain to be clarified, it is felt. that the practicality of the encapsulation technique has been demonstrated. With refinement a potentially useful new technique will be available for studying a very old problem.

The role of hydrolysis obviously needs further attention. Ideally, this should be eliminated and while this limit may not be possible there is evidence that it can be closely approached. One possible avenue of attack is the replace- ment of the sebacyl chloride with a higher molecular weight aliphatic diacid chloride. Wasley et al. (lot. cit.) have shown that the hydrolysis of such compounds diminishes considerably with increase in molecular weight. The use of such a material would still lead to the formation of a

Acknowledgment-This study was supported by a grant @P-2551) from the National Science Foundation which is gratefully acknowledged.

Department of Chemical Engineering University of Minnesota Minneapolis, Minn. 55455

B. J. MCCOY A. J. MADDEN

REFERENCES 111 MADDEN A. J. and MCCOY B. J., Chem. Engng Sci. 1964 l? 506 [2] MORGAN P. W. and KWOLEK S. L.,J. Polym. Sci. 40 299 1959. [3] NARCUS H., Metallizing of Plastics, p. 23. Reinhold 1948 141 SHINNAR R.,J. Fluid Mech. 1961 10 259. [5] WASLEY W. L., WHITFIELD R. E., MILLER L. A. and KODANI Y., Text. Res. J. 1963 33 1029.

Chemical Engineering Science, 1969, Vol. 24, pp. 419-42 1. Pergamon Press. Printed in Great Britain.

Equations for the overall axial diffusion coefficient in a bubble bed

(First received 17 June 1968; in revisedform 15 August 1968)

INTRODUCTION THE MIXING of the liquid in a bubble bed is ip(imatly linked with the hydrodynamics of the swarm of bubbles. The avail- able hydrodynamic information is however very incomplete. The motion of a single bubble has been analysed in numerous papers but the wake phenomena which are responsible for the entrainment of the liquid are not known in a satisfactory manner. Recently some qualitative information concerning the structure and behaviour of wakes behind single air bubbles in water[l-41 and behind single drops in a liquid[5] were published. The effect of the swarm of bubbles on the behaviour of the wakes were not even studied qualitatively.

Nevertheless, the qualitative observations of Crabtree and Bridgwater[4] and of Magarvey and Maclatchy[5] concem- ing the shedding of the vortices of the wake at quasi-regular distances along the path of the bubbles suggest a simple cellular model for the axial diffusion. In the cases in which the wakes are very small (Levich[6] has demonstrated that this is the situation for spherical bubbles moving at about Re * lo5 in a liquid free from surface active agents) the mechanism of mixing differs from the preceding one and another model is necessary. The aim of the present paper is to establish equa- tions for the axial diffusion coefficient in the two mentioned limiting cases.

419