ADSORPTION OF SOME ORGANIC SURFACTANTS ON RUTILE SURFACES Electron Microscope Studies GORDON D. CHEEVER' AND
E D W A R D G . B O B A L E K2
Case Institute of Technology, CleueIand 6 , Ohio
Polycrystalline films of rutile titanium dioxide were exposed to adsorbable unsaturated organic compounds in both vapor and liquid phase and stained with osmium tetroxide or bromine vapor to develop more dense contrast of adsorbed structures for observation with the electron microscope. This technique revealed that adsorption of such organics does not involve uniform coverage of the surface. The collection of organic material was restricted to active patches or sites on the surface. The number of these active sites was about 1 O Rper square centimeter. At least for adsorption from vapor phase, data of size and number of adsorbed species as a function of temperature can be interpreted b y theories of classical nucleation (as developed b y Becker and Diiring) and of chemisorption on active sites.
INvEsTIcx~roRshave used electron microscopy to obtain the pattern of collection of adsorbates on solid and liquid surfaces (8:72: 20. 24: 27). This earlier work proved valuable in developing the present techniques. Electron microscopy is useful because the adsorbed species can be observed directly, and it is 110 longer necessary to infer adsorption structure from indirect evidence, such as apparent surface areas or analysis of types of adsorption isotherms. The preparation and characterization of rutile T i 0 2 films have been described elsewhere ( 6 ) . 'Ihe method consists essentially of a vacuum deposition of titanium metal on a plastic substrate, collection of the metal-plastic films on electron microscope grids, dissolution of the plastic support, and air oxidation of the metal film under conditions which convert it to rutile films 100- to 200-A. thick. These rutile films have sufficient mechanical strength for convenient handling. They also are thin enough to be sufficiently transparent to the electron beam, so they are suitable for studying the adsorption characteristics of organic materials adsorbed onto the film surface. To observe organic adsorbants clearly: some special staining techniques are applicable to many materials. Osmium tetroxide has been used as a stain for examination of lipide-containing materials in electron microscopy (22), and bromine also reacts well with double bonds (73). Advantage was taken of the dual properties of these agentsthat is, their high density and great affinity for double bonds-in staining special surfactants to produce the contrast needed to locate the original positions of the adsorbed species. EVERAL
Materials
Oleic acid was obtained in 95% purity from Light and Co. (Colnbrook. England), and lead tallate was supplied by Heyden Newport Chemical Corp. Technical linoleic acid was used, and osmium tetroxide was obtained from Fisher Scientific Co. A group of four substituted oxazolines. Alkaterge A, E, C, and T, was obtained from Commercial Solvents Corp. The chemical name of the parent compound is 2-heptadecenyl4,4-R1,R~-2-oxazoline.where R1 and Rz are various groups. For A, R1 and R Bare both methyl; for E, R1 is hydroxymethyl and Rz is ethyl; for C, R,is hydroxymethyl and RB is methyl; 1 Present address, Glidden Co., 3901 Hawkins Point Road, Baltimore 26, Md. Present address, Department of Chemical Engineering, University of Maine, Orono, Me.
and for T, R 1 and R Qare both hydroxymethyl. The heptadecenyl group is obtained from oleic acid and as such has a double bond present. The oxazoline content in these commercial products ranged from 50 to 75%. Solutions of lead tallate and 2-heptadecenyl-4,4-bis(hydroxymethyl)-2-oxazoline were prepared in carbon tetrachloride, in the range of 0.024 to 0.24y0 for the former and 0.0065 to 0.65y0 for the latter. Solutions of oleic and linoleic acid in benzene, ranging from 0.1 to 3.3%, were also prepared. The benzene used had been dried and distilled over sodium metal. Experimental Methods
Detailed descriptions of the apparatus and techniques for treating and staining the rutile films with both solutions and vapors of the adsorbates are described elsewhere (5). Briefly. for solution treatment, the rutile films mounted on electron microscope grids were immersed or drop-treated with the adsorbates. For vapor treatment, the rutile films were heated a t 500' C. a t a pressure less than 5 X 10-8 mm. of Hg for 3 to 6 hours, cooled, and treated a t a pressure of about 5 X mm. of Hg for 30 minutes with adsorbate vapor. The temperature of the vapor treatment ranged from 60" to 150" C. For treatment at room temperature, the adsorbate vapor was allowed to condense as a liquid on the films for various periods of time, ranging from 2 to 10 minutes. After the solution treatment, the samples were exposed to either bromine or osmium tetroxide vapor in a closed container in the air. After the vapor treatment, the samples were either exposed to osmium tetroxide vapor in the air or in a vacuum. Either of the staining procedures revealed the presence of opaque, droplike structures collected on the rutile substrates. Since the adsorbed species were easily seen after staining, i t was possible to obtain quantitative data such as the surface density--that is, the number of species per unit area of projection surface and the size of the species. This information was usually obtained from the plates or from prints o b t ~ n e dfrom them. Results
Some preliminary results were reported earlier ( 3 ) . In all electron micrographs shown, except Figure 1, the rutile films were exposed to osmium tetroxide vapor either in the air or in a vacuum after treatment with adsorbate vapor. Figure 1 was taken with a n RCA Series E M U electron microscope which had a resolution of about 50 A. Figures 2 to 5 were taken with a Hitachi HU-11 microscope, and Figure 6 was taken with a Jem 6-A microscope, both microscopes having a resolution of about 10.4. VOL. 3
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1964
89
Figure 1. Rutile film treated with one drop of 0.33y0 oleic acid, followed b y exposure to bromine vapor, 7200X
Figure 3. Rutile film treated with R'-4,4-dimethyl-R at 120' C., 3 5 , 6 0 0 X
Figure 2. Rutile film control ( A ) treated with osmium tetroxide vapor in air, 13,600X; (6)treated with R'-4-hydroxymethyl-4-methyl-R vapor ot 65" C., 34,500X
C., treated with R'-4,4-bis(hydroxymethyl)-R at 1 5 0 ' C., immediately after oxidation, 22, 500X
A summary of the surface densities of the adsorbed species detected after solution treatment with various adsorbates is presented in Table I. A similar summary is presented in 'Table I1 from the resultsofvapor treatment of the rutile films. 'The vapor from the hydroxymethyl-methyl oxazoline derivative wax condensed in a ceramic boat and removed from the vacuum system. The boiling point of the material was determined as a function of rrduced pressure, and the data are presented in Figure 7. T h e material was analyzed (using procedures supplied by Commercial Solvents Corp.) after the boiling point determination and found to be 96% oxazoline. A series of experiments was conducted in which the temperature of the hydroxymethyl-methyl adsorbate vapor and the rutile substrate was varied from 65" to S50° C., with the pressureconstant at approximately 5 X 10-mm. o f H g a n d the time of treatment constant at 30 minutes. One will recall that these are the conditions of pressure and time used in ail the vapor treatment experiments. T h e resulting adsorbed species were located by osmium staining, and the surface density and size were determined as a function of the degree of supercooling. At 5 X l O P mm. of Hg, the oxazoline derivative had a boiling point of 139O C. T h e data are summarized in Table 111 and presented graphically in Figure 8, where surface density of the adsorbed species is plotted against the degree of supercooling. Prints were made of Figure 1, divided into equal areas, and 90
I.&EC F U N D A M E N T A L S
Figure 4.
Rutile film, not heated in vacuum at 500'
the number of dots appearing in each area was counted. T h e structures resulting from the trcatment with R'-4-hydroxymethyl-4-methyl-R at 65O C. w e r ~counted on the luminous screen in the electron microscope. T h e rutile film was moved to cover many different sections or the treated film. A Poisson distribution (27) was plotted, and the results from both the vapor- and solution-treated films are shown in Figure 9. Similar results were found with the distribution of the structures resulting from the treatment with the dihydroxymethyl and the hydroxymethyl-ethyl oxazoline derivatives. Several areas containing the structures from the treatment with R'-4,4-bis(hydroxymethyl)-R at 125' C. were photographed, and the resulting dots were measured. T h e distribution of the radii is shown in Figure SO. Similar distributions were found for the structures resulting from solution treatment with 0.33% oleic acid, the vapor treatment with the dimethyl, and the hydroxymethyl-methyl oxazoline derivatives. Discussion
Considerable difficulty was encountered in reproducing the results from the solution treatment of the rutile films with oleic and linoleic acids. Either circular species developed upon treatment with dilute solutions of the fatty acids or no Structures were detected on the films. Consistently, the more concentrated solutions gave a thick, uniform covering. The clue to difficulty in obtaining patterns from dilute solutions may be provided by the work of Harkins and Gam with rutile ponders
Surface Density of Adsor'bad Species Observed on Solution-Treated R I,tile Films
Tab1e 1.
0.33 0.33 0.024
Oleic acid Linoleic acid Lead tallate R'-4,4-bis(hydroxymethyl)-R
12 12 0.32
0.0065
1
10
4 0.7
0.10
Surface Density of Adsorbed Species Observed on Vapor-Treated Rutile Films Demity, Temp., No./Sg. Cm. Malarial Adrorbcd "C. x 70-9
Table II.
.
Figure 5. Control ( A ) treated with osmium tetroxide vapor only in o vacuum, 162,OOOX; (6) treated with R'-4-hydroxymethyl-4-methyl-R a t 85' C., 150,OOOX
R'-4,4dimethyl-R R'-4,4-bis( hydroxyrnethy1)-R R'-4-hydmxymethyl-4-rnethyl-R Oleic acid
120 125 150 150 120 25
1.3 1.1 1 .o
4.0
1.1
4.0
Table 111. Effect of Temperatura on Densify and Size of Adsorbed Soecies from R'-4-Hvdroxvmethvl-4-melhvl-R
65 85
120 126 135
144 150
. .gure 6. Rutile film treated with oleic acid v a p o r a t 80" C.: (A), 66,OOOX; ( 6 ) treated with R'-4,4-bis(hydroxymethy1)-R a t 25' C., 72,OOOX Oxazoline vapor an (B) was condensed on rutile filrnr for 10
. .
mlnYre5
(78), whcre it was reported that water interfered greatly with the adsorption of fatty acids on rutile powders. Powder with a content of 0.05% water adsorbed only one half as much oleic acid as the dry powder. After the rutile films were heated in a vacuum prior to vapor treatment, very consistent results were obtained with all the adsorbatenused. In Figure 4, there are clearly two main sizes of diffuse structures, one large and the other small. Each large structure contained a small structure in the center as a very dense opaque core, the Size of which corresponded to the size of the small diNuse spots. Perhaps water or some other poison had been adsorhrd on the active sites, and the dihydroxymethyl derivative had replaced the poison. 'The larger structures had started to grow beiorc the smaller ones. The dense core in the center may represent the region which started to grow first. In the case of the hydrouymethyl-methyl derivative, it was not possible to dctect adsorbed material unless the rutile films had been heated in a vacuum prior to treatment with the surfactant. Howcver, when the films were heated and vacuum treated, very intensc spots developed, some of which are seen in Figures 2 and 5. In Figtires 2 and 5; a halo clearly surrounds the opaque center
core. This may seem to be a common example of a focusing problem. However, occurrence of this halo seemed to depend on the adsorbate used. and it was not observed when oleic acid and the dimethyl oxazoline derivatives were used. Also, the halo was visible in the electron microscope at various focal lengths. and it was seen in three different types of electron microscopes, which indicates that the phenomenon is not peculiar to a particular microscope. Caution should always be exercised also in interpreting the composition of the adsorbed species because many changes of original structure can be caused by staining agents or by long exposure to the electron beam. This did not seem to be the case here. The same halo was seen with different stains and varying exposure times. I t may be that the halo resulted because the areas surroundine the opaque core had become more wettable with time, causing the adsorbate to spread from its original collection sites to the SImounding area. This same ,.I naio was omervea wiin me amydroxymethyl and the hydroxymethyl-ethyl axaeoline derivatives. In all thr micrographs of the treated films, except Figure 6 B. the adsorbed material appears to b'e collected into the rather opaque dots or spats. There does lint +~.ineor+n he continuous covering of adsorbate, except in Figure 6 B: whew the hales in the film a r not ~ visible.and the crystals are not sharp and distinct. Thus, it was possible to obtain complete coverag? of the films, but only from concentrated solutions or liquid adsorbate. Complete coverage was particularly easy to detect in the microscope because of focusing difficulties. I
.~
.
..
.
.._.- ~ ~ .__~ - . LI
VOL. 3
NO. 2 M A Y 1 9 6 4
il
I
91
l -
SOLU T l O N
VAPOR
-4.0
-4.4
I
I 2.40
1 2.44
I
I
2.48
I x T
I
2.52 ~
~
2.56
I 2.60
I
3
Figure 7. Variation of boiling point of R’-4-hydroxymethyl4-methyl-R with pressure
0 I 2
3 4
5 6 7 NUMBER P E R
0 I 2 3 4 5 SOUARE
Figure 9. Comparison between observed (bars) and predicted (arrows) Poisson frequency for adsorbed structures
32
KEY -
n
1. E T T E R
RPNGE,
!
170
A
-
B
200
C
2 9 0 - 350
0
370
-
430
E
450
-
520
F
540
-
600
270
Figure 8. Effect of supercooling on microdrop density RADII,
The staining techniques appeared to “freeze” growth of the adsorbed species and may give a n indication of the size of the species at the time of staining. In general, the bromine-stained adsorbates were stable in a weak to moderate electron beam but would disappear in an intense beam. T h e osmium-stained adsorbates were remarkably stable, even in a n intense beam for long periods of time. No rearrangement or changes in the spots were noted. However, there was a gradual diminution in surface density of the stained adsorbates with time. There was no evidence to suggest that the very opaque spots seen were produced by the collapse or rearrangement of a complete covering of adsorbate on the rutile films. T h e only effect even closely resembling this type of mechanism was sometimes seen with stained adsorbates from concentrated solutions when melting appeared in a n intense beam. The complete covering in some areas would flow into puddles or wormlike appendages over the surface. The melting adsorbate seemed to flow into the recessed areas of the film. I t is diffixlt to imagine a mechanism whereby the regularity in shape, size, and number of the adsorbed species recorded here could be produced repetitively by the collapse and gathering into spots of what were originally continuous organic films. Usually, it was not possible to have the holes, the edges of rutile crystals, and the adsorbed species all in focus a t the same time. Several photographs were taken to obtain different features of the film. each in good focus. In Figure 5, the holes are quite evident, as well as what appear to be thicker rutile crystals which give the very dark spots about 120 .4. in diameter. This effect has been described by Draley ( 7 7 ) in iron oxide films. 92
I&EC FUNDAMENTALS
Figure 10. Distribution of radii of structures from R’-4,4bis(hydroxymethy1)-Rat 1 2 5 ” C.
An upper limit of 5000 ’4. seems to exist for the size of the dots. When this size was exceeded, complete coverage became evident along with the dots. The factors which determined the lower limit in size of the dots are discussed below. T h e Poisson statistical distribution describes the occurrence of isolated events in a continuum (27). Thus, the fact that the frequency of the circular structures agrees fairly well with that predicted by the Poisson distribution would indicate that the active sites or patches are randomly distributed over the surface. Both the solution and vapor treatments of the rutile films showed that the heat treatment prior to adsorption of the surfactants did not significantly alter the number of active sites on the surface from that found under minimal oxidation conditions. For example. when films were oxidized a t 450’ or 650’ C., when the films were heated in high vacuum for as long as 8 hours, and whether adsorption occurred from solutio~i or from the vapor phase, the count of active sites remained on the order of 1Os per square centimeter, Seldom was the number much less. For particular specimens, active sites either appeared at this surface density or none appeared. The relative insensitivity of the adsorptivity properties of the rutile films to preparation conditions is somewhat surprising in light of published results tvith rutile powders. Sandler (25), Reyerson and Honig (2.3), Chessick (7). Wade and Hackerman 130), Gray e t d.(76), and Gebhardt and Herrington (75) have all shown that the techniques used in preparing the
samples determined to a great extent the surface propcrtirs of the matrrial. Because origin of the active sitrs in tlie rutile hlnis is unknown. only guesses are possible regarding their behavior. I t may he that the active sites arise from impurities> and because films were prepared from the same titanium source. all films used here could have essentially the same impurity content with the same total nnmber of active sites. 'l'here are a number of similarities between the present investigation and the results reported on surface phrnoniena by other lvorkers. Dintenfass ( 7 0 ) has reported that the surface of rutile powders appears to consist of active patches. (;ulbransen ( 7 7 ) reported that riuclri are formed first in the oxidation of iron and that complete coverage is found only \\hen the gas concentration is increased. The surface density of these oxide nuclei corrrsponded to the same factor found in this invrstigatiori -1 Os per square centimeter cm. XlcCormick and Barr ( I O j have rcported that tlie dropwise condensation of liquids takrs 1,lace on active sites. (:hessick 17) has cautioned that crrors can be introduced into interpretations from heat of immersion studies \vhcn unjustified assumptions are made concerning the structure and pattern of adsorbed species. Coincidences with Expectations from Nucleation Theory
'The data presented in 'Table I11 \vere examined to determine if the results Lvere capable of being interpreted on the basis of classical nucleation theory. as developed by Becker and Dijring ( 2 ) . Frenkel ( 1 x 1 ) ~and L-olmer and Weber (29). Frenkel ('7 I ) has derived a relation between degree of supercooling and critical radius of the critical nucleuq. r, = 2y~To,1?'IN,.
(1)
To appl!- E:quation 1 to the results in 'Table 111. the smallest nuclei and the smallest I T should be used because presumably the larger drops had been growing longer and are farthest rernoved from the critical nuclei stage. The following experimentally cletrrminrd bulk values for the hydroxymethylmethyl derivative wrre uwd in the calculation : f. 7'0
= =
17' = SI€,.
=
439 cc. per mole 139' C. = 412OK. 4' K . = 4' C. for 7'equal to 135' C. 18.000 cal. per mole
=
7.5 X 10" ergs per mole
'I'he bulk surface tension was estimated to be 33 ergs per sq. cm. 'l'his gives for r , the calculated value of 400 A. Referring to Table I11 for T equal to 135' C . or A7'equal to 4' - and size as a function of time a t constant adsorbate activity. If this information were available, it might be prmihle to decide whether the spots \\'ere generated by dynamic nucleation phenomena or by chemisorption, At the present time. no choice can be made, Acknowledgment
The authors express their appreciation to Eric Baer and TVarrcn Thompson. Case Institute, for valuable suggestions; to Marie Parker, Lubrizol Corp., and K . Takiyama and William Stanley. Case Institute, for many electron micrographs; and to the Paint Research Institute for a fellowship grant. Nomenclature
R' K 7' 7'"
= = =
37'
=
rV
= = =
rC = AHv =
2-heptadecenyl 2-oxazoline temperature of vapor treatment. O C . boiling point, ' C. drgree o f supercooling, 7'o - 7'. O c: surface tension. ergszsq. cm. molar volume. cc.;mole ciitical radius. A . heat of vaporization. ergs mole VOL. 3
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1964
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References
Becker, R.. Ann. Physik. 32, 128 (1938). Becker, R.. Dnring, Lf-., Zbid.. 24, 719 (1935). Bobalek, E. G.. Off.Digest 34, 1293 (1962). Bradley, R . S.,Quart. Xer.. (London) 5 , 315 (1951). Cheever. G. D., Bobalek. E. G.. Of. Dicest 35, 759 [1963), Cheever, G. D.. Parker. M. T., Rohileky E. G:. Ibtd’, 34, 1047 ’1962). (7)’ Chekick. J. J., J . Phys. Chem. 66, 762 (1962). (8) Cook, H. D.. Ries. H. E., Jr.. J . Phys. Chem. 63, 226 (1959). (9) Criegee. R . . Ann. 522, 75 (1936). (10) Dintenfass, L., Kolloid-Z. 161, 60, 70 (1958). (111 Dralev. J . E.. ArPonne ,Vatl. Lab. News-Bull. 3. 3 (1962). ( l 2 j Epstein. H . T., j . Phyr. ColloidChem. 54, 1053(1950). ’ (13) Fieser. I,. F., Fieser, .M., “Organic Chemistry.” p. 61, Heath, Boston, 1950. (14) Frenkel, ,J., “Kinetic Theory of Liquids,” pp. 366-426, Dover Publications, New York, 1955. (15) Gebhardt, J.: Herrington, K., J . Phys. Chem. 62,120 (1958). (16) Gray! T. J., McCain. C. C.. Masse, N. G., Zbid., 63, 472 (19-lO~. \-.--,.
McCormick, J. L., Baer. E.. J . ColloidSci. 18, 208 (1963). Mathieson, R. T., ’Vature 183, 1803 (1959). Moroney, IM. J.. “Facts from Figures,” pp. 96-107, Penguin Books: Baltimore, 1962. (22 Porter, K. R., Kallman, F., Exptl. Cell Res. 4, 127 (1953). (231 R eyerson. L. H.: Honig, J. M.: J . Am. Chem. Soc. 75, 3917, ~
3020 (1057). (24) R i & H.’E., Jr., Kimball, W.A . , J . Phys. Chem. 59, 94 (1955); Nature 181, 901 (1958). (25) Sandler. Y . L.,J . Phvs. Chem. 58. 54. 58 (1954). (26) Tammann, Y., “ThLStates of Aggregatidn,” Van Nostrand, New York. 1925 (Engl. transl.). P. A., 2’. Elektrochem. 48, 675 (1942). olmer, M., Ibid., 35, 555 (1929). (29 Volmer, M.. Weber, A., Z . Phyrik. Chem. 119, 277 (1926). (301 W ade, W. H., Hackerman, N.. J . Phys. Chem. 6 5 , 1 6 8 1 (1961).
RECEIVED for review July 22, 1963 ACCEPTED November 5, 1963 30th Annual Chemical Engineering Symposium. ACS Division of Industrial and Engineering Chemistry. University of Maryland. November 1963. Based on Ph.D. thesis of G. D. Cheever.
(17) Gulbransen. E. A , : McMillan, W. R., Andrew, K. F., Trans. AZME 200, 1027 (1954). (18) Harkins. \V. D.: Gam, D. &f.>J . Piiys. Chcm. 36, 86 (1932).
MECHANISM OF HEAT TRANSFER T O A
FIXED SURFACE IN A FLUIDIZED BED EDWARD N .
Z I E G L E R ’ A N D
W I L L I A M T. B R A Z E L T Q N
The Technological Institute, IVorthwestern Crniiersity,Ecanston, Ill. Simultaneous heat and mass transfer from the surface of a sphere was studied for comparable situations in a gas stream and a gas fluidized bed of solid particles. The systems were chosen so that the fluidized particles would have capacity for heat transport but not mass transport. Solid particles in the fluidized state increased heat transfer 10- to 20-fold, but increased mass transfer only 1 ‘/z to 2 times. On the basis of the particles’ unique property for heat transport, and assuming analogous heat and mass transfer in the gas phase, it was concluded that in any mechanism of heat transfer in the fluidized state, 80 to 95% of the transfer must be accounted for by particle transfer mode. The remainder may be accounted for in Q path solely in the gaseous phase. HE phenomenon of heat transport in fluidized beds has Tbeen the subject of numerous studies in recent years. Of particular interest is the heat transfer between the bed and an internal or external surface. T h e results of work on this topic have been summarized extensively by Zenz and Othmer (26). Another review by Botterill (7) includes all but the most receit literature. Several of the early investigators verified the improvement in heat transfer, and offcred accompanying rationales in the form of mechanisms of transport. For instance, Leva and coworkers (8--70) and Docv and Jakob (3) suggested that the increase in heat transfer was probably a consequence of the scrubbing action of particles against the transfer surface. This action was thought to disturb the gas film and hence decrease its resistance to the flow of heat. I n later presentations. such as those of Van Heerden, Kobel, and Van Kreveltm (78: 7 9 ) : \\*icke and Hedden (251, Wicke and Fetting ( 2 4 ) ;Mickley and Fairbanks ( 7 7 , 717), and Ernst ( 4 ) . rnechanisms were developed that appear to be more credible in explaining heat transfer improvement of the magnitude experienced. Although there are some differences in these siiggested models, common factors may be summarized as follokzs. T h e fluidized particles are visualized as a packeti.e.. closely locked assemblage of particles-moving from the I
Presrnt addrrss. Esso Rpsearch and Engineering Co., Linden.
N. J . 94
l&EC
FUNDAMENTALS
core of the bed to the particular boundary surface, absorbing or giving u p heat, depending upon the relative temperature of the surface, and then returning to the core of the bed. The interstitial gas serves as a stirring agent and as a heat transfer medium between the particles and the surface. T h e presence of the particles probably improves heat transfer by a combination of the two aforementioned effects-. conveyance of heat from the packet to the surface on contact and disturbance of the gas film adjacent to the surface. The simultaneous occurrence of these two effects has not yet been demonstrated by experiment. I t was the intention of this experimental investigation to verify the presence of these two effects and to determine their relative importance. T h e experiments performed involve simultaneous heat and mass transfer from a solid object to a fluidized bed. T h e system was chosen to allow both the particles and the gas to take part in the transport of heat a t the solid surface. O n the other hand, the particles in this system have negligible absorptivity for the diffusing species and consequentlv have no capacity for mass transport. Therefore! the only mechanism of importance in mass transfer is the diffusion of mass through the surface gas film. In systems without fluidized particles a t constant surface temperature and composition. it is known that the mechanisms of heat and mass transfer from a surface are analogous for low mass transfkr ra.tes. Both types of transfer may be considered to take place through
