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Ind. Eng. C he m. R e s . 1991,30, 689-691 589Shinji, 0.;Misono, M.; Yoneda, Y. he Dehydrogenation of Cyclo-hexane by the Use of a Porous-glaee Reactor. Bull. Chem. SOC.Jpn . 1982,56,2760-2764.Sun, Y. M.; Khang, S. J. Catalytic Membrane for SimultaneousChemical Reaction and Sep aration Applied to a DehydrogenationReaction. Znd. Eng. Chem. Res. 1988,27, 136-1142.Suzuki, Y.; imura, S.Separation an d Concentration of HydrogenIsotopea by Palladium-Alloy Mem brane (I). Nippon GenshiryokuGakkai Shi 1984,26,802-810.Uemiya, S .; Kude, Y.; ugino, K.; Sa to, N.; Matauda, T.; Kikuchi, E.A Palladium/Porous-Glass Composite Membrane for HydrogenSeparation. Chem. Lett. 1988, 1687-1690.Uemiya, S.;Matauda, T.; Kikuchi, E. Aromatization of PropaneAssisted by Palladium Membrane Reactor. Chem. Lett. 1990a,1335-1338.Uemiya, S.; ato, N.; Ando, H.; Kude, Y.; Matauda, T.; Kikuchi, E.Separation of Hydrogen through Palladium T hin Film Supportad

on a Porous Glass Tube. J . Membr. Sci. 1990b, n press.Uemiya, 5.; ato, N.; ndo, H.; Matsuda, T.; Kikuchi, E. SteamReforming of Methane in a Hydrogen-permeable Membrane Re-actor. Appl. Catal. 1991,67,223-230.Wood, . J. Dehydrogenation of Cyclohexane on a Hydrogen-PorousMembrane. J. Catal. 1968,11,30-34.Shigeyuki Uemiya,* Noboru SatoHiroehi Ando,Eiichi Eikuchi*Department of Applied ChemistrySchool of Science and Engineering, Waseda University

3-4-1Okubo, Shinjuku-ku, Tokyo 169, apanReceived for review J u n e 25 , 1990Revised manuscript received December 4,1990Accepted December 17,1990

Mass Transport in Finite Baths: Effect of Surface BarriersMass transfer of diffusants to he surface of solid polymeric material from some external m ediumcan occur through a diffusional boundary layer. Equa tions exist th at perm it the description of suchmass-tran sfer phenomena, b ut suc h equations are valid only for infinite bath systems, i.e., system sin which the concentration of diffusant in the external m edium is constant. A new technique ia giventha t permits th e ma thema tical description of mass transfer through a diffusional bound ary layerfor finite ba th systems, i.e., systems in which the con centration of diffusa nt in the externa l mediumchanges during th e sorption process.

Diffusion-controlled mass transfer of diffusanta to (orfrom ) th e surface of porous solids of various geome tricalshapes s strongly influenced by the th ickness of diffusionalboundary layer barriers a t the solid surface (Levich,1962).Newman was the first to describe in mathem atical termsth e effect of th e diffusional bound ary layer on rates ofsorption by the slab , cylinder, an d sphere (Newman, 1931).Newmans eq uations a re, however, only applicable to in-finite bath sorption systems, i.e., systems in which theconcentration of diffusant in the external medium isconsta nt during the sorption process. No equation existsth at desc ribes the effect of th e diffusional boundary layeron mass tran spo rt in finite b ath systems, Le., systems inwhich the conce ntration of diffusant in th e external me-dium is not constant during the sorption process.Since many real sorption systems are finite bath systemsin which a significant bound ary layer exists, it is useful tobe able to model such systems mathematically. Thepurpose of the pre sent work isto provide a new techniqueth at can be effective in describing sorption rates of dif-fusanta from finite bath systems in which a diffusionalbarrier exists at the solid surface. Th e tech nique will beillustrated only for the case of diffusant uptake by amorphologically stable, homogeneous, endless cylinder.However, it should be understood tha t the technique alsois applicable to he case of the plane sheet (slab) and thesphere.Infinite Bath SystemsTh e infinite bath, surface barrier equations of Newmanare notationally encumbe red and have been rewritten ina more straightforward manner by Crank (Crank, 1976).The functional relationship between fractional sorptionof diffusant, M t / M , , dimensionless time, D t / a 2 , nd di-mensionless bound ary layer, L, is given by

(1)For the case of diffusant sorption by a cylinder surroundedby a diffusional boundary layer, Cranks computationalsolution is given by

M t / M - = Fi = f(Dt/UZ,L)

where the P i s are the roots of th e transcend ental equation:OnJl(On) - LJo(Bn) = 0 (3)

in which Jo nd J1 re zero- and first-order Bessel func-tions. Equation 2 reveals that the rate of sorption isstrongly influenced by the num erical value of the dimen -sionleas param eter, L. As L decreases, the rate of sorptiondecreases. Equa tions similar to eq 2 also are given byCrank for the case of the plane sheet and the sphere(Crank, 1975).Finite Bath Systems

When no diffusional bounda ry layer exists at the solidsurface, i.e., when the dimensionless param eter, L, is equalto infinity , Wilsons equ ation (Wilson, 1948) an be usedto describe the relationship between fractional sorptionof diffusant, M t / M m , imensionless time , D t / a 2 , nd thedimensionless bath exhaustion parameter, a. In functionalform:

(4)Wilsons equation for diffusant up take by a cylinder fromf i i t e baths in which no boundary layer exists at the solidsurface is given by

M , / M , = Ff f(Dt/a2, . )

- 4a(1 + a) xp(-qn2(Dt/a2))F,= 1 - c ( 5 )MtM , n i l 4 + 4a + d q , 2- =where the qn s are the positive, nonzero roota of

Wn J o ( q n ) + 2J l (Qn) = 0 (6 )in which Jo an d Jl again are zero- and first-order Besselfunctions. Equation 5 reveals th at the r ate of sorp tion isstrongly influenced by the value of the dimensionless bat hexhaustion parameter, a. As a increases, the rate ofsorption decreases. Finite ba th equations for th e case of

(8 1991 Amer ican Chemical Society

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590 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991Table 1. Dimensionless Time for Various Values of Fractional Sorption (a = 0.010101,L = SO)

0.10 0.001 110 1.2605 X 2.3143 X 1.2616 X lod 2.4203X 10-3'0.20 0.002 494 3.0127 X lod 1.1130 X lo4 3.0236X 10" 1.2225 X 10"0.25 0.003 322 4.1264X 10" 1.9242 X 10" 4.1509 X 2.1697 X 10"0.30 0.004 67 5.4463X 3.0880X 10" 5.4956 X 10" 3.5810 X 10"0.35 0.005 56 7.0238X 10" 4.7233 X lo4 7.1159 X 5.6445 X 10"0.40 0.006623 8.9269 X 7.0003x 10" 9.0904 X 10" 8.6451 X lo40.45 0.008 115 1.1253 X lo-' 1.0169X 1.1533 X lo-' 1.2972X loa0.50 0.009901 1.4144 X 10" 1.4609X 10" 1.4615 X lo4 1.9323 X 10"0.55 0.012 075 1.7788 X lo-' 2.0919 X 10" 1.8573 X lo-' 2.8765 X0.60 0.014 778 2.2538 X lo-' 3.0084X 2.3843 X lo-' 4.3131 X 10"0.65 0.018 233 2.8899 X lo-' 4.3824 X 3.1091 X lo-' 6.5747X0.70 0.022 801 3.7149 X lo-' 6.5358 X 4.1514 X lo4 1.0301X lo-'0.75 0.029 126 5.0765 X lo-' 1.0131 X lo-' 5.7485 X lo4 1.6851 X lo-'1.6714 X lo-' 8.4283 X 10" 2.9495X IO-'.80 0.038 462 7.1502 X lo-' 1.3586 X 5.7697X lo-'.85 0.053 628 1.0881X 3.0642X lo-'0.95 0.159664 4.9323 X 2.4584x 10-3 7.8256 X 5.3517X lo"

FI Fi [Dtla'Io [Dtla211 [Dt/a2 12 [Dtla21s0.15 0.001 762 2.0669 X lod 5.6938X lo-' 2.0710 X 6.1001 x 10-7

0.90 0.082 569 1.9207X 6.8475 X lo-' 2.6201 X 1.3842x 10-3the plane sheet a nd t he sphere also are available (Wilson,1948; Cra nk, 1 975).New Techniqueform exists for the functional relationship given byIt can be shown, however, that for linear, transitionalkinetic system s, i.e., for system s (chara cterized by linearsorption isotherms and constant, concentration-inde-pendent diffusion coefficients) tha t change from infinitebath to finite bath systems during the course of diffus antsorption, the relationship between Fi an d F f at the pointof transition is given by (McGregor and Etters, 1979)

As previously sta ted, no analytical solution in equ ationM , / M - = f (Dt /a2,aL) (7 )

Equation 8 permits Fi to be calculated for all values of F fbetween zero an d unity for given values of a. All valuesof M t / M , for both infinite and finite systems are, there-fore, equated to each other through corresponding tran-sitional ualues. Through the use of such continuouslytransitional, fractional sorption values it is possible toestimate the effect of the dimensionless boundary layer,L, on the rat e of diffusant sorp tion in finite bath systemshaving a given dimensionless bath exhaustion, a.Computational ExampleTh e following example will serve to illustrate t he com-putational sequence employed in the new technique. I tis desired to compute the value of dimensionless timeassociated with various fractional sorption values, M t /M,= Ff,obtained under finite bath, boundary layer condi-tions; these values of dimensionless time are designated[Dt/a2Io. n th e present example, [Dt/a2Io ssociated witheach finite bath fractional sorption value, Ff,s determinedfor a system having an a value of 0.010 101, correspondingto a fractional equilibrium bath exhaustion E, = 0.99, andan L value of 50, orresponding to a small but significantboundary layer.Dimensionless time is iteratively computed for eachvalue of Ffby th e use of eq 5, using an a value of 0.010 101.These values are designated [Dt /a2I 1 .By the use of eq 8,values of Fiare determ ined for each value of FP For eachvalue of Fi,dimensionless time is iteratively determinedby the use of eq 2, using an L value of 50. These valuesof dimensionless time are designated [Dt /a2I2 .Finally,dimensionless time is iteratively determined for each valueof Fi by the use of eq 2, using anL value of infini ty. These

values are designated [Dt/a2I3.Dimensionless time for thefinite bath system having an a of 0.010 101 and an L of 50is given by[Dt/a210 = [Dt/a211 + [[Dt/a212- [Dt/a2131 (9)

Th e results of th e computations are given in Table I.Formal iterative solutions such as hose of Table I canbe expanded to include many different values of a an d L.An ultimate result of such computations may be the de-velopment of a useful analytical approximation, i.e., anempirical, modeling function by which the fractionalsorption, Ff,may be calculated directly from a knowledgeof D t / a 2 ,a, nd L.Nomenclaturea = radius of cylinder or sphere, or half-thickness of slab , mC , = initial concentration of dif fusant in exte rnal mediumC , = equilibrium concentration of diffusant in external me-Lj = diffusion coefficient of diffusa nt in solid, m2/sD = diffusion coefficient of diffusant in the external phase,m2/sE, = fractional equilibrium exhaustion of ex ternal medium,given by E, = (C , - C,)/C,Ff = fractional equilibrium diffusant uptake in finite systemsFi = fractional saturation diffusant uptake in infinite systemsJo = zero-order Bessel functionJ 1= first-ord er Bessel functionK = linear dis tributio n coefficient of diffusant between solidphase and external phaseL = dimensionless parameter given by L = (Ba) / (DKG)M , concentration of diffusant in solid a t time tM, = concentration of d iffusan t in solid a t equilibriumqn = positive, nonzero root of t ranscendental equation (eq 6)t = time of sorption, sCreek Lettersa = dimensionless finite bath exhaustion given by (1- E , ) / E ,p,, = roots of transcendental equation (eq 3)6 = thickness of diffusional boundary layer, mSubscriptsf = finite bath systemsi = infinite bath systemsn = root numbert = time, sa = infinite time, s (equilibrium)Literature CitedCrank, J. Diffusion in a Cylinder. In The Mathematics of Diffusion,

dium

2nd ed.; Clarend on Press: Oxford, 1975;pp 69-88.

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Znd. Eng. C hem . Res . 1991,30,591-594 591Levich, V. G. onvective Diffusion in Liquids. In PhysicochemicalHydrodynamics; Prentice-Ha& Englewood Cliffs, NJ, 1962; p39-138. Jamee N. ttersMcGregor, R.; Etters, J. N. Transitional Kinetics in DisperseDyeing. Textile Sciences, Dawson Hall, The U niversity of GeorgiaTex t. Chem. Color. 1979,11, 202159-206163. Athens, Georgia 30602Newman, A. B. The Drying of Porous Solids: Diffusion and Su rfaceEmission Equations. Trans. Am. Znst. Chem. Eng. 1931, 27, Received for review Ju ly 30, 1990203-220. Revised manuscript received January 7,1991Wilson, A. H. A Diffusion Problem in Which the Amount of Dif- Accepted January 17, 1991

fusing Substance is Finite. Philos. Mag. 1948, 39, 48-58.

Development of a Composite Palladium Membrane for SelectiveHydrogen Separatioq at High TemperatureA method is described for development of a composite palladium mem brane for selective hydrogenseparation a t high temperature. Electroless plating is used to form a thi n palladium film on a silverporous substrate. T he composite formed showed excellent mechanical streng th and very largeselectivity for hydrogen. T he s tudies performed so far suggest th at electroless plating can be utilizedin making a metal composite m embrane th at can be used at high tempe ratures. Composite propertiesseem fairly con stant at high temperatures. Th e permeability of the composite membrane is com-parable to theoretical permeabilities for pure palladium.

In t roduc t ionRecently there has been increased interest in applyinginorganic membranes for in situ separation of productspecies-particularly hydrogen-to achieve equ ilibr iumshift. From thermodynamic considerations, in a chemicalreaction , if one of th e reaction prod ucts th at slows downthe reaction rate can be continuously removed, th e equi-librium sta te of th e reaction can be shifted in the directof forward reaction, thereby increasing the conversion.Experim entalisb have shown that it is possible to removeproducts selectively through pores of thermally stableVycor glass (Shinji et al., 1982). Itoh (1987) obtaine denhanced conversion of cyclohexane to benzene fromequilibri um conversion of 14% at 473 K and 1-atm pres-sure to 100% by removing hydrogen selectively througha thin (25 pm) palladium membrane from the reaction

mixture. Recently, Zhao et al. (1990) have presentedsimilar experimental results for dehydrogenation of 1-butene t o butadiene using a palladium membrane reactor.However, th e productivity of these membrane reactorsis severely limited by th e poor permeability of th e mem-brane. Comm ercially available membranes are either thickfilms or thick-walled tubes. Since the perm eability isinversely proportional to th e film thickness, a thick mem-brane acts as a poor separator. However, the therm alstability and mechanical strength of a film is directlyproportio nal to its thickness. Hence, we need to providethe necessary mechanical st reng th to the th in film.Th us a major challenge lies in developing a permselec-tive thin solid film, without compromising th e integrityas well as he desired properties of the film. Availabilityof such a membrane for high-temperature application willopen a new area of research in membrane reactor tech-nology and gas separation.Metals like palladium can be used as membranes at hightemperatures owing to their selectivity toward certa in gaseslike hydrogen. However, to obtain high flux we need thinmembranes. These thinmembranes cannot withstand highpressure differentials,hence we need to provide mechanicalstrength to these mem branes. Thi s can be achieved if athin film of meta l can be supported by a thermally stableporous substrate. Th e composite thus formed will act asa membrane with high selectivity and high flux.Electroless plating can be used to plate a thin film ofmetal on any porous substra te. It involves reduction of

Table I. TyDical Platina Bath ComDositioncomponent concentrationpalladium chloride 0.375 /Lammonium hydroxide 30.0 mL/L

sodium hypophosphite monohydrate 10.0 /Lammonium chloride 4.5 g/ L

a metal salt by a reducing agent like hypophosphitepreferentiallyon a catalytic surface. Once plated the m etalon the surface acts as a catalyst for further reaction. Th emetal forms a thin uniform film on the surface.Although relatively expensive, electroless plating is su-perior to electrolytic plating because of the followingreasons (Lowenheim, 1978):1. Nonc onduc ting (ceramics, Vycor glass, polymeric)surfaces can also be coated by use of electroless plating.2. The deposits are thin, more dense, and uniform.3. Complicated apparatus like power supply and elec-trical contacts are n ot needed.4. Th e throwing power of electrolss plating is nearlyperfect.5. Th ere is no formation of projections or buil dup onthe edges in electroless plating.Th e objective of thi s paper is to describe the methodsand procedures used to achieve the goal of forming acomposite membrane using electroless plating a nd to de-scribe the characterization of the composite formed.Experimental Sect ion

Th e experiments were divided into two parts: platingof metal on a porous substrate and characterizing thecomposite formed.Pl ati ng . Porous silver disks (Poretics Corporation,Livermore, CA; 47-mm diam eter, 0.2-pm pores, 0.5-mmthickness) were used as porous substrate. These disks werecleaned in acidified boiling water fo r 10 min t o removeorganics and di rt. One surface was activated with a sen-sitizing solution consisting of ti n chloride a nd palladiumchloride. This activated disk wa s then plated with palla-dium by electroless plating. Th e plating bath consistedof a palladium-amine complex and sodium hypophosphiteas reducing agent. Th e pH of the ba th was maintaineda t 10.2 by using an am ine buffer (Athaval and To tiani,1989). Table I shows typical plating bath composition and0888-5885/91/2630-0591$02.50/0 k~1991American Chemical Society