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12 I NDUST R I AL AN D ENGINEERI NG CHEMI ST RY Vol. 21 , No. 1

TThe Drying of Solids-I

T. K. SherwoodaDEPARTMENTF CHEMICAL NGINEERIGG, ASSACHUSETTSNSTITUTEF TECHNOLOGY,AMBRIDGE,MASS.

H E air-dry ing of a solidinvolves the vaporiza-tion of th e liquid con-tained by the solid, followedby the removal of the vap orin a strea m of air. W et- anddry-bulb thermometry, air-conditioning, and the theo-retical moisture-carrying ca-pacity of air under differentconditions are fairly well un-derstood, bu t relatively littlehas been published regardingthe important processes ofliquid and vapor diffusion bywhich the liquid is conveyedfrom solid to air.I n th e drying of solids ofappreciable thickness, it is ob-vious th at th e water of th esolid must by some mecha-nism or other travel from t heinterior ou t to th e surface be-fore it can escape into the sur-rounding air . In the past ithas been assumed4 th at thew a t e r t r a v e l s t hr ou gh t h e

Th e possible ways in whic h the d r y ing of a solid take splace are classif ied und er fou r cases; evaporation ofwa te r m a y t a ke p l a ce at th e sol id sur face or a t p o i n tswi th in t he so lid s t r uc tu r e , a nd unde r e a c h he a d ing th eposs ib i l it ies occur of th e res is tance to in te rna l l iquiddif fus ion be ing grea t or smal l as c om pa r e d w i th theto t a l r e s i s t anc e to r e m ova l of vapor . Th e drying of apar t icula r ma te r ia l i s no t necessa r ily res t r icted to on ec ase, a s t h e m e c ha n i sm m a y c ha nge f r om one c a se toanot her as t he d rying proceeds .The case of drying by internal diffusion of l iquid toth e sur face , wi th negl ig ib le res is tance to th e removal ofvapor , i s d iscussed in de ta i l . Th e Four ie r equa t io ns ofhe a t c onduc t ion in so lid s a r e shown to a pp ly to t he d r y -in g of solid slabs by this m e c h a n is m , a n d a m e thod is de-sc r ibed by which the equa t ions may be used in theana lys is of dryin g da t a wi tho ut tedious ca lcula t ion oran in t im ate knowledge of t he mat hem at ics involved.The theore t ica l drying equa t ion is shown t o fit t h eda ta well for cases of t h e drying of wood a nd of clay,a nd to a pp r ox im a te th e r e su l t s ob ta ine d in th e d r y ingof soap. Th e di f fus ion con stan t of wa te r i n soa pc ha nge s w i th m o i s tu r e c on te n t in th e soap, expla in ingth e de v ia t ion of t h e a c tua l f r om th e the o r e t ic a l c ur ve .Da ta ob ta ine d on m o i s tu r e g r a d ie n t s in soa p du r ingdr y ing i ll u s t r a t e t he s a m e po in t .

solid by diffusion as liquid, although the possibility of it dif-fusing as water vapor has been pointed Th e outstand ingproblems in the drying of solid materials are th e questions asto exactly how the water travels through the solid up to thesurface, how an d where evaporation actually takes place, andhow these factors influence the moisture distribution throughthe solid; the temperature of the material; and th e rate ofevaporation u nder different conditions of the drying air as totemperature, humidity, and velocity.The drying conditions may be defined as the temperature,humidity, velocity, and direction of the air . In the dryingprocesses discussed below it is assumed tha t these conditionsare maintained constant, and further , that t he latent he at ofvaporization of the w ater is received by the solid directlyfrom the air by convection, and that the heat received bythe solid by radiation from the surroundings is negligible.

Classif ication of Drying M echan ismsIf one assumes that the mechanism by which the watertravels from th e interior to t he surface is th at of diffusion,either of liquid wa ter or of w ater vap or, one can visualizetwo distinctly different ways in which the drying process as

1 Received August 15, 1928. Prese nted before th e Division of &I n-dustrial and Engineering Chemistry at the 76th Meeting of the AmericanChemical Society, Swampscott. Mass., September 10 to 14, 1928.

2 Abstracted fr om a thesis entitled T he Mechanism of th e Drying ofSolids, submitted in partial fulfilment of the requirements for the degreeof doctor of science in chemical engineering a t th e Massachusetts Inst ituteof Technology, 1928.

a Present address, Worcester Polytechnic Institute, Worcester, Mass.4 Lewis, J. IND. NG.CHEM.,18, 427 (1921); see also Walker, Lewis,

and McAdams, Principles of Chemical Engineering, M cGraw-Hill BookCo., New York, 1927.

6 Lewis, McAdams, and Adams, P u l p Paper Mag. Can. , 25, 122 (1927).

a whole can proceed. Thes eare (a) the diffus ion of liq uidfrom the interior to the solidsurface, followed by vaporiza-tion of th e liquid a t th e sur-fa c e a n d diffusion of thevapor into the surroundingair; or (6) vaporization of theliquid at a point beneath t hesurface of t he solid stru cture ,f o l l o w e d b y d i f f u s i o n o fwater vapor from tha t pointthrough the porous solid tothe surface and thence outi n to th e a ir . B o th pr oc e-dures may be divided intothose cases where th e resist-ance to internal diffusion issmall or great a s compared tothe resistance to the removalof th e vapo r. Fou r generalcases result:

I-Evaporation a t the solidsurface; resistance to internaldiffusion of liquid sm all as com-pared with the resistance to re-moval of vapor from the surfa ce.11-Evaporation at the solid surface; resistance to intern aldiffusion of liquid great as compared with the resistance torem oval of vap or from t h e surface.111-Evaporation in the interior of the solid; resistance tointernal diffus ion of liquid small as compared with th e tot alresistance to th e removal of vapo r.IV-Evaporation in the interior of the solid; resistance tointernal diffusion of the liquid gre at as compared with t he t ota lresistance to th e removal of vapo r.

It should be made clear th at th e drying of a particularmaterial need not be restricted to one of the above cases.Thus , th e drying of very wet solids is similar to the evapora-tion of a liquid from a liquid surface, and is an example ofcase I, in which the rate of d rying usually remains constan t.However, as the liquid content decreases th e mechanism usu-ally changes to one of th e other three cases, and th e rat e ofevaporation falls as th e evaporation proceeds. Furtherm ore,under different air conditions the sam e solid at th e same liquidcontent may dry by different mechanisms, a phenomenonwhich will be illustrated below by experimental data. Whenthe solid is wet enough to d ry initially a t a constant rate , th edrying process may be divided into th e constant-rate a ndfalling-rate periods. T he former is an example of case I, t h elatter may be any one of the four cases described. It iswith the falling-rate period (often constituting the wholeof the drying process), and with case I1 in particular , thatthis paper will deal.Discussion of Case I1

Case I1 i s tha t of the diffusion of liquid through the solidto the solid surface, w here evaporation take s place, followedby diffusion of t he vapo r into t he main body of the air. Amore or less stagnant air film on t he solid surface presents a

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January, 1929 I NDU ST RI AL AND ENGI NEERI NG CHEMI ST RY 13resistance to th e passage of v apor from the surface into the air.Th e sum of this surface resistance to vap or diffusion an d theinter nal resistance to liquid diffusion throug h the solid togethe rconstitu tes the tota l or over-allresistance to transf er of liquidfrom the inte rior of th e solid to the main body of th e air. Thus,in a case where the surface resistance is negligible comparedwith the interior resistance t o liquid diffusion, variables affect-ing the latter will affect the over-all drying ra te t o th e same de-gree, and laws governing the inte tnal diffusion of liquid w illapply equally well t o the drying process as a whole.T he assu mptio n of a negligible surface resistance t o vapordiffusion corresponds to th e as sum ption of a negligible free-water concentration a t thes o l i d s u r f ace , s i n ce n omoisture gradient is neces-sary to cause the water todiffuse through th e surfaceai r f ilm. The m oi s t ur econcentrations across thes l a b t h i c k n e s s m ay beshown graphically as inFigure 1,which represents

the cross section of a slab ,drying taking place fromf a c e s AC and BD . A Brepresents the initial con-centration gradient, andCD the ul t imate gradientwhich corresponds to theequilibrium water content.Realizing its limitations,Lewis4 made the assump-t i o n t h a t t h e m o i s t u regradients during th e dry-Figure 1-Graphical Represen ta- ing were linear from sur-tion of Moisture Concentrations face to center line, as EC ,across Slab Thickness ED. This assumption was

foun d serviceable in the derivatio n of appr oxim ate equations.Since the slope of the grad ient cu rve is proportional to thera te of diffusion of w ater a t an y point, th is slope must fall offfrom surface to center line, an d approa ch zero a t th e center.T he ac tua l grad ient curves are, therefore, of th e natu re of CFD.I n term s of t he calculus, Newtons law of diffusion in aninfinite sheet may be written

where v is the moisture concentration (per unit volume) a t anypoint in the sheet , 8 epresents time, 2 the dista nce of th epoint from the sheet surface, and K is a constant. A solutionof this equa tion, which is ident,ical with th a t for t he diffusionof h eat in a similar solid, may be written .

2RA = -

sin !E + ., ( 2 )12 5 (;).E e 2Rwhere free liquid concentration per unit volumeinitial free liquid concentration per unit volume=x = distance from surfaceR = half slab thickness

7 = K@/RZ8 = timeK = diffusion constant, where driving force is expressed asa concentration gradient with concentration as weightof liquid per unit volumeTh e free liquid concentration is tha t over and above the

liquid concentration in equilibrium with the su rrounding air.

Th e assumptions involved in the derivation of this eq uationare: (a ) th e vali dity of New tons law of diffusion; (b) th econstancy of t he diffusion consta nt; (c) a uniform liquid con-centrat ion throughout the sol id at the s tart ; ( d ) tha t thediffusion is wholly normal t o th e surface plane; ( e ) tha t theevaporation takes place a t the surface and tha t the surfaceresistance to vapor diffusion may be considered negligible,i. e., that the liquid concentration on the surface falls tozero immediately aft er the sta rt of th e drying.Equat ions (1) and (2) are familiar in connection w ith themath ema tics of heat conduction in solids. I n 1923 Gur neyan d LurieG published a series of curves which represe nts thesolution (2) of th e differential equ atio n (1) in a general formof a chara cter such tha t by means of these cu rves one canreadily evaluate the series (2) for any values of the variablesr and z. This makes it possible to employ the exact equationwithout the tedious algebraic computations that formerlymade its use impracticable.A similar procedure may be followed in th e use of equation(2) in connection w ith th e dr ying of solids, as shown in Figure2. T he percentage of the initial free liquid concentration,which is 100 times the variable A, is shown plotted againstthe location in the slab of the po int considered. Th e variouscurves represent th e relations a t different stages in the d ryingprocess, as indicated by th e values of E noted on the plot. Erepresents the r atio of th e to tal free-liquid con tent to the ini-tial tota l free-liquid conte nt, and is therefore eq ual to the areaunder the liquid gradient curve at any time divided by thearea under the liquid-distribution curve a t the sta rt of th edrying. Since the first termlof the series in equa tion (2) be-co me s large com-pared with ih e laterterms when E is lessthan 0.7, the liquidg r a d i e n t s m ay beseen to be repre-sented by sine curveson Figure 2 for suchvalues of E .Equa tion (2) givest h e t h e o r e t i c a ll iqu id d i s t r ibu t iona t a n y t i m e in aslab where internalliquid diffusion con- SURFACE CENTERC R OSS S E C T I O N or S L A B .

Figure 2r & t h e d r y i n g .Knowledge of t h etotal free water left, or of th e var iable E , is, however, ofgrea ter practical interest. E might be determined by graphicalintegration of the area under th e liquid distribution curve a tany time, or, sinceE=-?--x R S O A d r

which is the theoretical drying equation when internal diffu-sion is controlling. Fro m its deriva tion i t is seen to be sub-ject to the same limitations as equation (2).Figure 3 shows equation (3) plotted on semilog paper, asE vs. r . Since r = K8/R2, quation (3) or Figure 3 obvi-ously represents the relation between E and 0 for any givenslab. If the assumptions are valid, experimental data ob-tained under conditions where the surface resistance wasnegligible would indica te a similar relation between E and 8.6 IND. END.CHBM.,16, 1170 (1923).

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14 I XDUST RI AL AX D ENGINEERING CH EMI ST RY Vol. 21, No. 1

whence K = 8.05 X a4 5in e. g. s. units.This is an approximate adovalue of K for Sitkaspruce used, diffusion

1.0 In order to compare ex-o s p e r i m e n t a l d a ta w ith0 8 the theoretical curve,0 7 a special plotting paper0 6 was constructed, usinga uniform abscissa scalebu t so c ha ng ing the

o r d i n a t e sca le a s t oforce the theore t ica lr e l a t i o n (3) to be as t r a i g h t lin e. W i t hthis special pap er, sincet h e a b s c i s s a s cale i suniform, dat a followingthe theoretical relation(3) will fall on a straightline when plotted as Evs. r , as E vs . 8 / R 2 , ras E vs . 8 . By com-0 1 Z r n0 1 O P 03 m 0 4 0 5 06 a 7 parison of the location0 5

L0 4

0 3

h\,

Figure 3-Plot : Equation (3) of such a straight linewith tha t of the theo-retical line, the value of K may be calculated directly. Th eda ta of se veral run s on slabs of the same material but of dif-ferent thicknesses, when plotted as E vs. 8 should fall onstraig ht lines, the slopes of which vary inversely as the squ areof t he s lab thickness.Lewis4 has derived a n equatio n for the d rying of suchmaterials as soap where the internal liquid diffusion is veryslow, which when rewritten in terms of the symbols used inthis paper is co(1 - E) = -R2 (4)where C is a constant and the exponent n is approximatelyequal to 2.0. The theoretical relation (3) may be comparedwith this equation by plotting 1- E as calculated from (3)vs. r on logarithmic paper. This has been done as shown inFigure 4, and it is seen tha t a linear relation results, as calledfor by (4), over a wide range of values of E . ?Moreover, be-tween E = 0.9 and E = 0.4 the slope is very nearly 0.5,corre-sponding to a value of 2 fo r n in equation (4) . Lewis equa-

l

I WasOb0 50 403

- e

02015

01o m

a5 4001 M P MS 0.1 a2a0

iFigure 4-Relation between Equations (3) and (4 )

tion (4) is therefore seen to compare closely with equation(3) for the drying of a slab und er con ditions of negligiblesurface resistance, during the period in which the first 60per cent of th e free water is being removed . Since E ap -proaches zero as the drying proceeds, the curve on Figure 4must approach 1- E = 1as an asym ptote a t large values of r.Equat ion (4) is similarly limited t o values of 1 - E less tha nunity.Application of Fourier Heat-Conduction Equations toDrying of Wood

The use of the Fourier heat-conduction equation s in theanalysis of wood-drying data was suggested in 1925 by Tuttle

and Loughborough. Moisture-gradien t dat a on 5.08-em.slabs of Sitka spruce were compared with the theoreticalequation and a value of K so found. Th is value of R wasthen used with the theoretical drying equation to predict thedrying curve for a similar 5.08-em. spruce slab. Th e predictedcurve was found to compare well with experimental data ob-tained in drying such a slab. It is believed that the specialplot method described above is a considerable improvementover their method of finding K from experimental data , sincenot only are the required calculations much less, but littleknowledge of the ma them atics involved is necessary. Th edat a of only one experiment are shown by Tuttle , and th atin th e form of A plot, so it is impossible to use his data t o com-pare th e actua l with the theoretical effect of sla b thickness onthe drying time. In this single experiment reported, theinitial water content was 51 per cent and t>he equilibriumwater content 8 per cent. E was therefore 0.60 a t 33.8 pe rcent water, which from ,.oothe plot corresponded 0.90t o a b o u t 28 h o u r s . ,,,From Figure 3, E = 0 7 00.60 when r = 0.126. 0 6 5

0 55

KOR2= 0.126 = -28 X 3600 X K 0 50(2.54)2

Application of Drying Equation to Drying of ClayAs pointed out above, various factors may determine inwhich of th e possible classifications of dry ing mechanisms agiven example will fall. Practically any ma teria l, if wet

7 Fordyce Tuttle, J . Franklin I n s l . , 200, 609 (1928).

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January, 1929 IND US TR IAL AN D ENGIiYEERI-VG CHE MISTRY 15enough, will dry at a constant rate and the drying will beclassed under case I. Th e thickness of th e mat erial will alsoaffect the drying mechanism, as will be seen when it is con-sidered th at th e dryin g of a n infinitely thin sheet must be anexa mp le of case I, no matter w hat the m aterial or how wet i tmay be. A thin poplar slab, 4.1 mm . thick, when dried simi-larly to those samples described above, gave indications tha tthe drying should be classed under case I over nearly thewhole drying range.T h e d r y i n g c o n d i-tions, such as the airv e l o c i t y u se d, m a yalso affect the dryingmechanism, a s sug-

As an example, thedata obtained on thed r ying of i d e n t i c a lb l o c k s of brick clay7.0 X 7.0 X 2 54 cm.thick may be noted.S o wood frames wereused, but drying fromthe edges of the blocks

I 000a800 50 700 5e'0 60 gested above .0 550 0

0 5

0 40

0 50 100 m - a s p r e ve n te d byfaces w i t h t i n f o i l .The first block, con-taining initially 27.3per cent total w ater, was dried in a small flue through which airnasforced a t 15.2 meters per second and a t room temp erature.The ra te of loss of m t e r was found torem ain constant down to16.5 per cent. below n-hich it fell off rap idly t o zero at the equi-librium water con tent of abo ut 3 per cent. Figure 6 showsthe da ta of this experiment, taken during the falling-rateperiod, plotted as E' vs . time on the special plotting paperpreviouqly described. E' is defined as the free water co ntent

divided by th e free mater content a t the s tar t of the falling-rate period. Th e points are seen to fit a straight line fairlywell, and the theoretical relation (3) is therefore approxi-mate d. Thu s the drying of this clay under these conditionsis an exam ple of case I between 27.3 and lG.5 per cent totalwater , and of case I1 below 16.5 per cent total w ater. Th eoth er clay slab of t he same dimensions was dried with outforced air convection, an d the drying ra te remained cons tantdown to about 8 per cent total water. Durin g this constan t-rate period th e mechanism was t h a t of case I, so tha t between16.5 and 8.0 per cent total w ater the tw o slabs of t he samema terial an d of th e same dimensions dried by different mech-anisms. Th e rate of loss of water du ring the coiist,ant-rateperiod in the second case was only abou t one-sixteenth of t hecorresponding rate in the first casc. W ith natura l convectionthe surface resistance to vapor diffusion was therefore ap-proximately sixteen times as great as with the forced convec-tion used in the first experimen t. Th e rati o of surface tointernal-diffusion resistance was therefore changed approxi-mately sixteen-fold, which was enough to change the dryingmechanism from case I1 to case I over this rang e of m oistureconcentration.

Drying of Soap SlabsIn order to obtain additional data for comparison with theequatio ns derived, several soap slabs were dried in a c urrentof slightly warmed air. Borax laundry soap was cut up andwell kneaded with w ater, and formed into five wood frames,each 14.2 X 14.2 em. Th e wood frames were shellacked toprevent absorp tion of water from the moist soap. Five thick-nesses were used-0.63, 1.27, 1.90, 2.54, an d 3.17 cm., re-spectively-although the 2.54-cm. slab was used to obta in

MI N U T L SA F T E R S T A R T OF F A L L I N G R A T E PERIOD 'Over ing these sur-

Figure 6-Data Obtai ned on Drying ofClay Blocks

moisture-gradient data. Th e drying was carried out over aperiod of several mon ths in a small tunnel drier at 23-30" C. ,wit h frequ ent weighings of each sample. Th e initi al moisturecontent was 20.2 per cent on th e dry basis, as determined byanaly sis of a sam ple of th e bat ch of well-mixed met soap.Although the purpose of the wood fram e was t o prev ent loss ofwater from the slab edges, a certain amou nt of shrinkage tookplace, wit h conseq uent retre at of t he slab edges from thewood frame. Since the length of this exposed edge surfacewas similar in each sample, the areas of these surfaces wereroughly proportional to th e slab thickness. It amounted toabout 22 per cent ofthe face area in thecase of the t hick estslab, and t o about 4per cent of the facearea in the case of thethinnest slab.Figure 7 s h o w thedat a obtained plottedas E vs.0/(2IQ2, imedivided by t he squareof th e thickne ss. using

l o o0900 800 50 700 650 600 50 50

0 4 5

the special plo ' t t ing 0 4 0p a p e r d e s c r i b e da b o v e . T h e a ct ua lp o i n t s , h a v i n g a nfroin the line of less

0 800 1200 160000H URSa v e r a g e d e v i a t i o n @ = (THICKONES5 I N C M ) a

' l H l C K N E S 5 I. 0.63 CM. 2. 1.27 CK3. 1.90 C M 5. 3 17 CM.han 2 per cent, areno t sho'F-nJ as therewere so many as to Soap SlabsFigure 7-Data Obtained on Drying ofm a k e t h e d o t con-fusing. Tw o abscissa scales are used, and the theoreticalcurve shown plotted as E vs. 7. The lines for the variousslab thicknesses are seen to coincide fairly well, altho ugh the reis a twenty-five-fold variation in the term R L . Althoughthe theoretical relation is represented by a straight line onthis plot, th e lines representing th e d ata on soap are Seen tocurve in each case a t values of E of 0.50-0.55. Th is curv atur emay be explained as being due to the decrease in the diffusionconstant K as the d rying proceeds and th e moisture concentra-tion falls off. Th e decrease in K is undoubtedly connectedwith the shrinkage ofthe soap. I t s h o w s 2 2up in the plot of th e 2odata as a decrease in 1 8

the slope of the drying 2 I6c u r v e a n d a c o n s e - ;Dquent curvature. =- 12Th e decrease in thediffusion constant K Ewith moisture concen-tration is also indi-cated by the moistureconcentrat ion d a t a , 2obtained on the 2.54- ocm. slab. These were

thin slices cut parallelto the drying face from a square chu nk cut from the soap slab.After the chunk had been removed for slicing, the edges ofthe hole formed in the slab were lined with t in foil to preven tdry ing from these surfaces. Figure 8 show the m o i s tu r egradients, or free moisture distribution, plotted as per centfree water on the dry basis us. the location in the slab. T hepoints are placed at abscissas representing the center lines ofth e slices analyzed. Th e initial moisture gradient is repre-

$ I o

e SURFACEobtained by Figure 8-Moisture Gradi ents Obtai nedon Drying of Soap

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16 IND UST RIAL AND EN GINEERING CHEiMIxTRY VOl. 21 , No. 1sented by a horizontal line at 20.2 per cent free water. Da tawere obtained on the moisture gradients in the same slabafter 166, 383, and 1152 hours, and are represented by t8hethree solid curves on Figure 8. By graphical integration ofthe area under the third curve the average free-moisture con-centration a t tha t t ime was 13.1 per cent; E is therefore13.1/20.2 or 0.65. Th e theoretical moisture-gradient curve(from Figure 2) corresponding to a value of E of 0.65 is sho wn

by the dashed line on Figure 8. The actual gradient curveis therefore seen to be m uch flatter than the theoretical curvefo r the sam e conditions. This ma y be explained as beingdue to th e lower vaIues of th e diffusion constant K a t he Iowermoisture concentrations-i. e., near the faces. Where K islow a steeper gradient curve is necessary to cause the waterto diffuse than in the center where the moisture concentrationand consequently K are greater.

Lead =Tin-C adm ium a s a Substitute for Lead-TinWiping Solder'Earle E. Schumacher and Edward J. Basch

BELL E L E P H O N E LABORATORIES,63 WEST ST., N E W YORE,N. Y.Data are presented which show that certain lead-tin -cadm ium alloys m ay be advantageously substituted as soldersf o r lead- tin alloys. Data are given showing the physical and chemical properties of these alloys.

HE high cost of tin is stimulating investigation of meansfor curtailing its use. Since large quan tities of tin areT sed in wiping solder, th e sa tisfactory substi tution ofa ternary alloy containing less tin for the present lead-tinalloy would result in a considerable saving of this metal.A review of th e literature indicated t ha t alloys of lead, tin ,an d cadmiu m offered good possibilities as substitutes. Aphase diagram for these alloys has been prepared by Stoffel.2Burgess and Woodward3 state t ha t cadm ium appears as apromising substitute for part of the tin in solders. This isnot because cadmium is cheaper than tin, but because itallows th e use of a higher percen tage of lead. Phy sical prop-erties of several lead-tin-cadmium solders are given by. S c h w a r t ~ . ~ ince the previous work did not include any ex-am ina tion of t he behavio r of the se alloys as wiping solders, itseemed desirable to continue the work and examine theirproperties in this respect.The results discussed in this paper were collected fromlaboratory tests. Field tests have not yet been made withthese solders, and until their behavior under actual operatingconditions has been ascertained it is, of course, unwise tomake a ny statem ent regarding their practical value.

Properties of a Wiping Solder1-The melting point of the solder should be som ewhat be-low th at of th e parts being joined.2-The solder should hav e a solidification rang e of at leas t50" C. in order to provide adequate time in which to moldit easily into the shape desired.3-Joints ma de with th e solder should be readily unwiped ;that is, the solder comprising the joint should be readily re-movable. Th e parts being joined should not be harmed dur-ing the unwiping procedure.4-The solder should not change in composition when sub-jected to prolonged heating in the melting pot a t temperaturesranging from 300" to 400" C.5-Joints made with the solder should have tensile andshear strengths greater th an the p arts being joined.6-The solder should have no injurious effects on the partsbeing joined and should readily tin them.

1 Received August 18, 1928.2 Z. anoyg. Chem., BS, 137 (1907).6 Am. Inst. M i n . Met . Eng. Tech. Pub. 86 (1928 ) .Bur. Standards, Tech. Pap e r 109, 8 (March, 1919).

7-The joints must be non-porous when joining cables inorder to prevent damage to the insulation of t he cable by t heintroduction of moisture.8-The joint should not deteriorate with age.Procedure

SELECTION OF ALLOYS o BE TEsTm-The main objectiveof this investiga tion was to find a wiping solder th at w ould bea t least as sat isfactory as and cheaper than the 62 per centlead-38 per cent tin alloy which toda y is generally used forwiping purposes. (This alloy is referred to hereafter as stand -ard solder.) Since lead is by far the cheapest of th e constitu entsof lead-tin-cadmium solders, an d cadmium a nd tin are ab ou tthe same price,5 any cheaper solder in this system must con-tain a higher percentage of lead. (Figure 2)

PREPaRATION O F ALLOYS-High-purity co ns tit ue nt s we reused in preparing the test alloys. Bunker Hill and Doe Ru nleads, containing less than 0.01 per cent impurities, wereused. Th e cadmium was 99.5 to 99.9 per cent pure; the tin,99.9 per cent.Th e cons tituents of the alloys were carefully weighed witha maximum possible error of +0.1 per cent. Th e lead wasmelted in a graphite crucible under a covering of palm oil toprevent oxidation. As soon as the lead was molten, the tinand cadmium were added. Most of the melts were cooled inthe crucible bu t those from which tensile specim ens were to becast were heated to about 50" C. above the liquidus andpoured into m oIds only slightly cooler.Experimental

PHASEDIAGRAM-cooling curves of lend- in-cadmiumalloys containing a high percentag e of lead showed arre stswhich agreed closely with those previously found by Stoffe12a nd S c h w a r t ~ . ~ rom Stoffel's diagram (Figure 1) he coolingranges and the percentages of primary, binary, and ternarysolidifications of the alloys given in Ta ble I were calculated.I n the range of com positions satisfactory as wiping solde rsthe lead-tin-cadmium alloys have a longer cooling range th anthe lead-tin.arbitrarily chosen as having satisfactory workability; th at is,WOR KA BIL ITY HARACTERISTICS-Standard sold er was

6 At the time of writing cadmium and tin are both selling for approxi-mately 60 cents a pound.