Industrial and Engineering Chemistry : analytical edition, Vol. 6, No. 2

E d i t i o n

V ol. 6, N o. 2

M ^{a r c h}

15, 1934

I n d u s t r i a l

AN D E N G I N E E R I N G

C h e m i s t r y

VOL. 26, C O N SE C U T IV E NO. 10

Pu b l i s h e d b y t h e Am e r i c a n Ch e m i c a l. So c i e t y Ha r r i s o n E . Ho w e, Ed i t o r

Ed i t o r i a l Of f i c e:

R oom 7 0 6 , M ills B uilding, W ash in g to n , D . C.

T e l e p h o n e : N a tio n a l 0 8 4 8 C a b l e : Jiechem (W ashington)

Ad v e r t i s i n g De p a r t m e n t: 3 3 2 W est 4 2 n d S t.,

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T e l e p h o n e : B ry a n t 9 - 4 4 3 0

Capillary Penetration o f Fibrous M a t e r ia ls ...

...7?. L. Peek, J r., and D. A . M cLean 85

C O N T E N T S

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Determ ination of Fluorides in Natural W a t e r s ...

...J . M . Sanchis 134 Physical E valuation o f F in is h e s ...

...A . E . Schuh and II. C. Theuerer 91 Significance of Solvent Extraction and Rational Analysis in

Coal C a rb o n iz a tio n ...

... E. B . Kesler, E . J . Schneider, and F. W. Jung 98 Determination of Butadiene in G a s e s ...

... Hans Tropsch and W . J . M attox 104 A nalytical R eactions o f Rubidium and C a e s iu m ...

... W in. J . O'Leary and Jacob Papish 107

R etention of D ichrom ate by Glassware . . E dw in P . Im uç 111

Comparison o f W et- and Dry-Filra H iding-Pow er Testa . . ... Roscoe II. Sawyer 113

Com parative Clarification o f Sugar S o l u t i o n s ...

... L .G . Saywell and E . P . P h illip s 116

D etection and E stim ation o f Sm all Am ounts of Fluorine . ...I . M . Kolthoff and M aurice E . Slansby 118

A cidity T itration o f Low-Grade Rosins . . W . C. Sm ith 122

Q uantitative E stim ation o f Furfural a t 0 ° C. w ith Bromine ...Elizabeth E . Hughes and S . F. Acree 123

A Stu d y o f S yn th etic Cryolite A nalysis . . . F. J . Frere 124

M ethods for the Control o f Lubricating G r e a s e s ...

C. L. K n o p f 126

A ction o f Sodium Amide on Silicates and Refractories . . ... P . Victor Peterson and F. IF. Bergstrom 136

Inclusion o f Rarer M etals in Elem entary Q ualitative Analysis. I ... Lym an E . Porter 138

N ew Absorption T u b e ... G. E . Le Worthy 139

D eterm ination of the Acids o f P lan t Tissue. II . . . . ... , ...George W. Pucker,

Hubert Bradford Vickery, and A lfred J . W akeman 140

Pectin Studies. I I ...

... It. Stuewer, N . M . Beach, and A . G. Olsen 143

A Shearing D isk P lastom eler for Unvulcanized Rubber . ... M elvin Mooney 147

Rem oval o f Im purities from M e t h a n o l ...

... . A very A . Morton and J . G. M ark 151

Preparation o f M icroscopic Glass S p h e r e s ...

Sam uel Sklarew 152

Preparation of Sintered Pyrex Glass F il t e r s ...

P au l L. K irk , Roderick Craig, and Richard S . Rosenfels 154

A Sim ple Radio R elay C i r c u i t ...

...G. B . Ileisig and D. C. Gernes 155

A utom atic Vacuum Regulator George F . Liebig, J r. 156

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4 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2

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6 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2

K I M B L E J L , B R A N D

N

I M P O R T A N T F E A T U R E S

1. T H O R O U G H L Y R E T E M P E R E D ( S T R A IN - F R E E ) T O I N S U R E M A X I M U M S T R E N G T H .

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A n. x **

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8 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2

7 A D V A N T A G E S IN THE N E W C O N T A I N E R S OF M E R C K L A B O R A T O R Y C H E M I C A L S

M erck Laboratory Chem icals are now packaged in specially-designed containers w hich offer these seven im p o rta n t advantages:

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A N A L Y T I C A L E D I T I O N Vol. 6, r

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I l e a t P o s s i b l e

^v /\\U e

SsX'.

V i»s o f

A l» V '

C u tu » c ®’

i t I s t f U s

tV*e

l. V Æ ^ e -

rj v c»tS ‘ ' w ar** s " ‘~ r\^t°ïtx

^ is * utl

f°r 1 •- t C ^ - > ”*>£ r Itn '» " o'

r c t ^ a \VVWvC S ° *

cV iet^ 1

1 6 0 0 - * ; { o r ViVi i n 8 *

n V ' c ‘

I n d u s t r i a l

V o l u m e

6 AND E N G I N E E R I N G

15,

N uM BEn 2 C h e m i s t r y 1934

Pu b l i s h e d b y t h e Am e r i c a n Ch e m i c a l So c i e t y Ha r r i s o n E . Ho w e, Ed i t o r

Capillary Penetration of Fibrous Materials

R .

L.

Bell Telephone Laboratories, Inc., New York,

Y.

N

tially in the penetration of fibrous m aterials by liquids.

As examples of such processes m ay be cited the treatm ent of wood w ith p r e s e r v a t i v e sub­

stances, th e dyeing of textiles, and the im pregnation of paper, wall board, and felt w ith m aterials which increase their resistance to h eat or moisture, or which im­

prove their properties as electri­

cal insulators. Any understand­

ing of these processes m ust rest upon a knowledge of the dy­

namics of capillary penetration into such m aterials. Moreover, it is known th a t the interfacial forces which cause such penetra­

tion are related to the adhesion between the penetrating m aterial and the medium impregnated.

Hence th e determ ination of the forces effective in impregnation

should afford inform ation bearing on the nature and extent of the adhesion obtaining in the im pregnated material.

T he experim ental investigation of th e capillary penetration of fibrous m aterials presents a num ber of difficulties. Capil­

lary forces are commonly investigated by means of the rise in capillary tubes or the spreading on plane surfaces. These m ethods cannot be applied to fibrous m aterials. For cellulose m aterials, use m ight be m ade of tubes or plates of regenerated cellulose, b u t these m ight well exhibit different interfacial forces w ith a given liquid th a n would the parent substance.

In these laboratories, attem p ts have been m ade to use the m ethod of Bartell and Osterhof (i), in which there is measured the pressure required to prevent th e penetration of a liquid into a porous m aterial packed in a cell. These attem p ts have n o t been successful, presum ably because of the difficulty of 'packing fibrous m aterials in th e cell in such a way as to

assure uniform pore size.

I t is, however, possible to study th e capillary penetration of fibrous m aterials directly, in some eases, b y observing the ra te a t which the liquid will rise in a strip of th e m aterial when dipped in the liquid. W hile this is a fairly common qualitative test, it does not appear to have been employed for

the quantitative determ ination of i n t e r f a c i a l f o r c e s . By a slight e x t e n s i o n o f available theory, h o w e v e r, it has been found possible so to analyze the data from a test of this type as to obtain q u a n t i t a t i v e l y com parative r e s u l t s . Experi­

mentally, th e m ethod is attra c ­ tive, as it is simple and rapid and m a y b e r e a d i l y applied under c o n d i t i o n s affording a relatively high degree of repro­

ducibility.

Th e o r y o f We t t i n g

In order to present th e theory a p p l y i n g to t h e m e th o d , it will be c o n v e n i e n t to review briefly the concepts involved in the general theory of capillary a c t i o n in t h e f o rm in which they have been p r e s e n t e d by recent w riters (6, 7). W hen a liquid spreads over a plane surface, each u n it of area covered involves th e loss of the energy (Sso) required to form unit area of solid-gas interface, and the addition of the energy

( S s l ) required to form u n it area of solid-liquid interface, and of th e energy ( S l g ) required to form u n it area of liquid- gas interface. The increase in free energy involved in spread­

ing over u n it area is therefore

A F — Ss l — Ss g + Sl o (1 ) S l g is numerically equal to the surface tension of the liq­

uid. T he q u an tity S s g — S s l , a constant of th e solid- liquid pair, is th e Freundlich “ adhesion tension,” A s l . If the ratio of th e adhesion tension to th e surface tension for any solid-liquid system is w ritten as K , so th a t

As l = K Sl g (2 )

th e condition th a t spreading will occur— i. e., th a t AF in E quation 1 be less th a n zero— can be w ritten K > 1. If this condition does n o t hold, K being less th a n unity, th e liquid will come to rest w ith its surface m aking an angle 0 w ith the solid surface, such th a t cos 0 = K .

T he case of capillary rise differs from th a t of spreading in T h is p a p er is a stu d y o f the penelralion o f

liquids into porous m aterials, w ith special refer­

ence to the use o f capillary rise in strip s o f fibrous m aterials as a test m ethod fo r the evaluation o f the penelralion tension o f the liquid-solid system (the penelralion tension being the product o f the su r­

fa c e tension a n d the cosine o f the contact angle).

I t is show n theoretically that the rate o f rise, d h /d t, varies linearly w ilh the reciprocal o f the height o f rise, 1 /h , an d that the slope o f the straight line obtained by a plot o f these quantities is proportional to 7 / 1?, where y is the penetration tension a n d 7/ the viscosity o f the liquid. T he propo rtio n a lity constant is show n to be dependent not m erely on the average pore size, but on the extent o f the range o f pore sizes represented.

U sing a single solid m ed iu m , therefore, relative values o f the penetration tension fo r various liquids m a y readily be determ ined. E x p e r i­

m ental data sup p o rtin g the theory are presented.

85

86 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2 th a t no liquid-gas interface is formed. Hence for each unit

area of capillary wall covered, the energy loss is equal to the adhesion tension alone, so th a t th e condition for such rise is merely th a t K > 0, or th a t 0 < . The effective force per u n it length causing capillary rise will be here term ed the penetration tension, and denoted b y th e symbol y . The

penetration te jsio n is equal to th e a d h e s io n te n s io n when th e oontact angle 0 is greater than zero. If K >

I, th e penetration tension is m erely the surface tension (Sio) of the liquid, as this is the greatest force which can act on th e periphery of the advancing column. W hen K > 1, the li q u i d w ill spread out along the walls of the capillary faster than the column of liquid will advance.

I t m ay be further noted th a t while j I s l cannot be directly m e a s u r e d w h e n K > 1, it m ay be obtained indirectly b y m easuring th e capillary rise of th e liquid in a tube containing it and

F i g u r e 1 . A / R , B / R 2, A / V B another liquid, immiscible

AS FUNCTION'S OP X FOR U n I - ^ t h f i r s t f o r w h i c h A f o r m Di s t r i b u t i o n o f Po r e . , , , , ,

Si z e s is k n o w n ( a s w i l l b e t h e c a s e

if for the s e c o n d li q u i d K < 1). For a t the interface of the two liquids th e equi­

librium condition gives

Sl l' c o s O ' — Ss l — Ss l' — As l — As l' (3 )

where S l l ' is the energy per u n it area of th e interface be­

tween th e two liquids and 0 ' th e angle this interface makes with the solid wall.

Ca p i l l a r y Pe n e t r a t i o n

T he penetration of liquids into capillary tubes has been considered by W ashburn (9) and Bosanquet {2). The lat- te r’s treatm en t is more complete than the form er’s, in th a t inertia effects are considered. These were shown b y Wash­

burn to be trivial after the penetration has proceeded a measurable distance, and for small capillaries m ay be neg­

lected. Taking the simplest case, in which th e viscosity of the displaced gas is neglected, the treatm en t consists simply in substituting the force producing th e motion for th e total force producing flow in Poiseuille’s law'. As noted above, the capillary force per unit length of periphery, or penetration tension, will be here w ritten as y . T he to tal force producing motion is given for a circular capillary b y 2 ir R y , less the hydrostatic head, so th a t for a vertical capillary

dh R*P 1 _ .

d l = S ^ h = S ^ h {2Ry ~ R gM) (4) where R is the radius of the capillary, h the height of the column, dh/dt the ra te of penetration, g the acceleration due to gravity, and -q and d are the viscosity and density of the liquid, respectively. W ashburn (9) gives an integral of Equation 4, b u t this is not convenient for comparison with actual data. By evaluating th e slopes of tangents drawn to a plot of h versus f, or by means of interpolation formulas, values of dh/dt m ay be determined, and if these are plotted against 1/A, a straight line should be obtained, if E quation 4 applies. The validity of this equation, as applied to a single

straight capillary, has been confirmed by experiment, as will be shown below.

In a similar maimer equations can be derived for th e ra te of m otion in various possible experiments in which one im ­ miscible liquid displaces another in a capillary tube. In such cases th e force acting a t th e interface of the two liquids will be given b y 2 ir R y ', where y ' is th e difference A s l — A s l ' ,

given b y E quation 3.

Po r o u s Pe n e t r a t i o n

T he problem of flow into or through a porous or fibrous m edium is obviously m ore complex th a n th a t of flow through a single uniform capillary. T he channels in a porous medium will be similar in shape and arrangem ent to the spaces be­

tween spheres piled together, while in a fibrous m aterial they will resemble the spaces w ithin a bundle of cylinders. The liquid flowing a t one in sta n t in a large pore space will a t the next be divided into stream s flowing through smaller spaces, which will unite with each other or w ith other stream s a t the next large pore space. T he sim plest model of these channels th a t will bear any relation to th e facts is one involving a set of capillaries in parallel alternating in series w ith larger capil­

laries, each capillary w hether small or large varying in radius along its length, and therefore sim ilar in its viscous resistance to a set of shorter capillaries in series.

An exact m athem atical trea tm e n t for th e viscous flow through such an aggregation of channels could be developed only b y assuming a specific arrangem ent of pore spaces.

T he essential distinction between th e flow through such channels and through a group of uniform parallel capillaries, however, can be brought o u t by considering a hypothetical case in which each channel consists sim ply of a num ber of single capillaries in series. This case will differ from the model described in th e preceding paragraph only in th a t each group of small capillaries in series th a t feed or are fed by larger capillaries will be replaced by single capillaries having th e same resistance to viscous flow.

For this hypothetical case, then, it will be assumed th a t the pores in th e medium v ary in size in accordance with some distribution function, such th a t th e fraction d N of the total num ber of pores having a radius lying in th e interval from r to r + dr is given by

(IN = <t> (r) dr (5)

I n any single channel, then, th e various capillaries in series of which it is constituted will occur w ith a frequency given by E quation 5. Now the pressure drop per u n it length in a uniform capillary is given b y Poiseuille’s law as

P = d V L irr* dt

E vidently the pressure drop through a series of capillaries in series is additive, so th a t the to ta l pressure drop through a channel of length h is given by

P = 83 d V r a H r ) dr

h r d l

J

If th e particular channel in question has, a t the height h, a radius R , th e pressure P effective in producing vertical capillary rise is given by

tv R*P =■ 2 i R y — r r 7ghd

so th a t th e ra te of efflux from this channel a t th e height h will be

d V m [ } ? ~

* C m<L I ! * -

J - CO ^

87 T he to ta l efflux will be given by adding th e efflux from the

various channels, and as th e radii th a t these have a t any height are distributed in accordance w ith E quation 5, the total efflux is given by

d V 8,h dt

8

v h [ f _

2 y $ (r) dr hdg

f:

— I—

from which,

dh dt

d V = dh f ' dt dt

J _

I -

ir r ! | t (r) dr

2 y 4> ( / ) d r - hdg

J ' r 2 <f> (r) dr J ' i> (r) dr

(6)

dh _ A y _ Bdg

dt 4 r)h 8ij ( 7 )

(r) = C for Ri < r < Äi

$ (r) = 0 for r < R \ and r > R t

As by definition th e integral of E quation /•<

ion 5, I

integrations indicated in E quation 6, the constants A and B of Equation 7 are found to have th e following values

A = B =

9 i ] log, x (x - 1) (** + x + 1)'

9a:3

R

( i s + i + 1)*^{R 2}

Now a t an y height the ra te of rise, dh/dt, will n o t be uni­

form, b u t will vary from channel to channel. If it is as­

sumed, however, th a t the average distance along & channel from m axim um to minimum radii is small, the rate of rise will be ap parently uniform, the variations from channel to channel appearing only as m inor irregularities in th e surface m arking the average height attain ed throughout the medium. This is, indeed, w hat is actually observed. This approxim ately uniform ra te of rise, dh/dt, can be evaluated by equating the efflux corresponding to a uniform ra te in every channel with th a t given by th e preceding equation. I t follows th a t

s

¡5

E quation 6 gives the ra te of rise in a porous m edium having the stru ctu re of the hypothetical case considered, in which each channel consists sim ply of a num ber of single capillaries in series, or of a single capillary varying in radius along its length. T his hypothetical case differs essentially from th a t obtaining in any actual porous or fibrous medium only in th a t in the la tte r each channel will include groups of small capillaries in parallel.

F or practical purposes, E quation 6 m ay be w ritten in the form

where x = R1/ R2 and R 2 is w ritten sim ply as R . In Figure 1 are plotted as functions of x, th e values of A / R and D /R 2 given by these equations. If the values of A and B thus obtained are substituted in E quation 7 and th e resulting e x p r e s s io n com­

pared w ith E q u a­

tion 4, it will be seen th a t th e two expressions differ only in th a t Equa- tio n 7 th e n i n ­ volves the func­

tions of x plotted in Figure 1. If x equals unity— i.e., th e p o r e s iz e is constant— the two e x p r e s s io n s are identical, as they should be. If x is

small, however, corresponding to a wide variation in pore sizes, the two expressions differ in th e relative m agnitude of their term s.

T he other quantity, A / s / H , plotted in Figure 1, is ob­

tained from the expressions given above, and is a function of x only, which can be evaluated from th e ratio of th e slope of the plot of dh/dt versus 1/h to th e square root of th e intercept, which can be seen from E quation 7 to be equal to

/ t'AOVANC'NO MENISCUS

s c o p e tUTCRCEPT ■ -QKJH

Z 4

2-RECCCHNG WCNiSCuS 5LO PE-3 9 M IN TERCCPT.-O W O «

00>2 O.O* 0020 0024 0028 0032 00J4 00*0 0044

F i g u b e 2 . 877d L /d T v s . l / L f o b W a t e r i n G l a s s C a p i l l a r y

A y I 1 Vb y 2i)<

where A and B are dependent only on the distribution of pore sizes in the m edium, and are therefore constants for a given medium. I t follows th a t the ra te of rise, dh/dt, should give a straig h t line when plotted against l / h . Using the same medium, th e intercepts of such straig h t lines, obtained with different liquids, should be proportional to d/t], affording a check on th e equation. As the slopes of these straight lines should be proportional to y/rj, relative values of y can be thus determ ined.

Before presenting a comparison of experim ental d ata with E quation 7, there will be given a qualitative dem onstration of the significance of this equation in so far as the effect of the distribution of pore sizes is concerned. This is readily done by assuming as a simple ideal case th a t all pore sizes between upper and lower lim its are equally frequent, or th a t the distribution function of E quation 5 has th e form

2 i)dg

Ex p e r i m e n t a l: Si n g l e Un i f o r m Ca p i l l a r y

E xperim ental confirmation of th e expression given above for uniform capillaries is m ost readily obtained b y considering a somewhat more general case; th a t of a uniform capillary inclined a t an angle a to th e horizontal, and having a length L 1 dipping below the free surface of the liquid. P araphrasing the argum ent used to derive E quation 4, the expression for this more general case can be shown to be

d L _ 2R y + R 2 Lidg sin a _ R 2 dg sin a

dl 817 L 817 ( 9 )

(8) dN, m ust be unity, th e constant C of E quation 8 m u st equal l / ( i ?2 — R{). Applying to th e form of $ (r) given b y Equation 8 the

where L is th e length of tube penetrated.

I t follows th a t a plot of 8tj ^ against ^ should be a straight line of intercept — R 2 dg sin a and of slope 2R y + R*Lidg sin a.

Figure 2, curve 1, shows such a plot of th e d ata for dis­

tilled w ater penetrating a capillary inclined a t an angle of 9°22' to the horizontal. Previous to th e test, th e capillary had been w et b y forcing the liquid back and forth several tim es. Curve 2 of the same figure shows th e d a ta for w ater in th e same capillary when flowing back toward th e equi­

librium position from a greater height. Calculation on th e basis of E quation 9 gives the results shown in Table I.

These values of R are in excellent agreem ent w ith th e value R = 0.0250 obtained by calibration with a m ercury thread.

T he value 72.4 dynes per cm. for y agrees well w ith the value of th e surface tension of w ater a t 20° C., 72.75 dynes per cm.

(4). T he value obtained w ith th e advancing meniscus, 70.1 dynes per cm., is significantly lower than th e other, b u t

88 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2 agrees closely w ith a num ber of sim ilar determ inations made

by th e authors, and with the value (70.2 dynes per cm.) obtained b y W ashburn (5) w ith an advancing meniscus (though a t a slightly higher tem perature).

Ta b l e I. Wa t e r i n Gl a s s Ca p i l l a r y a t 20° C . C o r y e M e n i s c u s

1

2

Lv

A dvancing Receding

= 2 . 5 c m . 9 ° 2 2 \

In t e r c e p t

D ynes/cm .

-0 . 1 0 1 1 - 0 . 1 0 0 6

Sl o p e

Dynes 3 . 7 8 0 3 . 8 8 8

R Cm.

0 . 0 2 5 2 0 . 0 2 5 1

y D ynes/cm .

7 0 . 1 7 2 . 4

The experim ent ju s t cited is of interest here in supporting the theory discussed above. I t has independent merit, however, in affording a simple m ethod of determ ining surface tension under dynam ic ra th e r th a n under static conditions.

T he com putation of results is simplified by using a horizontal capillary, so th a t a = 0, in which case E quation 9 can be integrated to give

L* ^{R y}

2t,

3 ÎCOO

i

/

/ 5U< «>€* IÎ

/

• .0 Pt »-

f a

/

VALUES Of i i n SECONOl

Fi g u r e 3 . L 1 v s . t f o r Wa t e r i n Ho r i z o n t a l, Gl a s s Ca p i l l a r y

1. C ap illary w et 2. C apillary d ry

Although in this case it is necessary to m ake a separate determ ination of the capillary radius, y can be computed much m ore simply, as a direct plot of L 2 versus t gives a straight line of slope Ry/2-q. In Figure 3 are plotted d ata for the penetration of w ater into a dry and into a w et horizontal glass capillary of radius 0.03556 cm. a t 26° C. The value (70.3 dynes per cm.) obtained w ith the wet capillary agrees closely w ith the value (70.1 dynes per cm.) cited above for

penetration into an inclined capillary a t 20° C. a n d w ith W ashburn’s value of 70.2 dynes per cm.

a t 30° C. The ex­

trem ely low value (38.5 dynes per cm.) found for penetra­

tion into a dry capil- l a r y h a s b e e n checked b y a num­

ber of careful repeti­

tions of th e experi­

m ent, and similar low values have been observed by others using different m eth­

ods, notably H aller (S). No discussion of this phenomenon will be attem pted here, b u t it is cited to illustrate th e im ­ portance in penetration studies of determ ining interfacial forces under dynam ic conditions comparable w ith those ob­

taining in the type of penetration under consideration.

Ex p e r i m e n t a l: Pa p e r St r i p s

In studying th e ra te of penetration into paper, strips of filter paper about 1.0 cm. -nade and about 20 cm. long were employed. These were m arked lightly w ith pencil a t each half-centim eter along th e length. In each te st a strip was suspended vertically w ith its lower end dipping into the liquid.

T he liquid could be seen to rise in the strips, the upper borders of th e w etted portion usually being even and horizontal and always clearly dem arcated from th e unw etted portion. The tim e a t which th e rising liquid reached each half-centimeter m arking was read with a stop w atch and recorded. H aving th u s determ ined corresponding values of height of rise, h, and tim e, t, values of the ra te of rise, dh/dt, were obtained by graphical differentiation, and plotted against corresponding values of l/h .

To reduce evaporation as much as possible, the strip was

suspended over the liquid in a closed system . T he ap paratus employed in the tests reported below is shown in Figure 4.

T he strip is fastened a t both ends to hooks on a glass rod which is suspended by a fine wire from a glass windlass by m e a n s o f w h ic h i t c a n be raised or lowered. An ordinary stopcock above th e windlass can be opened to evacuate the system if desired. T he bulb sealed to th e side of the main tube perm its the atm osphere in th e la tte r to be d r ie d or brought to a n y d e s i r e d hu­

m idity. W ith this arrange­

ment, th e vapor in the tube can be brought into equilibrium with the liquid, and th e sample lowered into contact w ith the liquid w ithout disturbing this equilibrium.

In Figure 5 are shown the results obtained on the penetra­

tion of liquids into a paper strip, as com puted from d ata obtained as described above.

T he corresponding values of dh/dl and l / h give a good fit to a straight-line relationship, in agreem ent w ith the theory de­

veloped above. This agree­

m ent was found w ith all liquids examined— namely, benzene, ethyl benzene, carbon te tra­

chloride, ethyl alcohol, m ethyl alcohol, and ethylene dichlo­

ride. In another article (o) the

m ethod is shown to apply to studies of the penetration of m olten waxes into paper strips.

In Table I I are listed the values of slope and intercept obtained in four runs m ade w ith each of th e liquids tested.

The approxim ate tem perature of each run is noted in th e table. F or each value of slope and intercept there have been computed the corresponding values of A y (or 4rj tim es the slope) and of B (or 8tj/dg tim es th e intercept) as given by E quation 7. F or each liquid th e m ean values of A y and of B thus obtained are listed in Table I I I , together w ith the standard (or root m ean square) deviations of th e individual values from their mean, as a m easure of th e reproducibility of th e results. T he standard deviations of B are given in the same units as th e values of B (sq. cm.), while th e standard deviations of A y are expressed as percentages of the corre­

sponding values of A y .

I n T able I I I are included th e grand m ean value of B and the m ean values of the standard deviations of A y and of B . T aking each of these la tte r quantities as an estim ate of the expected value of a in samples of size four, the standard deviation {a') of a single determ ination will be given by the relation c — 0.798 a ' (8, p. 185). The value of u ' for A y is thus found to be 3.8 per cent (corresponding to a probable error of about 2.5 per cent for a single determ ination, or of about 1.3 per cent for th e m ean of four determ inations).

V ariability of this m agnitude m ay be ascribed wholly to the experimental error of the m ethod.

As, for such fine capillaries, th e hydrostatic head has b u t a small effect on th e ra te during th e earlier stage of penetration, the intercept which measures th is effect is so small th a t a

Fi g u r e 4 . Ap p a r a t u s f o r St u d y i n g Pe n e t r a t i o n o f Li q u i d s i n t o Pa p e r St r i p s

March 15, 1934 89

Ta b l e II. Va l u e s o f Sl o p e a n d In t e r c e p t

Li q u i d Te m p. Sl o p e In t e r c e p t

° C . S q . cm./sec. Cm./sec.

Benzene 2 9 .8 0.081 0.0030

2 9 .8 0 .0 8 2 0.0024

3 0 .0 0.0 8 9 0.0032

3 1 .4 0.0 8 5 0.0025

C arb o n te trach lo rid e 2 4 .5 0.0 4 8 0.0022

2 4 .2 0.047 0.0026

25 .3 0.052 0.0028

24 .8 0.0 4 8 0.0024

E th y l atcohol 2 6.5 0.0 3 6 0.0006

25 .9 0.0 3 5 0.0005

2 4.7 0.032 0.0003

2 5 .0 0.0 3 3 0.0006

E th y l benzene 3 0.9 0 .0 8 0 0.001S

32 .2 0.0 8 6 0.0021

3 1 .7 0.0 7 2 0.0004

27 .9 0.0 7 6 , 0.0004

E th y len e dichloride 27 .9 0 .0 7 0 0.0024

28 .1 0.0 7 4 0.0022

2 7 .8 0.0 7 6 0.0023

2 7 .8 0 .0 6 8 0.0019

M ethyl alcohol 2 5 .5 0 .0 7 0 0.0020

26 .0 0 .0 6 6 0.0017

2 6 .3 0.0 7 2 0.0020

2 6 .8 0.067 0.0009

Ta b l e Li q u i d

Benzene C arbon

tetrachloride E th y l

alcohol E th y l

benzene E th y len e

dichloride M ethyl

alcohol M ean values

quite small experim ental error will serve to explain the large percentage errors in B listed in Table III . The q u antity B is of interest principally in affording a check on th e theory given above, according to which it should depend only on the pore distribution in th e paper strips, and be independent of the liquid tested. Hence the values of B obtained with the different liquids, as listed in T able I II, should show no greater variation th a n the random one associated w ith v aria­

bility of the order observed in individual determ inations with a single liquid. T his condition requires th a t each individual determ ination differ from the grand m ean value (9.5 X 10 8 sq. cm.) b y less th a n 3 cr', where tr' is the standard deviation of individual determ inations, which has th e value 2.5 X 10-s sq. cm., when com puted as described above. Also this condition requires th a t the m ean value for each liquid shalj differ from th e grand m ean value by less th a n 3 t r '/ \ / - ! (8, p. 309). E xcept for th e mean value of ethyl alcohol, which lies ju s t outside th e lim its, all these conditions are satisfied.

I t seems reasonable to conclude th a t these d ata support the theory in showing B to be independent of the liquid tested.

A complete experim ental check of E quation 7 is impossible, lacking a m ethod for independently determ ining the distribu­

tion of pore sizes. A rough qualitative check, however, can be made b y com puting from th e experim ental d ata the range of pore sizes th a t would correspond to a uniform pore distribu­

tion. F or this com putation B can be taken as having the grand m ean value of T able I I I (9.5 X 10 ~8 sq. cm.) and A as given by th e mean value of A y for benzene, assuming (for reasons discussed below) th a t for this liquid y is equal to its surface tension (27.6 dynes per cm .), so th a t A = 68.1 X 10~8 cm. F rom these values it follows th a t A / \ / l i = 0.221, to which corresponds th e value 0.10 for x in Figure 1. This perm its A / R to be evaluated, giving R = 0.004 cm. and x R = 0.0004 cm. Hence, on the assum ption of a uniform distribu­

tion, th e range of pore sizes would be from 0.0004 to 0.004 cm.

T h a t th e actual pore sizes are of this order of m agnitude can be seen from th e photomicrographs shown in Figure 6 of thin

III. Me a n Va l u e s o f A y a n d B

A y a B a

D ynes % Sq. cm. Sq. cm.

0.00188 3 .3 13.05 X 10-» 1.58 X 10“»

0.00177 3 .3 11 .7 0 X 10-» 1.0 3 X 10“»

0.00146 3 .3 5 .6 0 X lO “8 1.35 X 10-»

0.00184 6 .2 6 .5 5 X 10-» 4 .3 5 X 10-*

0 .00212 3 .0 10.80 X 10-» 0 .9 0 X 10-»

0.00149 3 .8 9 .3 0 X 10-» 2 .5 8 X 10-»

3 .8 2 9 .5 0 X 10-» 1 .9 7 X 10-»

cross sections of th e paper used in these tests, which were prepared by Miss A. K . M arshall, of these laboratories.1

In Figure 6, A and B were taken from nearby points in a single section, and illustrate the considerable variation in density apparent in th e paper. I t is evident from these pictures th a t any a tte m p t to represent the channels between fibers by a system of circular capillaries m ust be necessarily highly approxim ate. Com parison of th e spaces between fibers w ith th e scale shown in the figures, which has a total length (when reduced by the magnification factor) of 0.05 cm., shows th a t the mean diam eter of th e largest of these spaces is of th e order of 0.005 cm. T his is in fairly good agree­

m ent with the maximum mean diam eter of 0.008 cm. calcu­

lated as described above.

T a b l e IV. R e l a t i v e V a l u e s f o r y

Av e r a g e y Sl o

Li q u i d Te m p. ( Re l a t i v e) Sl o ( Re l a t i v e)

° C . D ynes/cm .

Benzene 30 1.000 2 7 .6 1.000

C arb o n te tra ­ 25 0 .9 4 2 26 .1 0 .9 4 6

chloride

E th y l alcohol 26 0.7 7 9 2 1 .8 0 .7 9 0

E th y l benzene 31 0 .9 8 3 2 8 .0 1.014

E th y len e dichloride 28 1.133 . 3 1 .2 1.130

M eth y l alcohol 26 0.7 9 4 2 2 .1 0 .8 0 0

Having thus subjected E quation 7 to such comparison with experimental results as is possible, it m ay be tentatively assumed to apply, and relative values of y m ay be com puted for the liquids tested from the values of A y listed in Table I II . In Table IV are given such relative values for y , taking th a t for benzene as 1.00. In the same table are listed for comparison values

( a t t h e a v e r a g e tem perature of test) of S lo , or the values of the surface ten­

sion of these liquids, as given in th e In ­ ternational Critical Tables. In a th ird column are given values of S lo , rela­

t i v e to b e n z e n e (1.00). T h e o b ­ s e r v e d a n d c o m ­

puted values of rela- F i g u r e S . dh/dt vs. \/h f o r S e v e r a l

tive surface tension L i o u i d s i n F i l t e r P a p e r

agree well w i t h i n

the estim ated precision of A y . As it would be very unlikely th a t these liquids would all have the sam e contact angle unless th e la tte r were zero, it was concluded th a t for all these liquids th e contact angle against paper is either zero or very small.

Di s p l a c e m e n t Te s t s

B y putting two immiscible liquids in a single vessel w ith a strip of paper projecting through the surface of separation, one liquid can be m ade to displace th e other, and the rate of penetration of th e displacing liquid can be observed and measured. T he theory for this case can be worked o u t on lines analogous to the treatm en t given above of sim ple pene­

tration, th e effective force a t th e interface being th e difference in adhesion tensions (y ') given b y E quation 3. Experi­

m entally it was found easy to observe and tim e such displace-

* A s trip of p a p er was em bedded in a block of paraffin an d sectioned w ith a m icrotom e in a p lane norm al to th e len g th of th e Btrip. T h e sec tio n was fasten ed to a slide, th e paraffin dissolved o u t, th e fibers stain ed w ith eosin, an d p h o to g rap h s tak en a t a m agnification of 122. I t sh ould b e n o te d th a t th e d irection in which th e m icrotom e m oved in m aking th e c u t was a t rig h t angles to th e w idth of th e s trip , a n d i t is th erefo re e v id e n t from th e p ic tu re s th a t th e fibers were c u t clean a n d n o t dragged ou t.

90 A N A L Y T I C A L E D I T I O N Vol. 6, No. 2 m ent in the cases of w ater and benzene, and w ater and carbon

tetrachloride. U nfortunately, however, the results were not consistent or reproducible, presum ably because of th e unusual sensitivity of w ater surfaces to th e presence of foreign m a­

terials. As there are few pairs of immiscible liquids of prac­

tical interest th a t do n o t include w ater as one of the liquids, th e study of this displacem ent te st was n o t pursued further.

I t is possible, however, th a t in porous m edia othe- th a n paper

results would be obtained of sufficient constancy to m ake the displacement test a useful m ethod of determ ining adhesion tension. The theory for such cases m ay be readily developed along th e lines indicated.

Su m m a r y

T he theory presented above for capillary penetration into fibrous m aterials is an extension of th a t developed by W ash­

burn for uniform capillaries. I t has been shown th a t this simpler case m ay be conveniently studied in term s of the relation between rate of penetration and the reciprocal of the distance penetrated, and th a t in this way both th e radius of the capillary and the penetration tension m ay be computed from the te st data. T he m ethod is of value in th a t the m easurem ent is m ade under dynam ic conditions.

I t has been shown th a t the treatm en t for penetration into a porous medium is similar to th a t for a uniform capillary, save th a t consideration m ust be given to the fact th a t th e variation in pore size causes the resistance to viscous flow of each channel to be similar to th a t of a num ber of capillaries in series. The final expression therefore involves quantities whose values depend on the distribution of pore sizes. The general character of these quantities has been indicated by evaluating them for the case of a uniform distribution of pore sizes.

D ata have been presented on the penetration of six organic fluids into strips of filter paper. I t has been shown th a t these d a ta agree with the theory in character. These experiments

have been directed entirely to checking the validity of the theory presented. Such a check cannot be complete, and m ust be supported by th e m utual consistency of results ob­

tained in fu rth er work. Assuming the theory to be suffi­

ciently accurate to justify its use in interpreting data, it perm its the determ ination of relative values of penetration tension in paper and further studies m ay show it to be ap­

plicable to textiles and thin wood sections. The experi­

m ental procedure requires merely the m easurem ent of the ra te of rise of the liquid in a strip of th e m aterial, th e strip and the liquid in which it dips being held in a v e s s e l c lo s e d to p r e v e n t evaporation. B y p lotting the observed liquid height, h, against tim e, (, th e rate of rise, dh/dl, m ay be evaluated graphi­

cally and plotted against 1/h. This la tte r plot is a straig h t line of slope pro­

portional to y/rj (the ratio of penetra­

tion tension to viscosity), th e slope be­

ing a function of the distribution of pore sizes in th e medium.

Values of the viscosity of the liquid multiplied b y the slope of the plot of dh/dt versus h give, therefore, relative values of penetration tension for liquids tested w ith a given medium. Com parison of th e values of penetration tension for a single liquid and several different media can be m ade only when it is known th a t th e m edia are identical in pore structure or in the distribution of pore sizes, or when te sts can be m ade w ith a reference liquid which is known to have a zero contact angle with all th e m edia to be tested.

While the m ethod of analysis given applies prim arily to fibrous m aterials in which the rate of rise m ay be observed directly, it m ay be used to interpret d a ta on th e ra te of pene­

tration into porous systems for which only the rate of weight increase by penetration is known, provided th e m ean cross- sectional area of pore space is known, so th a t the linear ra te of penetration can be calculated.

Li t e r a t u r e Ci t e d

(1) Bartell, F. E., and Osterhof, H. J., I n d . Eng. Chem., 19, 1277 (1927).

(2) Bosanquet, C. H., Phil. Mag., [6], 45, 525 (1921).

(3) Haller, W., Kolloid-Z„ 54, 9 (1931).

(4) H odgm an-Lange, "H andbook of Chem istry and Physios,” 16th ed., Chemical R ubber Publishing Co., 1931.

(5) M cLean, D . A., and K ohm an, G. T., paper to be published in Electrical Engineering.

(6) M cM illan, E. L „ I n d . E n g . Chem., 21, 1237 (1929).

(7) Osterhof, H. J., and Bartell, F. E ., J . Phys. Chem., 34, 1399 (1930).

(8) Shewhart, W. A., “ Economic C ontrol of Q uality of M anufactured P ro d u ct," V an N ostrand, 1931.

(9) W ashburn, E. W., Phys. Rev., 17, 273 (1921).

R e c e i v e d Sep tem b er 2 , 1 9 3 3 .

0 0.01 0.0 2 0.03 0 .0 4 0.05

Fi g u b e 6. Ph o t o m i c r o g r a p h s o p Pa p e r Us e d i n Te s t s

Fi r e- Ha z a r d Te s t s w i t h Ci g a r e t s. T ests have been con­

ducted in the fire-resistance section of the Bureau of Standards to determine the fire hazard of discarded lighted cigarets. The efficacy of certain modifications, such as slow-burning paper and the application of tips over one end, was also investigated. The burning cigarets were placed on representative specimens of grass and forest floor materials.

Under the conditions of the test, w ith the m ost favorable drafts and with relative hum idities in the range 25 to 50 per cent, fires were caused on the average b y 9 out of 10 lighted half- length untipped fast-burning cigarets discarded on grass, forest litter, or duff. The percentage of cases resulting in fires in­

creased som ewhat w ith decrease in relative hum idity. T he fire hazard of the slow-burning cigaret was much lower than for the fast-burning type. In the former the glow will not progress ap­

preciably after the cigaret is discarded, while the latter will continue to glow until fully consumed.

T he fire hazard of discarded lighted cigarets can be decreased by applying tip s of cigaret paper. In tests with half-length fast- burning cigarets having tips 1 inch long o f paper similar to th at used on this type of cigaret, 4 fires occurred on the average for every 10 trials. W ith tips of the same length made of the paper used on slow-burning cigarets, the occurrence of fire in the ex­

posed m aterials was reduced to 1 out of 4 trials.