OREGON FOREST PRODUCTS L.AaDEATC! 9Y
LIBRARY
THE EFFECT OF CHANGES IN TH E
EQIJILI13RIIJM RELATIVE VAPO R
PRESSURE UPON THE CAPILLAR Y
STRUCTURE OF WOO D
October 193 5
No. 81075
UNITED STATES DEPARTMENT OF AGRICULTUR E
FOREST SERVIC E
FOREST PRODUCTS LABORATOR Y
Madison, Wisconsi n
In Cooperation with the University of Wisconsin
F,OU
LFHE
T
.nqn
U a+JRATOR g
EFFECT OF CHANGES Iiv TET EQUILIBRIUM RELATIVE VAPO R
PRESS i `,
ATTHE CAPILLARY STRUCTURE OF WOOD ,
By
ALFRED J . STAiM, Chemis t
Introductio n
E
The rate of penetration of various liquids into :.soft g oods ha s
and by Sutherland, Johnston, an d
been studied by Johnston and Maass
Maas:, (12) from the standpoint of pulping . They-found the rate o f
penetration of transverse heartwood sections with thicknesses greater tha n
the fiber length to be about 100 times greater than the 'penetration of lik e
thicknesses in the radial and tangential directions . Unseasoned sapwoo d
was as much as 200 times more permeable than the corresponding unseasone d
heartwood.. An increase in pressure caused . a slightly greater rate o f
penetration at higher pressures than would be expected if it were directl y
proportional to the pressure . This the authors believe to be due to a
stretching of the pit membranes at higher pressures, resulting in an increase in the size of the openings . The use of back pressures had n o
apparent effect . The rate of penetration in all cases decreased wit h
time to a final equilibrium rate . Presoaking di d, not hasten the attain ment of an equilibrium rate .
(0
The capillary structure of wood has been recently studied b y
Buclaaan, Schmitz, and Gortner (2) . They found the rate of penetration
of transverse sections of softwoods to water, aqueous solutions, an d
various organic liquids to decrease with time to a final equilibrium value .
The change in the rate of penetration of water caused by the addition o f
electrolytes was not a function of the viscosity . This they believe t o
be due to electrokinetic ; effects which modify the resistance to flow . They
also found the rate of penetration of benzene to decrease with increasin g
moisture content of the wood, indicating that the swelling of wood cause s
a decrease, in the size of the effective openings .
1
`Presented before the Colloid. Division, American Chemical Society, at It s
89th meeting in New ?or City, April 22-26, 1 935 .
R1075
The author has determined the effective size of the openings i n
wood through which flow occurs by several different physical methods : The
effective capillar=y cross section of various softwood sections wa s
determined by means of electro-osmotic flow (7 ) 8) and by measuring th e
electrical conductivity of salt solutions filling the capillary structur e
( ) . These data, combined with .data obtained from pressure-permeabilit y
.
measurements to water, made possible the calculation of the average
effective capillary radius .( 7 )
, ) . Measurements of the air pressur e
,-required to overcome the effect of the surface tension of water held i n
the caillary structure furnished data for the calculation of the maximu m
effective capillary radius (7; 8, .2) . The average effective capillar y
radius was found to vary from 10 to 70 mid for the heartwood of differen t
species tested and from 180 to 2,000 ii for the sapwood . The heartwoo d
values are of the same order of magnitude as the size of the opening s
found in synthetic membranes by other investigators 6 , )4) . The maximum
effective capillary radius was found to vary from CFO to 120 n7a for th e
heartwood of several s pecies and from 180 to .11, 000 mid for the sapwood .
The maximum effective openings are thus about two to five times th e
average in size . The data indicate, that these effective openings ar e
either normal pores in the pit membranes or checks across the membranes .
In the case of thin transverse sections less than the minimum fiber lengt h
in thickness, the flow is through the open fiber cavities . . Measurement s
made on these sections gave capillary sizes of .the same order of size as .
the fiber cavity dimensions determined microscopically .
The only available data to give an indication of the effect o f
shrinking and swelling of wood upon the effective capillary sizes are thos e
of Buckman ; Schmitz, and 'Gartner (2) which ' indicate that the effective
,
.
capillaries increase in size upon drying of the wood . More complete
information along this -line should be of considerable value in . determinin g
and understanding seasoning, preservation, and pul3jing practice .
E:erimental Procedure.
An attempt was first made to determine-the equilibriu m
-permeability of wood sections to air of different relative vapor presmtre s
using the differential pressure drop apparatus previously described (z~) •
It was found, however, that when green sections were securely clampe d
the apparatus so as to avoid leakage, the 'sections subsequently choc .:ea .
when brought to equilibrium with air of lol-T relative vapor pressures . Th e
apparatus was hence modified as shown in figure 1 .
It consisted esse
n tially
of three compartments, 1 and 2 separated by the wood section and 2 and 3
separated by the standard capillary tube C the same as in the previou s
apparatus . Manometers were provided to determine the prase are drop betwee n
compartments 1 and 2,and 2 and 3 .
The means of holding the sections wa s
x1075
-
I
.1
hl
0•1r F
Figure 1 .--Low-pressure permeability a pparatus usect for making,
measurements on transverse sections of )- .root? .
modified as follows : Holes were drilled in one end of cylindrical piece s
of wood
in the fiber direction with a centerless bit, the bottom servin g
as a transverse section . A soft rubber stopper R connected the section t o
the apparatus . It shored no tendency to lobsen or exert an appreciabl e
stress on the section over a complete moisture change cycle . The woo d
section was enclosed in a large cylindrical glass tube with rubber stopper s
at each end . A stopcock S was provided in compartment 2 to prevent th e
passage of air through the wood section during .the course of bringing i t
to moisture equilibrium . During this process the air entering at A,
ci iculated around the section, and was then discharged at B throug h
stopcock S' . This was done to cause humidification to occur from th e
outside of the specimen so as to more nearly duplicate normal drying an d
reabsorption conditions . An electric heating coil was wrapped about th e
exit tube B to prevent condensation of water from air at a high relative .
vapor pressure when being discharged from the apparatus . The apparatus wa s
held at a temperature'of )40° C . in a . thermostatically controlled water bath .
The air waa humidified by bubbling through saturated salt solutions i n
10-inch high glass jars filled with glass beads . About an inch of mercur y
was placed in the bottom of the jars and the air first bubbled through thi s
to prevent salt from working back into the jet . The air passed through a
trap filled with glass wool to remove any traces of entrained spray befor e
entering the apparatus . The relative vapor pressures given -in table 1 wer e
obtained from gravimetric determinations of the rmoi .sture content of the ai r
at approximately the same rate of flow as that used in the experiments .
r
This apparatus proved satisfactory for determining th e
permeability of transverse sections . It could not be used, however, fo r
radial and tangential flow as practicall y, all the air would pass . through
the end-grain part of the cylindrical wall of the wood section rather tha n
through the end, In the case of the transverse sections the passage of ai r
through other than the end-grain ends was entirely negligible (1 percent or .
less) . Further, this glass apparatus could not be used for other than th e
transverse sections because it would not stand the pressures required fo r
obtaining measurable permeabilities with some of the resistant sections .
It was thus necessary to devise another means of making the measurement s
using a more rugged apparatus .
It was found that sections clamped . in the old type of flus h
rubber--gasketted flange,' when carefully marked, could be removed from th e
clamp and reinserted in practically the same position with a variation i n
the pressure drop reading s r of not more than 2 to 3 percent . It wras henc e
decided to use this type of flange clamp and remove the sections and pre humidify them to approximately the equilibrium relative vapor pressure o f
the air to be used in the next permeability test . In this way checkin g
.of the sections was entirely avoided . Although the source of error i n
these measurements was somewhat greater than in those made with th e
•apparatus of figure 1, there was the distinct advantage of being able to .
make measurements on one series of sections while another series wa s
being prehumidified .
R 1 075
Table 1 .--Relative vapor pressuresobtained with different saturate d
salt solutions
Temperature
Material
:•Relative vapor pressur e
-------------------------- --------- -------- ----------------------- 0
ti
C.
Distilled water :
40
96 . 3
Saturated BaC12
:
40
SG . 7
Saturated NaCl
:
CIO
73 .1
Saturated gnC12
40
50 . 5
Saturated MgC12 . . .
4o
3 1`0 0
4o
11 . 7
Saturated LiCl
. •:
0.0
Distilled water
:
23-2 5
9g . 0
Saturated BaC12
:
23-25
g 9! 3
Saturated NaCl
:
23-25
74 . 5
Saturated MgCl2
:
23-2 5
31 . 0
P205
23 -2 5
0 .0
R1075
- 4-
e4
• More substantial humidifiers were also •necessaxy for these ,
measurements . They were .mado of 1S-inch lengths of 1-inch galvanized iro n
pipe . Pritted glass discs were clamped to the lower end of the pipe wit h
a 1 by 1/4 inch reducer with rubber gaskets•between . Pieces of 1/4-inc h
.
galvanized pipe were threaded to the reducer .and bent in a U shape .
Similar reducer s' with short 1/4-inch nipples were screwed into the uppe r
ends of the 1-inch •apes . The humidifiers were coated inside with a
mixture of half beeswax and half rosin wax to decrease corrosion . They
were then half filled with water or . saturated salt solution s'. Air pressure
applied to the bent intake pipe was broken up into fine bubbles in passin g
through the fritted glass disc, and thence through the saturated sal t
solution. . To prevent the salt from clogging the 'ritted glass discs, ai r
was always passed through a water prehumidifier first . The salt 'solution s
thus always reduced the relative vapor pressure of the air rather that .
raised it'. A similar humidifier with an inside 1/4-inch standpipe served '
as a trap . Glass' wool was inserted in the upper part of it to remove an y
traces of (pray . Five humidifier tubes and one trap were assembled-on a
rack . They were used only at room temperature, 23°•to 25° C . The relative
vapor pressures obtained with thq e humidifiers are give n . in table • 1 . Th e
sections were prehumidified in humidity rooms held at SO° F . and 30, 75 ,
90, and 97 percent relative humidity, respectively, and in a desiccato r
over P 0 for at least a week . The equilibrium relative vapor pressur e
change 2 In the apparatus was so small that readings could be made a s
quickly as pressure equilibrium was established .
The velocity of the flow of air through .both the standar d
capillary tube and the wood sections can be expressed by Peiseuill e t s
equation :
i
4
V _ ~' rcPc
. °
E q 1c
(for standard capillary tube c)
4
rw pvi
V1v = HQ,"A(for the wood section )
S
lt ,
(1 )
(2)
' in which Vc and•Vw are the velocities of flow through the capillary an d
through t wood section, rc and rw are the radius of the capillary and th e
' average effective radius (to be more exact, the fourth root of the averag e
fourth power) of the` wood capillaries ., lc and ltiq are the correspondin g
lengths and Pc and Pr the corresponding pressure drops, 1 the viscosit y
of the ai r? Iti the number of .effective caaillarien in the we0a sections i n
parallel per unit of cross section and 2, the effective cross section, al l
expressed in centimeter-gram-second units . When the standard capillary
and the wood section are connected in series as in this investigatio n
x1075
f.
(3 )
vc
and
iARv = 1 r Pc
iw
lcc Pw
b
(4 )
Both N and rtiw are unmiown so that in order to determine either, farthe r
data are necessary (8, .) . During the course of the shrinking and swellin g
of wood, N will, however, remain constant unless checking occurs . The
pressure drop ratio Pc and the standard pressure drop rati o
Pw
1.
should thus be proportional to the fourth power of the capillary radii .
The change in size of the capillary openings in wood have hence bee n
expressed in terns of the pressure drop ratio in this investigation .
Experimental Result s
Measurements of the pressure drop ratio for thin transvers e
sections less than a fiber length in thickness of the heartwood of initiall y
green western hemlock and air-dry white pine at different equilibriu m
relative humidities are shown in table 2 . Air was passed around the outsid e
of the sections and out through stopcock S! (fig . 1) for 2 days before
passing it through the section in order to bring them to equilibr iu wit h
the vapor pressure of the air . Pressure drop readings were then made ove r
a period of 2 days . The total pressure drop used was never greater tha n
20 cm . of water . The data show that the fiber cavities change but ver y
slightly in size with shrinking and swelling of the wood . The mean
deviation of the effective capillary radius for the white pine was abou t
0 .5 percent and for the western hemlock specimens still less . In the cas e
of the white pine a part of the permeability may have been through resi n
ducts . These are entirely absent from western hemlock so that th e
permeability of these sections was entirely through open fiber cavities .
This approximate constancy 6f the size of the fiber cavities is i n
agreement with findings of Schwalbe and Reiser (6) and Geiser (1),en d
with the density-shrinkage relationships for small sections of wood drie d
under as nearly stress-free conditions as possible developed by th e
author (10) .
j,
R1075
-6-
Table 2 .---Effect of cI .an,ses in relative vapor pressure upon the permeability
of transverse sections of wood less than a fiber length i n
thickness
:Dimensions of : Capillary
sections
: constant
Species
:
re
:
: Thick : Cross :
c
ness :section:
--------- :
-- -car . :
:
White pine
heart
.
: 0 .22
:'
Mean
:Relative :Equilibrium :
vapo r
pressure : deviatio n
dro p
:pressure :
ratio,
: of air :
-----Percen t
---------- -
1.37 : 1.85 x 10 0: 0.963
: .867
2.0)4
.505
2 .08
:
:
a
.310
.117
.000
.117
.310
.
.
Western . hemlock :
.heart
.73)4
5 .30
1 .47 x
.
.
.
_
5 .30 : 1 .47 x 10-7 :
.117
.310
.505
4 734
.867
.963
I;
:
-7--
2 .08
260 2
2.00
9 .50
9 .50
9,69
9 .53
9 . 63
2 .89
.73 )4
2 .8 6
.117
2 .93
2.
2 ..96
2 .98.
2 .9 4
.
.
.
.
.
:
.:
:
2 .01
', :
9.6 8
.963
.505
.73)4
.067
:
9,8 8
9 .62
9 .6T
.000
.117
.310
810 75
.
1.95
.31 0
:
2 .05
2 .05
1 .99
.734
.505
.310
.117
.000
.
.4o
l0_7 : .
:
2 .10
17.34
•.963
. 22
1 .96
2 .90
2 .89
:
.94
1 .43
Similar measurements were made on initially green transvers e
sections of both the sapwood and the heartwood of western hemlock greate r
than the maximum fiber length in thickness . The results obtained fo r
several relative vapor pressure change cycles are shown in figure 2 . Th e
curves are numbered in order and the desorption part of the cycle indicate d
with open circles and the adsorption part with black circles . There is a
definite increase in the pressure drop ratio with ,decreasing equilibriumrelative vapor pressure indicating that the effective capillaries in the pi t
membranes increase in size-'when the wood shrinks, During the first cycl e
true equilibrium was not obtained or a slight checking of the sections '
occurred . After this the relative vapor pressure cycles were quit e
case s
reproducible . Adsorption values of the pressure drop ratio were in
.
These
hysteresi
s
slightly greater than the corresponding desorption values
e
loops are entirely comparable with those for the moisture content-relativ
vapor pressure (11) and electrical conductivity-relative vapor= pressur e
The electrical conductivity-moisture content relation relationships
ship calculated from the relationships of each with the relative vapor pressure .
Hive a relationship free f ;com'hysteresis effects .' The same is true when th e
pressure drop ratio-relative vapor pressure relationship is converted to a
pressure drop ratio-moisture content relation 'Ship basis . The pressure dro p
ratio is proportional to the fourth power of the effective radius (se e
ovation 4) . The square root of the pressure drop ratio is hence proportiona l
to the effective cross-sectional area of the capillaries . The relationshi p
between the square root of the pressure drop -ratio and the equilibrium moistur e
content is plotted in figure 3 for the sane data as in figure 2 . A linea r
relationship free from hysteresis effects is obtained below' a moistur e
content of approximately 20 percent . The external volumetric and crosssectiiongl swelling of wood is directly proportional to the moisture conten t
from oven-dry to the fiber-saturation point (10) . .The cross-sectional area ,
of the pit membrane openings thus appears to be inversely proportional to th e
extent of swelling of the membranes . Evidently - the thin pit membrane s
respond to changes in'the relative vapor pressure more rapidly than doe s
the relatively heavy rim about the membrane . In the course of desorptio n
the membrane tends to shrink on drying . As the response of the heavy ri m
is considerably slower the membrane is put under tension . This tension i s
relieved by internal shrinkage which results in an increase in the cross
section•of the openings .
all
(O.
Similar determinations of the relationship between the moistur e
content and the square root of the equilibrium pressure drop ratio were mad e
on sections of both seasoned white pine he-tirtwood and initially green heart wood and sapwood of western hemlock cut in the three different structura l
directions using the second apparatus .
The measurements were made with total pressure drops ranging fro m
'5 to 100 cm . of mercury for the different sections . Readings at at leas t
three different pressures were taken with each section . The pressure drop
R1075
Relative Vapor Pressur e
Figure P .-Pffect of changes in the relative va p or Pressure of air p assin g
through transverse sections of the heartwood and the sapwoo d
of west e rn hemlock upon the resulting equilibrium pres s ur e
dro p ratio .
:!,''mr.bers indicate'or d er of measurements .
() Desorption : Okisorption .
I
1
16
18
20
22
Moisture Content (Percent )
Figure 3 .- Pffect of changes in the moistu r e content of transverse section s
of the heartwood and the sapwood of western hemlock canon th_ e
square root of the equilibrium uressure dr o p ratio . Numbers on
curves ref e r to those of figure 2 . 0 Desorution ; (Adsorption .
ratio Pc
was plotted a : ;ainst the total pressure drop Pc plus Pw and the
_eh
_se
value o Pc extrapolated to zero ap plied pressure was used in th e
calculations . This graphically corrects for impact turbulence effects ( g ) .
The pressure drop ratios built up to a maximum and then decreased to a n
e quilibrium value which was used in these calculations . This effect fo r
the vapor flow was considerably less than that reported by Buckman, Schmit z
and . Gortner (2) for liquid flow,as might be expected for electrokineti c
effect would undoubtedly be less for vapor flow than for liquid flow .
If Sutherland, Johnston and Maass' (12) contention that the pi t
membranes stretch under higher pressures, thus increasing the permeability ,
is correct, then the effect should be greater for the passage of air at hig h
relative vapor pressures than for dry air because of the increased elasticit y
of the pit membranes . The slope of the Pc versus Pc plus Pw lines wa s
greater, however, at zero relative vapor Dress-are than at 90 percent relativ e
vapor pressure . This is just the reverse of what it would be if the plasti c
membranes stretched appreciably . The results obtained can, however, b e
explained on the basis of the imp Act turbulence effect increasing at highe r
velocities of flow . This will explain the deviations from the linear
velocity of flow-pressure relationship obtained by these authors as wel l
as the data of this paper .
The results of these measurements with the second apparatus ar e
given in figures Li, 5, and 6 .
In all cases the square root of the pressur e
drop ratio increases in a linear manner with a decrease in the moistur e
content from about 20 percent to oven dry . Further, the ratio of the square
roots of the pressure drop ratios at 0 percent and 20 percent moistur e
content are practically constant for sections of different thickness and '
even for sections cut in the different structural directions, but the value s
seem to vary with the species . The values of this ratio are given i n
table 3 together with the thicknesses of the sections and the standar d
pressure drop ratio for unit effective thickness . The measurements mad e
by the first method are for a varying cross section caused by shrinking an d
swelling of the section . The measurements made by the second method are . .
for a fixed cross section determined by the size of the opening in th e
flange . As the wood shrinks the number of capillaries that are effectiv e
for flow increases . For this reason the ratios of the square roots of th e
pressure drop ratios obtained by the second method are higher than thos e
obtained by the first . The values obtained by the second method wer e
corrected to the basis of the first by dividing by 1 plus the cross- sectional shrinkage from 20 to 0 percent moisture content (see last colum n
of table 3) .
These ratios of the square roots of the equilibrium pressure drop
ratios seem to depend upon the nature of the membranes traversed rather tha n
the arrangement and number traversed in series or parallel . If the pi t
81075 .
-9-
1. 8
1 .6
Figure - .--Ffiect of changes in the moisture content of transverse sections o f
the heartwood of white pine upon the square root of th e
equilibrium pressure drop ratio .
Desor .:tion ; Q Ansor ;tion .
{
Moisture Content (Percent )
Figure 5 .--Effect of changes in the moisture content of tangential and radia l
sections of the heartwood cf e;hite ;.p ine upon the square root o f
the equilibrium pressure drop ratio . LS Desor)tion ;C Adsorption .
oTqug do,ac a .znsss .ld do 4cog aatenb g
Figure 6 .--Effect of changes in the moisture content of transverse, tangential ,
and radial sections of both the heartwood and sap w ood of western
hemlock upon the square root of the equilibrium pressure dro p
ratio . All desorption curves .
Ordinates as given ;
>< lU ordinates ;() 100 '1, ordinates .
Table 3 .----Changes ih permea=4lity of wood with changes in thickness and.
moist - ire content
Species : Kind of
. section
(1)
•
(2)
Ratio of the .
Standard.
:
: Thick- :pressure drop : square roots of :
:Sec- : , ness
ratio for : the pressure :
:tion :
: effective : drop ratios fot :
of
No . : sections : unit thica- : dry wood and :
:+ wood at 20% .
• . ness of '
dry wood_' ' :moisture content :
(6)
: (3)
(4)
(5)
• -___ : __ _-;
Do
Do
Do
Do
1«300 ' : 5 .15 x 10 5 :
: 1 .3WI
:
: 1 .857,
: 2 .8e0
:
: .184:
: .189'
: 5 .25 x 1J
1 .200
: 1 .26 x 10"80 :
-: 1 .18 x 10_ :
: 1 .1'4 x 10 -0 :
1 .25 2
1 .30 2
1 .26 8
1 .17 6
f 1 .193
1.180
.
: 5 .57 x 10 - 13 : ;
: 1 .79 x 10 - 13 :
.1 .215
1 .230
1 .15 3
1 .16 8
.186 . :J) .50 x 10-12 :
.
.196
. 4 .58 x 10-1 3 ;
.169
: 6 .29 x
:
:
:
:
:
1 .20 0
1 .245
.
1 .222
1 .4'2 0
1 . 475
1.47 5
1 .32 2
1 .37 3
1 .373
: 2 .45 x 1o- 12 :
: 1 .56 x 10" 12 :
: 1 .03 x 10"' 12 :
' 1 .400
1 .385
. 1 .368
1 .33 0
1 .31 5
.112• : 1 .10 x 10- 13 :
.140 : 5 .00 x .10-14 :
'1 .365
1 .352
1 .335
2 :
.158
.202
3 :
.255
:
1 :
2' :
?
1,.23 3
1:
:Heart
. tangential : 1 :
1 .17 5
1 .17 5
:Hear
t
c
1
: transverse : 1 : 1 .14& - : 4 .13 x lo - -' :
r,'
: . . .do
x 10`• 9 :
2 : 2 .12-5 ' : •3 .70
do
1.85 x 10"-' :
3 : 2.980
: . .' .do
: . . . do
:Heart
: radial '
do
(7 )
.M_-_ ;
Western :Sad
: 10
hemlock . : transverse :
Do
:Heart
: 10
• 1transverse :
Do
:---- do
: 1
Do
: . . : .do
2
Do
: . . . .do
: 3
Do
:Sap
:
. : tangential : 1
: . . . . do
Do
: 2
Do
:Sap
radial . . . . •: 1
Do
:Hear t
: tangential :
Do
:Hear t
radial
White
pine
Do
'
Do
Do
Column (6 )
corrected.
fo r
externa l
swelling
1 .32 2
was 3 .73 x 10 `9 '
-These measurements were made with the first apparatus ;
and the effective cross section 1 .37 sq . cm ;.
1 .30 0
c
.
4
r
The other measurements were made with the second apparatus ;. - 2 was 5 ..27 x 1 0
lc
and the effective cross section 0 .353 sq . cm .
R1075
-10- .
membranes which are composed of lignin have a similar hygroscopicity t o
that of the wood as a whole, 'which seems to be the case, the volumetri c
shrinkage of the membrane substance from 20 to 0 percent moisture conten t
should be about 20 percent . If it is assumed that the rim of the membran e
changes dimensions by a negligible amount wring the course of the shrinkag e
of the membrane, hypothetical values for the ratio of the square roots o f
the pressure drop ratios for 0 and 20 percent moisture content can b e
calculated for various specific cases . If the shrinking manifests itsel f
entirely as a change in the thickness of the membrane, the ratio would b e
1 .12 . If the shrinkage of the membrane manifests itself entirely b y
increasing the size of the openings in the plane of the membrane, the valu e
of the ratio would depend upon the fractional void cross section of th e
membrane . If this were one-half, the ratio would be 1 .20, if one-quarter ,
the ratio would be 1 .40 . In reality . there is very likely a change in bot h
the thickness of the membrane and in the size of the openings . If one-hal f
of the shrinkage manifests itself in the direction of the thickness of th e
membrane and the other half in the plane of the membrane and the void cros s
section of the membrane is one-quarter, then the ratio of the square root s
of the pressure drop ratios will be 1 .20, This hypothetical value is i n
reasonable agreement with the actual experimental values .
If the capillary structure of wood were quite uniform th e
standard pressure drop ratios per unit of effective thickness should b e
fairly constant for each structural direction . This is only approximatel y
true in the fiber direction and not at all true in the other direction s
(table 3) . All the measurements made on transverse sections were fo r
sections only a few fiber lengths in thickness . The effective thicknes s
of these sections is hence appreciably less than the actual thickness a s
air passing through the sections traverses on the average one-quarter o f
an open fiber length at each end . The number of pit membranes traverse d
in series is hence approximately proportional to the thickness ef th e
section minus one-half of the average fiber length (0 .17 era.) .. Thi s
effective thickness was used in the calculations of the standard pressur e
drop ratio per unit effective thickness for the transverse sections . The
number of membranes traversed in series for the other sections was so grea t
that the difference between actual and effective thickness was negligible .
The standard pressure drop ratios per unit of effective thickness decreas e
somewhat with increasing thickness even for the transverse sections . Thi s
is due to the fact that the probability of maximum-sized openings occurrin g
in series decreases with an increase in the number of membranes traversed i n
series . It can be readily demonstrated that the permeability is greate r
if the maximum-sized openings occur in series rather than when they occu r
in parallel .
The data show an appreciable deviation from the linear moistur e
content-square root of the pressure dr op ratio relationship at moistur e
contents exceeding 20 percent . The square roots of the pressure drop ratio s
arc less than the linear relationship calls for . This is dub to the fac t
that moisture condenses in part of the effective capillaries even belo w
the equilibrium saturation pressure because of their minute size an d
R1075
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eliminates them as a source of flow . The relationship between the
curvature of a drop and its equilibrium vapor pressure is given by Kelvi n1 s
equation
x-- .
2 Cr M pRT In po
p
.,
(5 )
in which r is the radius of the drop or of the capillary in which i t
forms, po^is the saturation vapor pressure at the absolute temperature T2
p is thr vapor pressure over the drop or liquid in the capillary, R i s
the gas constant, 0 -is the surface tension of the liquid, M the molecular
weight, and %o the density, all expressed in centimeter-gram-seconds . The
-relative vapor pressure in equilibrium with the moisture content at whic h
the deviation from the linear relationship begins is practically 0 .9 fo r
all of the curves . This corresponds to a capillary radius of 10 rn7 .. I t
is slitly less than the average effective capillary radius previously
n
determined by other physical methods (a) . At moisture contents i
equilibrium with higher and higher relative vapor pressures more and mor e
of the capillary structure is`obstructed due to condensation of films o f
water that cannot be broken at the pressures under which the measurement s
were made . Measurements were also made of the pressure required to over come the effect of surface tension of water in the saturated section s
using the second apparatus . This proved to be more sensitive to th e
detection of the initial flow of air than the method previously used .
For all the transverse sections, detectable displacement of water by ai r
occurred at lower pressures than previously reported (8) . These pressure s
in the case of the transverse white pine sections were less than the maximu m
operating pressures used in making the measurements on the same sections a t
lower moisture contents (15 to 20 cm . of mercury) . Finite values of th e
square root of the pressure drop ratio were hence obtained at th e
saturation moisture content of 29 percent (fig . 4) . In the case of th e
transverse sections of western hemlock (fig . 6.) the pressures required t o
overcome the effect of surface tension ranged from 0 .5 to 2 kg . per squar e
centimeter . Although these values exceed the pressures used in th e
measurements, the corresponding capillary sizes, 70 to 2 , g00 mp, are s o
large that the vapor pressure depression bY them is less than 0 .1 percent .
The square root of the pressure drop ratio will thus be zero at practicall y
the saturation moisture content (30 .7 percent) . In the case of th e
tangential and radial sections of both species the pressure required t o
overcome the effect of surface tension ranged from 20 to 25 kg. per squar e
centimeter, corresponding to capillary sizes of 75 to 60 mpl and relativ e
vapor pressures of 90 .6 to 9S .2 percent . These correspond to moistur e
contents of 27 .2 percent for the white pine and 2E .9 percent for th e
western hemlock .
R1075
--12 -
r
The distribution of size of the capillaries effective i n
controlling the rate of flow of air can be calculated from the deviation s
from the linear moisture content-square root of the pressure drop rati o
relationship . The rate of change of the pressure drop ratio or the rat e
of change of the velocity of flow with changes in the effective capillar y
radius are plotted in figure 7 for a tangential section of white pine .
The relative humidities in equilibrium with a number of different
arbitrarily chosen moisture contents along the part of the curve whic h
deviates from the linear relationship (fig . 5) were used to calculat e
the capillary radii at which the formation of films across the capillarie s
occurs . The fractional change in the pressure drop ratio divided by th e
corresponding capillary radius change increment was plotted against th e
average capillary radius for that increment . Sufficient experimenta l
values for the pressure drop ratio at different equilibrium relative vapo r
pressures were not obtained to determine the distribution curves with an y
certainty but the example given gives the general nature of the curve .
! The most probable radius is 25 m .t ana the average 27 mil. This latter valu e
is in good agreement with the average values previously obtained b y
combining :electrical conductivity data and pressure permeability data ( ,2) .
This method for obtaining the distribution of size of pore s
should be applicable for all kinds of membranes in which the openings ar e
sufficiently small to appreciably reduce the relative vapor pressure . I n
the case of nonswelling membranes the linear part of the relationshi p
would, of course, be parallel to the abscissa axis .
Summary
Measurements have been made of the equilibrium permeabilitie s
of softwoods to air of different relative vapor pressure . Transvers e
sections less than the average fiber length in thickness, in which th e
open cavities account for practically all of the permeability, show
practically no change in permeability with changes in the equilibriu m
relative vapor pressure, thus indicating that the size of the fibe r
cavities changes but slightly upon shrinking and swelling of the wood .
Sections thicker than the maximum fiber length, the permeabilities of whic h
are dependent upon the size of the pit openings, show an increase i n
permeability with a decrease in equilibrium relative vapor pressure . The
same is true for all tangential and radial sections . When the square roo t
of the permeability is plotted against the moisture content of the wood i n
equilibrium with the various relative vapor pressures of air, practicall y
a linear relationship is obtained from 0 to 20 percent moisture content .
The ratio of the square roots of the pormea bilities for 0 end 20 percent
moistur e content are practically constant for sections of differen t
thickness and sections cut in the different structural directions but diffe r
R1075
-13-
1
A
I
cr.;
0
F-I
r--l
r-i
•rl
(
sr:77ra
MU.
0
0
0
Ca
SnTpV
,--c,
P.
"S''F- A
0
O TC-CCCIO .I(T q.53 0
re-)
ap
(T13) 0TIT03E Lre TTT d O aA T4 00
'T Se2UaI 7qTA JAOTJ ;O 1CqTOOT9A jO
0.
;g @1,1 4
GUrT.,10
04).
Figure 7 .--Distribution of the size of t,- ..e capillaries effective i n
controlling the flow of air in a . tangential sectio n
of white pine (Tl) .
for different species . At higher moisture contents the permeabilitie s
are considerably less than the linear relationship calls for . This is due
to films of water forming across the capillaries . Higher pressures than
those used are recruired to overcome the effect of the surface tension o f
the water in these capillaries . A new means of determining th e
distribution of size of openings in a porous membrane based on these finding s
is given .
r
Literature Cite d
(1) Beiser, W . Kolloid Z . 65 :203 (1933) .
(2)
Buckman S . J ., Schmitz, H . :and Gortner, R . A.
39 :103 (1535) .
J . Phys . Chem.
(3) Duclaux, J .) and Errera, J . Rev . Gen . Colloides 2 :130 (192+) .
(4) Hitchcock, D . I . J. Gen . Physiol . 9 :755 (1926) .
(5) Johnston, H . W., and Maass, O . Can. J . Res . 3 :140 (1930) .
(6) Schwalbe, Co G ., .and Beiser, W . Papierfabr. 50:655 (1933) .
(7)
Stamp; A . J- Colloid Symposium Monograph
( 1 927) ; 6 :83 (1928) 0
4:246 (1926) ; 5 :36 1
(8) Stamm, A. J.- J . Agr . Res . 38 :23 (1929) .
(9) Stamm, A. J . Phys . Chem. 36:312 (1932) .
(10) Stamm, A . J. Ind . Eng . Chem.
(1935) .
(11) Stamm, A. Je, and Loughborough, W . K. J . Phys . Chem. . 39 :133 (1935) .
(12)
Sutherland, J . H ., Johnston, H . W ., and Maass, 0 . Can. J . Res .
10 :36 (1934 ) .
(13) Walker, A . C . J ._ Text . Inst . 24 :T145 (1933) .