Title Studies on the drying of wood

Author(s) MAKU, Takamaro

Citation 木材研究 : 京都大學木材研究所報告 (1954), 13: 81-120

Issue Date 1954-11

URL http://hdl.handle.net/2433/52796

Right

Type Departmental Bulletin Paper

Textversion publisher

Kyoto University

Studies on the drying of wood

By Takamaro. MAKU

Introduction

In drying of wood many equations have been developed on the moisture movement

through wood. Among them, hitherto the diffusion equations 1),~),1l),~7) or the differential

equations .J),I,~),tl;,~?),~4) similar to the heat conduction equation had been used, and recently

yet many other equations 10),2:» are established.

[n the range of high moisture content, the movement of free water is mainly due to

the capillary force, nevertheless the diffusion equation by the moisture gradient or the

differential equation are used. In hygroscopic range besides the above mentioned equations,

VOIGT ~7) explained it by the capillary movement in cell membrane near the fiber satu­

ration point and by the diffusion equation similar to Stefan's law, STAMM 2:» considering

it as a diffusion and an electric stream in wood structure, calculated the drying diffusion

constant and KROLL 10) explained it as a capillary movement in cell membrane near the

fiber saturation point and Knudsen's molecular stream in pit membrane pore in the lower

moisture content.

It may be distinctly' an error to apply the differential equation in high moisture

range, but it comes into problem in hygroscopic range. According to MARTLEY 17),

LUDWIG 11), and EGNER~), the diffusion coefficient varies with the moisture content, so

that the coefficient of differential equation i. e. drying diffusion constant K becomes

the function of the moisture content and the actual calculation by its solution is difficult.

On the other hand, according to BATEMANN 1), SCHLlh'ER to), STAMM 2~), ond KROLL 111) it

may be considered that the drying diffusion constant is independent upon the moist ure

content at least from 30 to 10% moisture content.

Thus, for the application of the differential equation some deny it clearly and some

have the different opinions even in hygroscopic range as well as in high moisture range,

nevertheless the differential equation is often used for the convenience that (1) it repre­

sents directly the moisture content of wood (2) other equations can not be directly conne­

cted with the relative humidity and the velocity of the drying air, but it can be easily

- 81 -~

WOOD RESEARCH NO. 13 (1954)

connected with them (3) at least from 30 to 1096' moisture content, it coincides well with

the drying process (4) it is convenient for the calculation of the drying time.

At the above mentioned standpoint, the present author treated of the differential

equation from the drying process and the moisture gradient, and obtained the influences

of the drying air conditions to the drying coefficient. In drying, the heat-- and moisture­

movement take place together but in the present study only the latter was researched.

1. Differential equation of drying of wood

The general differential equation of the moisture movement through wood is given

as the same as that of the heat conduction, that is, when U is the moisture content based

on dry weight, the amount of moisture d W which diffuses through the area A in time

dfl, is

dTV=~k du -A dfj··· .. ···.·················· .. · .. ·························(1)dx

where k is the diffusion coefficient (g/cm h) and x the direction of moisture flow. Using

equation VII = Vo (1 +0.84 r aU) (VIt , Vo is a wet and dry volume, r o is the specific gra­

vity) the differential equation is written in the form

where K (==.kjr o) is the drying diffusion constant (cm~/h) and subscript r, t, I, and u

and 0 repre3ent the radial, tangential, longitudinal direction and moisture content u, and

0, respectively; u in (1 +O.84roU) is 0-0. 3 in hygroscopic range and O. 3 in higher mois-

ture range.

Obviously from equation (2), drying diffusion constant K is the function of the mois­

ture content for a given wood species but its value is approximately equal to 1 in ordinary

wood specie as shown in Fig. 1. Hereafter the present author makes in· unidirection the

investigation whether K is constant or not.

- 82

T. MAR U : Studies on the drying of wood

7.Jr------r-----r----.-------.

0.'1

1~_---4 ro=rJ0.80.70.60.50.40.302

0.2 0.3content u

0.7

Moisture

~ /.2~

::::t-O:><:::)-+- 1.7......

1'°0

Fig. 1 Values of 0+0.84 rou)

11. Differential equation under steady drying conditions

When we assume that the amount of moisture evaporated from the wood surface to

the drying air through the fluid film is proportional to the difference between the mois­

ture content at the wood surface and the equilibrium moisture content of the drying air,

at the boundary x= - a (ref. Fig. 2),

-a.)

I

II

--oI-I

/Fig. 2

d W= - k au A dOaxd W = - a (u., - ueq ) A

(from the wood surface)ldO (through the fluid film)~ (3)

so that

where a is the coefficient of surface evaporation (g/crn2h) and h = alk.

When the initial moisture gradient in wood is j~ x), then

--- 83 -~.

WOOD RESEARCH NO. 13 (1954)

a2UK--o - .••.••.•••••••••••••••••••••••••••.•••••••••.••.••••••••.••• (4)ax-o : u = f( x) (5)

____ au.+a : a£- +-h (u.,-- up',) = 0 · · · (6)

au0: ax = 0 (7)

If we write v = u - Ue'l' equation (4)-(7) are transformed into

}~ = K _Q.~~-- '" '" '" (4)'ao ax· .0=0 :. v=f(X)-ue'l=F(x) · .. · · .. · .. · .. · (5)'

x = +- a : lv..... ~ hv = 0 (6)'axx = 0 : .av = 0 (7) fax

the particular solution, thus

v- K (~ytJ

~-X-_~)-I.----e a.a _J 01/ +sin On cos 01/

(" x.I,a)1/

X cos---­a

F( }.) cos _.2~I_}. d J. (8)a

where On is nth real root of cot u = u / ha.

111. Case where the initial moisture distribution U o is uniform

Let F(}.)=Uo-Ue'l= Va, from solution (8) we have

K( On ytJ" . "_v_ = 2Xe - a cos~x _" __,~~!1_o~ (9)Va - a On+sm On cos On

for average moisture content v"" at time fI,

The water evaporated

- 84-

T. MAKU : Studies on the drying of wood

where Gill) is the oven dry weight of wood,

then

Fig. :3 shows the dimensionless diagram of equa60n (10).

J.O~~~~~0.90.80.70. 6 11---__ ~~-"""otod--=-t,,"=-~~~-.d:--r--+--~---l

0.5 r-'-r---"'~~;:t-~~--+=::'!!Iooo""..d--_.L_----+~-......l-=---1

~~0.4

o03 r---r----+--t--3~~~;::--_+-~~-I__-+_~!IIj

0. 2 t--+---+--f--~-+-~!'ooP~-~--+---4--=::!Io,,""'"

O. 7':-~~~~_...L.:-_....Io-_....J-_..J-_-L-_--J.~~~---Jo 0.7 02 0.3 0.4 05 0.6 0. 7 0.8 0.9 10k:z

Fig. 3 Dimensionless diagram of eq. (10)

For the drying period Hell which required till the wood equilibrate with the drying air,

we can take

then

- K('~I/-')~tJC . ([. '. 0.01

4.6a~T7" •nO'

............................................................... (13)

112. Case where the initial moisture distribution 1S given

as parabola ( x ~

f( x) = Uil/. - ( U III• - U.~) 0 __'-)'. a .

Let" 'x ~]«x)= V

,II-( V

II1,- V,)(·· -) (14)

a

then, from equation (8)

- K( ?1i..)"~t1 "V = 2.!.::e \ IJ cos Vii

a

...- 85 -

and

.WOOD RESEARCH NO. 13 (1954)

( °Il .)~. - K -- /Ivo1,=2.2..:e \ a ,.

sino ll. ---~---_._--~--_._~------- ..-

()n(()i/-f-sinoi/ coso lI )

where V, = U,·~ up,(/, VIII = U/II- U Pr/; the former is the moisture content at the wood surface

and the latter is one in the mid--plane.

If the initial moisture distribution satisfie; the boundary condition (6)', then

therefore

from parabola

therefore V,

from (6)'

from (14)

2Vm

-2-f-na2 V m + V,

.3

3(2+ha)2('f-j.:)zG) V o /)······································· ( 17)

Using these, equation (16) is transformed into

.' Dn . ~v-KI-'-:"")/I

- I'" = 2)~e \ a .'Vl I '"

sin 011rJlIUJII +sllld',; -cos li ll )

3'3't: Ill1--

and the moisture evaporated

sin_(~I/_!·-l· (18)()} I)

then

'-." } (cos () IIX smoll~ 1ft \-~,,--'---

~ 0 II

sinlJ ll ),

O}J~ )......... (19)

dWerfj

" J j cos OnX sIn/h. -- 1a '1.

011

86 -

sin li l,.

51 ~vn.................. (20)

T. MAKU Studies on the drying of wood

Fig. 4 shows the dimensionless diagram of equation (18)

1.0~~~~0.9QaO'7I---~~

0.6 t---+--.--'"~~..=---t="''''''''=::_+"'----+-="''''''-llol::::"--+_-+_-~

0.5 t--t----.;r-~~~I-c----1~~k:-_l~_4---=~-..........d

1Ja;v o./f/i7av

0.3 t---t--t--t--+---=~~~----=:~---+--+-~

0. 70 0.7' 02 0.3 0.4 o.S 06 0.7 0.8

f(~2

Fig. 4 Dimensionless diagram of eq. (18)

12. Differential eauation under unsteady drying conditions

\·\Then the drying air conditions vary with time, we may use UI!'1 = <p(O), but in this

case drying diffusion constant K may be not always constant for the change of the

drying conditions or the m::>isture content. Few experimental results have been reported

about the relation between K and the drying conditions. KAMEl (1937), BATEMAN

(1939), and STAMM (1946) repJrtej the agree1.ble conclusions that K varies with the

temperature, hJwever, there h1.ve heen an heterodoxy about the relation of K to the

relative humidity of the drying air and the moisture content of wood. According to the

present author, K varies with the change of the temperature and the relative humidity,

but in the lower temperature or the higher humidity the variation is very small and for

the change of the moisture content of wood, also, K can be regarded as a constant in

practice, and changes of K by some degree give not so large influence on moisture

content therefore under the confined unsteady drying conditing assuming K as constant

OU Flu60" = K ax ·,>··································,····························· (4)

(I = 0 : U = I( x) (5)

.,' au JIx = -t- ([ : -ax' ~+ h tU _. v:{ {) ) ( = 0 (21 )

the particular solution thus

-- 87 ._-

WOOD RESEARCH NO. 13 (1954)- --

- () '~

1 - K(------.!':...) 0 anU =----;x'e a cos---a ~J a

OnX ~------'------

oJ/,+sin On cos On

r- • . 0 e K ( OJ/, )~Xi \(/ !(A)COS§r~AdA+2a-~I~afLK (-~!~r \' e -0- ~ (!)(~)d~; .. ", .... (22)

:.... '-II a On \ a,' .0 '-,

121. Case where the initial moisture distribution is uniform

Let !(x)=Uo

\

'(J e K (,~al1,-- \) ~~p ( ~ ) d~ .""",.,.,." (24 )

" ~

122. Case where the initial moisture distribution is parabolic

Let I(x) = U'I/,- (U"'-- U g ) ( :-)~

1-t =2'>":c - K(-~-)-e cos-~!~- x------c--------!-~---------a on+sin an cos lin

("U '., 2( U U ) { cos aIIX! ,; SIno II-", - .~ , ---'i---~ Un

sin On ) -,iJ 11

2 r_;

('IU '" 2(U [/ ) ( cos 01/X ,I g SlnO/I - 1/1- g_ 'j--i---~ \ Un

sin On)­~ ljn~~}·-~

" 0 U K(' ()n 'J' \! 0 '. ·u , '- -- s '-I--sinon K( n~) \ea. 9(~)d~)......... (26)

, a, "II

~. Experin1ental discussion

21. Experimental methodJ~)

- 88 --

T. 1\lAKU : Studies on the drying of vv'Ood

The schema of the experimental apparatus is Sh0W11 in Fig. 5, the dryer body was

made of galvanized steel plate and was covered with insulating material of 5 cm thick.

BaLance

Dry bulb temperature controller (1)

JW'-et bulb temperatu.re. controllerl2J

I Bc:J...ffle net·

Heater (Connected.. to (/»)

Supplementa.ry heatet·~_-;- ..-_--TtI--""'---1t"-jHtr--.J~ehr_·-- Fa.n

J1Iet and dry bulbhYfJrometer

Healer (co nneeted to ('2))

Fig. 5 Experimental apparatus

Heating system. The air was warmed by two unit of Nichrome wire, the one was

used to warm the dryer quickly and to maintain a temperature slightly below the desired

operating tempe;-ature and the other was connected to an automatic dry bulb temperature

controller.

Humidifying stystem. Damper placed in the exhaust pipe and the heater placed in

hot water bath were used, the heater was connected to an automatic wet bulb temperature

controller and used to maintain the desired relative humidity.

Drying air velocity. The air circulation was regulated by the rotating speed of fan

to maintain the desired air velocity and was evenly distributed by the baffle net installed

ahead of the test section.

The weight of test pieces were directly measured by the balance placed on the dryer

body.

Test pieces used in this study were cut from the same stock as lOx 20 cm~ area and

0.2, 0.5, 1. 0, and 3.0 cm thickness for the transverse direction (edge grain or flat grain

pieces) and 10x20 cm~ area and 1.3, 2.2, 3.0 and 5.0 em thickness for the longitudinal

direction (end grain pieces) and 15x15 cm~ or 20x20 cm~ area for drying of veneer or

plywood. .Previous to the test, the side surfaces of pieces were covered with synthetic

resin for damppro6f and one part was soaked. in \-vater with the vacuum and pressure

treatment and the other saturated in water vapour until they attained the fiber saturation

... - 89 .--.

WOOD RESEARCH NO. 13 (195f1)

point. The latter particularly, had been kept to the operating temperature preVIOUS to

the test in order to avoid the error caused by the temperature difference between wood

and the drying air at the beginning of the experiment.

The test pieces for moisture determinations were timely taken out from the apparatus

and the small piece (about 3 X 4 cm) was taken from each cel1tre and cut into several thin

Side coati77{j (synthetic resin)

,

r3cm lr~\.J

.",

Fig. 6 Test piece for moisture determination

layer for the moisture gradient (Fig. 6), on the same time, for the purpose of check, the

distribution was measured by the electric moisture"meter. In case of need, the tempera­

ture gradient was measured by the thermocouple.

22. Drying of timber12)

221. Drying in the range of high moisture content

The test pieces of ThujojJsis (RlBA) whose initial moisture distribution was approxi­

mately uniform, were dried under the steady air condition of 55'C, 40% and 0.4-0.5 m/s.

The relation between the drying rate and the moisture content were the most typical

as shown in Fig. 7. Obviously, in the timber of 0.2 and 0.5 cm thick, the three stages

of drying, that is, the constant rate zone, the first and second zone of falling rate

appeared, but with increase of thickness the former two disappeared gradually and in the

timber of 3 em thick only the second zone took place from the beginning of the drying.

This phenomenon, as HA WLEY 'j) had jx)inted out,', Shows the fact· that the movement of

free water is active only in the confined distance and is explained by the temperature

····90

T. MAKlJ : Studies on the drying of wood

16074060 80 700 720

Moisture content ZL

o

0. 03 1---+---'-''1-- -,JF--+-- "-----4---+-----+tP'----+-----I

Ii~.02!:--+----+----1

Thud·OpSiS (H IBA )

5SoC, 40 %-' o.4~ 0.5 ny,'s0.04 +----.,.----.,.----...,...---460-1-----,...+""=:.-..::..--+--+--+----1

\UN~:..:.. 0.02 I----~J

~

~~ 0.07

Fig. 7 Drying rate of l'hujopsis (HJBA)

0.03

0.04

IU~

~

a02 ~"

(\~

0.07

140720LfO 60 80 100DrY/179 period B

20

I I ".--....~..'".-( -O-G- .or ...........1

I v~~ ~ .'I ~c;o t:'

.. Temperaf,vI':, -..-....0........

r •1~ 0

\o~

"t)

~~I~I10o

Fig. 8 Drying and temperature behavior of 7'hujojJsis (HIBA. 0,2 cm thick)

drying rate diagram in Fig. 8 and 9, that is, in the timber of 0.2 cm thick, as

KEYLWEKTH Ii) reported on drying of veneer, the temperature of wood during the con­

stant drying rate keeps the wet bulb temperature of the drying air and the constant

surface evap::>ratio:l takes place during this period. In the timber of 3 cm thick, however,

this correlation between the drying rate and the temperature of wood disappears. This

shows that the movement of free watel" from the interior to the surface is not so easy as

in veneer, and the temperature rising process indkated by KEYLWERTH for timber may

WOOD RESEARCH NO. 13 (1954)

o.03<:\)i-.:l

~

a02.~~

R)

0.01

0.04

80 0/j706030 40 50

Dryi71fJ rate ()2070

I I I

~~_L-I Te~erature (o.3cm ill1J,r ~om.surf.;.._.......;...e- - -A ~.:::!::::4'=:"'O- . '( -ynid ri/er17P 1

- -""--

r

~\~

Q

~(:-.nru-O-f"oooo£Z~~ral'"e

'1 0-1-0-0 1--0

700

-tl 50Cl

~'t- 40

Fig. 9 Drying and temperature behavior of l'huiopsis H1BA. 3.0 em thick)

60,..---r----.,,.---,·C

&=241472

50 J37.6

~1.0

.J~IfO LfO min

~~ 20

30

10

20 L.-_-L..--L.---'7.5cm 0

Thickness a

Fig. 10 Temperature gradient in Thu;opsis (HIBA, 3.0 em thick)

not ocCur. The temperature gradient of Thujopsis (HII:>A) of 3 cm thick is shown in

Fig. 10.

As obvious from the above mentioned result, the mechanism of the drying varies with

thickness of wood, and so we can not apply the differential equation in all range from

the high moisture content to hygroscopic range and moreover to make it applicable, the

plots of vav / V" us. Kfi /a 2 i. e. tJ/a 2 rnust be all straight lines on a semi log scale as

shown in Fig. ;\. In Fig. 1J vo ,'/ V, is plotted a.gainst fI/a 2 for Cryptoyneria (SUGI) and

T. MAKU Studies on the drying of wood

7()60502010

I~~ =t =t ---ri:iIQt1..-.:-..: ....... (f

\. ~v rio.. -( : , .. ;'" (<::1" )

f-" "-~~\. ., '" x ~)\. ~'x~

'~ ,,~, ' ~'x 1'('1'-"~\ x ....

""""x ...... ""IIi

'" ~

'- '- x .... "', "\. '" "-X T. '."3011 thick X ...... "( C. 7C)7)-, "- th/ck

XX C. 3cm t ick I'.

T. 7fJ17 thick

07Qa3

Q06

005ao/;.0.03

002(;

70

OB060504-

0.3

'Va~ 0.2/10

Fig. 11 vu/)/Vo-tJ/a~ diagram

Thujopsis (HIBA) of 1 and 3 cm thick, respectively. The results have not so a good

agreement with the differential equation as that of SHEKvVOOD and KAMEl, and it seems

that the differential equation is not applicable in general, to say nothing of high moisture

range, even in the case where the second -zone of falling rate appears from the beginning

of the drying.

222. Drying in hygroscopic range

222,1 In the transverse direction

222,11 Determinations of the drying diffusion constant K

In the case where drying begins from the fiber saturation point, there is the great

possibility to apply the differential equation. The present author used the rectangular

slab of Chamaecyparis (SAWARA, r o=O.4 and HINOKI, r o= 0.41), Fraxinus (TAMO, r o=

0.56), and Prunus (SAWARA, r o =O.63) in this study. As shown in Fig. 12, the relation

between v((v/ Vo and f)/a~ agrees well with the differential equation diagram in the range

from the fiber saturation point to 109-6 moisture content, but below 10% moisture content,

as KROLL 10) stated, the molecular stream may take place instead of the diffusion and no

differential equation can be applicable.

As the value of h i. e. ha has never been determined hitherto, the value lIf K can

not he direct.1 y obtained here. The presen t aliI hor has determined Ittl and K by the

- 93-

WOOD RESEARCH NO. 13 (1954)

\...~~~

'YO'L..........

~~-~~~

~CI'I:..O_I'o...X_~~Oy~ X -----.. -;:::-~O7.y

.................. I •-y................. x 4

"_3........ 27. Chamaecyparis (SAWARA)

2. // ( H/NOffl)

3. Fraxinu5 ( TANG)

/f Prunus (SAKURA)

7.00.90.8070.6

7Ja 0.5

~ 0.4

0.3

0.2

0.7o 5 20 25 30

Fig. 12 va ,,/Vo--o/a2 diagram in hygroscopic range

following manner.

As shown in Table 1, K and K o for various ha were calculatej from the drying data

and as the most probable value of ha, the one for which the coefficient of variation of

K o was minimum was determined (ref. Table 2). On the other hand the moisture distri­

bution was measurej and the results were shown as an approximate curve in Fig. 13,

from which the moisture content at the wood surface and the mid-.plane can be calculated.

Table 1 Fmxinus (TAMO) 3 cm thickness

. Imoisturel I "!I IUJ ~ .~ 11· ha 0 20

time e'lcontent IllJa/l/Vo: o/a- /1

\ _ .... - - - -11----------1----, Urw I I:K"ia'! K I K"*!K",.K,,I\(KW,-K,j)2\\KH/a"1 K II Ko K'u·-KJ

O! 31. 9 II r i /~ 10-411 I

0.3i 30.0 0.925, 0.2221i 0.004\0.018 10.0158 0.00591 0.34811 0.004:0.018 0 0158 0.0092

2.01 27.9 0.8141 0.88811 0.0201°.0224[°.0198 0.0019\ 0. 0361 1 0.02°;0.02241°: 0198 0.0052

4.01 26. ° 0.770 1.7761

1 0.043\°.0242\°.02161 0.0001\ 0.0001, 0.0461

°.02591

°.0232 0.0018

7.01 23.9\ 0.687 3,12 II 0.0721°.023°\°.0208\ 0.0009, 0.0081\ 0.092[0.02950.0266 0.0016

10.01 22. 01 0.6131 4.45 I.i 0. 116iO. 0260[0. 02361 0.00191 0.03611111 0.143:,0.03210.0292 0,0042I I II iii

16.0: 19.8 0. 5271 7. 11 Ii 0. 173iO' 02431°' 0222 0.00051 0. 002511 0. 211iO. 02961

°. 0270 0. 002

20. 01 18. ° 0.45618. 90 II O. 233[0. 02521°. 0242 0. 0025 O. 062511 O. 27510.03091°. 0284 0. 0034

26.0! 16.5 0.398111.57 II 0.291\0.0252:0.0234, 0.0017 0.028911 0.346:0.030°1

°.0279 0.0029

......_::i_.:::L::::t:::.:__ il··:·_~~I:·;::i~:~:_:·:~~I** ~ ::::11

1 :.::~:: ::;~::. ::::1 ; ::::_Kau =O.0217 C. V. =0.107 II Kav=0.0250 C. V. =0. 161

1I

T. MAK Ii : Studies 1m the dryi J1l.( of wood

I1m = 10 I lin = 51

rK,,:=-;'" KeIn'I~-~F=- K,!~,"= ~"),:I :/:r;;--K, .K", K,:rKffl- K)! ~'Inr K;<10- 1 ,<H) - ': 1 ,; '/10- 1:' IIi" : I" I

0.846 ;: O. 008!0. 0360. 0316! 0.0002, 0.oo04 ii 0.019 O. 08!'i!'i0. 075o! 0.023fji, !'i. 57 0.03900.176

I',I Ii ':

0.270 0.029 0.0326,0. 0288: O. 003 0.00361 1 0.059 0.06650. 059a! 0.0076! 0.578 ;0.114 10. 128

I'I' I[ ":I I" I '

0.0324: 0.064 0.036 iO. 0322: 0.0004 0.001611 0.11:'5 0.06480. 0579[ 0.0065! 0.422 :0.194 0.109

1 ' II I I

0.0256i: 0.118:0. 0378!0. 03401 O. 0022 0.0484:1 0.190 O. OGlO:O. 05501 0.0036i 0.130 !0. 293 0.0940iii II ,I I

0.176, 0.1741°.03921°.03561 0. 0038, 0.14411 0.259 O. 0584io. 05301 0.00161 0.025610.388 0.087l

0.04 '; O. 251p. 0352:0. 03221 O. 0004 0.0016,1 0.356 0.050010. 0457! 0.00571 0. :~25 i,O.520 10.07:-n

0.116 ': 0.31+.0358:°.03301 0.0012 0.0144'11

, 0.444 O. 05000. 046]! 0.0053[ 0.281 :10.644 10.0724

0.08411: o. 38710. 033510. 03111 0.0007 0.00491 0.5331

0.04600.0427: 0.0087! 0.757 10.760 10.0659I : II I II 'I I I I

0.0196' 0.47] 10. 0320 o. 02991 0.001 9 0.03611 0.644 0.043810.0402, 0.01121 1. 2f5 i0.910 10.0620

I 'I II I 1 'O. 0036'1 o. 5981

1

°. 031310. 0296 O. 0022 0.0484 0.794 0.0415 0.0391 0.0123[ 1. 51 1. 11 0.0f580I ~ I I 1, '-------------------11--------------------'1------ ---

K w =0.0318 C. V. =0. 0548 ,i K av =0.05H C. V. =0.265 "I

i ~ i,

lin =- 2 110 - ] , Ii(l -- O. 5

I: - , -' -- ~K o Kw-Ko!IKol1-Kr»)li Kfi!a~! K : K" IK",,--K8!IK/I,-Ko)~ Kfi/n~! K I K0iK,n,--Ko:(Kw-K0J~

, 'I'! i ii .'lC-41 iii i :<10-4 I I I :<10- 1

I Ii I I II , 1 i I I0.154 0.07061 4.98 ,i O. 085

jO. 384 !0.337 O. 1391 193 I 0.2151 0.96810.8481 0.549' 301

i 'I' ii' 1 '0.113 i 0.0296! 8.76 !i, 0.21°1°.237 '0.209 I, 0.011 I, 1. 21 0.4251 0.479,0.4231 0.124 154

I ii' I I! i i0.0976! 0.014 i 1. 96 'I 0.33010.186 iO.165 I 0.033 10.9 0.6381 0.3600.321] 0.022 4.84

i Ii I I· I I I0.0844 0.0008! O. 0064!1 0.4851°.155 10. B9 I 0.059 34.8 I 0.920 0.295 0.2651 0.034 11.6

i ,: I I .

0.0788: 0.00481 0.23]1 0.6311

°.142 !0.129 1 0.069 34.8 1. 1751

1

0.26410.2:39: 0.06 36

. I 'Iii0.0667] 0.016g, 2.86 0.84210.118 ,0.108 0.09 81 1. 554 0.21810.1991 0.100 100, ,I I I

0.0668] 0.01681 2.82 i: 1. 04 10.117 io.l08 0.09 81 1. 875' 0.210,0. 193! 0.106: 112

0.0612\ 0.02241 5.02 !I:. 1. 32610.115 1..0' 107 0.091, 82.8 2.200 0.190110. 176i 0.123 151, . I: I I '

0.0580! 0.0256 1 6.55; 1. 4tOIO. 0994,0. 0928

10.10521 11] 2.600, o. 17T' 165: 0.134 ]80

0.0547' 0.02891 8.35 i 1. 775!0. 0930!0. 08781 0.12 i 144 3.24°1 o. 170e. 160; 0.139 19:3~--~--'------- r~---- .1 1 1

1

J - _

K.w=0.0836 C. V. =0.351 Ii K,1,=0.198 C. V. =0.463 I K",,=0.299 C. V. =0. 501Ii I

" K=Ko(1+0. 84rou)

** coefficient of variation of K"

- ~5 --

WOOD HESI<:AI~CII NO. 1:-3 (1954)

Table 2 The values of lia detenninated from drying process and themoisture gradient (Transverse direction)

Wood

species at C. V.

lia

.. *lTIIl11mUn1

Cha1llaeLYparis(SAWARA)

10 2.3 O. 02 0.045 0.033 3.5

//

(HrNOIJ

J"faxinus(TAMO)

Prunus(SAKURA)

10

10

6

12

11

0.034

0.032

0.020

* C. V. : coefficient of variation of K j

Now, take the first term of equation (19) for approximate using, V s and V,ti, is given

as

sin () 1 cos 0:/i 1 ·T~srn-~ 1.. co'si)'.1

( ;), ')~v 11"-_=2e- K -t- IiVo

sin 01()1 +sin 01 cos 01

therefore =cos o~··· ' , , . (27)

o

PnmU5 (SAKURAl

5.'----L._-'-_........._.&----J

?..fem 0Thiclfne::,s a

oThickness a

f--1--4-,'A-+--+--+----i '" 751-_+--b~+_-:±-t'-1L:,;

+.:></)

j~70 1-:-.-:'-.b\o:';-t=~p-f'---+--;

-+->~«'

1---'++--+----:lA---+---lF:~I--+--+-+--+---lou

fraxinus (TAMO)3'r'--:--=;,:,~-r--.-",,-----,

%

Thick-ne5S a

5'-----'---"---'----'--.... 5 '---~_ _1__.L_.--L_ _'

J.Scm 0 /.5Cm

Chemaecyparis (HINOI<I)JO

5/..fcm 0

Thickness a

ChamEJecyparis(54WARA)

30

Fig. 13 Gradient of moisture content in transverse direction(Drying conditions: 55°, 40(j;;, OA--O.5m/s)

-- 96 -_.

T.M A" l r : Studies on the drying of wuod

Using V.~ and VII/. in Fig. 13, cos (j, i. e. ha were determined by equation (27). The values

of ha thus obtained, as shown in Table 2, have a good agreement with previous one

excepting Chamaecyparis (SAWARA), and may seem to vary with wood species as will

be observej later in the longitudinal direction but the details could not be clarified in

here.

Now, using k

D S-~- udxr Df} .

- 0- ---- ---- b-100 du yax

Egner's method the values of K E were obtained

graphycaliy from the moisture gradient as follows (ref. Fig. 14)

• 0 •0 )(

0

0 • •X )( X •X 0

CfLa.maecyparis (HINOKI)

2010 1,)

Moi sture content-u

Prunus (SAKURA)

•• o 00• • 'j{){

'--- •~

)If;) ~:t::. A 6. D

.~t-­

% 30 CJ75 20 25Moisture content u

/0

~ 0.04§ em}'~ /,{

"3 0.03s::::C)

'(j)::s~ 002~.

~

~ O,!Jl S

Fig. 14 Relation between the drying diffusion constant K c'llculatedby Egner's k and the moisture content

for ChamaecyParis (SAWARA) K h.'=0.034 cm~/h

// .0' (HINOKI) // 0.027

// Fraxinus (TANIO) // 0.032

.(/ Prunus (SAKURA) .0' 0.0197

Somewhat smaller as K 8 is for Chamaecyparis (HINOKI), K E have a good agreement

with K o for Fraxinus (TAMO) and Prunus (SAKURA) and with the mean value of K o

at ha = 2.3 and 10 for Chamaecyparis (SAWARA) (ref. Table 2), therefore, according

to these results the drying diffusion constant is regarded as a constant independently of

the moisture content. The dotted line in Fig. 13 is the one calculated by K = 0.034, 0.032,

and 0.020 for Chamaecyparis (H!NOKI), Fraxinus, and Prunus respectively.

222,12 Determinations of the coefficient of the surface evaporation a

From equation (3) the coefficient of surface evaporation is given as

dW(1.= -----.-----

af/ A V"

- Y7 --

WOOD RESEARCH NO. 13 (1954)

Then, by the diagram of dimensionless equatjon (12) fJ. can be obtained as in Table 3, as

Table 3 Transverse coefficient of surface evaporation IX

(Praxinus, 3 cm thick, Ko=0.0318, V o=0.256, Gau =298)

H fI/a~ KH/a~ 12; of eq. (2)1dlV A dW--tlH- aH/f OX II:

_____ .._..._..f ...._

0.00'106!I

0.5 0.222 0.0504- 3.84- 401 0.00957 I 0.119 0.0804I

I

II1 0.444 0.0141 i 0.0456 3.48 399 0.00872 0.0969 0.0900

I i

ii

2 0.888 0.0282I

0.0388 2.96 ~i98 0.00744 i 0.0730 0.102

I

Ii

;) 2.22 0.0706 0.0280 2.14 394 0.00543 I 0.0496 O. 109III

I!10 4.44 0.141 0.0204 1. 56 ~i89 0.00401 i 0.0366 0.110i

20 8.88 0.282 0.0153 1. 17 385 0.00304 I 0.0253 O. 120

i30 13.32 0.424 0.0106 0.809 382 0.00212 0.0188 0.113

40 17.79 0.566 0.0080 0.610 379 0.00161 I 0.0141 0.114I

fJ. (Ill = 0.105

obvious from this table the values of fJ. are nearly constant independently of the moisture

content excepting the short period at the beginning of drying. Calculating ha from fl.<I"

ha = fl.",a/k = f/..f/"a/Kr o = 0.105.1.5/0.0318 . 0.56 ~-=;: 9, this value of ha is nearly agreeable

with previously determined ha (= 10).

From the results of 222, 11, 222, 12, the drying process in hygroscopic range coincides

weB with the differential equation from· the view of the drying rate and the moisture

gradient occure:l in practice. Conseque~Ttly, even in hygroscopic range the surface moisture

content does not reach the equilibrium moisture content U pq given by the drying air and

the moisture movement is occured by the correlation between the surface evaporation based

on this moisture difference and the internal diffusion. So that the drying diffusion constant

K is to say nothing of the temperature, directly influenced by the relative humidity and

the velocity of the drying air.

Many results hitherto gave[).~= 0 i. e. U x = U u / in hygroscopic range, in these cases,

the thinner the timber is, the steeper the moisture gradient becomes for the same U m and

this is inconsistent with the fact that the thinner the timber is the easier the drying

becomes, on the contrary definite value of ha gives above fact the appropriateness. Using

K=0.034, 0.032, and 0.020 for Chamaecyparis (HINOKI), Fraxinus (TAMO), and Prunus

(SAK liRA) respectively, the calculate::! moisture amount based on equation (11) and the

measured values are shown in Fig. 15.

--- 98 -

T. MAKU : Studies on the drying of wood

70 ~----r---~---r----,-----.-----,;j

60 ~----+----+--­$

"'tj 50 I-----+-----+-~(\J~

fQ8 /,I 0 1------.+-------::;."Jy.::-.-----1f------::::.,--=----T----1Ct"§:\V J0 1-------,,:.,;.::----

~,J 20 I----..~-\1)

(j< !()

Of~,)---~---.L-----::f-----;/,"'=----~t:::O';:;------;-'601)L' 70 20 30 ~O JI n

Dryirlc;} peyiod 8

Fig, 15 Evaporatacl moisture in drying

222.13 Relation of K and (J. to the thickness of timber

The similar experiments were done on Thujopsis (HIKA) and Cryptomeria (Sucr)

of 3, 1, 0.5, and 0.2 cm thick from the high moisture content. As the differential equation

is applicable after the moisture content of midplane reached the fiber saturation point,

determining the time by means of V"n for [JII/, = 0.3 and putting ha = 6 for 3 cm thick

timber (ref. Table 2), consequently ha = 2, 1, and 0.4 for 1, 0.5, and 0.2 em thick respe-

ctively, the values of K were obtained as shown in Fig. 16. Obviously in timber

4em

37 2Thickness 2a

Cryptomeriq ( SUG-/ ) ° 40 'J:555; 0%,0.45 s

I Ix

,,...-Xj,,)("')(

--

Fig. 16 Relation of transverse drying diffusionconstant to the thickness of wood

of belm,v 1 em thick for which 3 stages of the drying rate appeared the value of K

decreases a little with decreasing of thickness. The same inclination is recognized in plate

of below 4 cm thick in the longitudinal direction, too (ref. Fig. 24). In both cases this

relation between ha and K is shown as Fig. 17 in general. If the drying is controlled by

-- 99 -'--

\\loon HESEARCH NO. \:3 (1%'11

~

1--:)/::::.

~V)I

/::::

8~

.~V)

~--ti'*'.j;;;: I

~ !}a~h) I

Fig. 17

Fig. 18

the differential equation the values of K must be independently of thickness, that is,

smaller value a' must be used instead of a. Now, in the porous material as wood, the

effective surface ae must be somewhat inner than a (ref. Fig. 18). As there are hardly

reported on the relation between ae and a', it may be concluded at least that ae is

connected with dimension of cell. The thickness of aa' obtained from the experiment are

about 0.3 - 0.8 mm in radial direction and 2 - 3.5 mm in fiber diretion (the former is as

10 - 25 times as diameter of tracheid and the latter nearly equal to the length of tracheid).

From this result, the present author assumes the surface phenomenon similar to the fluid

film which may occur in the surface of wood with above order of dimension. The ex­

istence of this anomalous thin layer is confirmed a certain extent by the fact that when

the wet timber which seems to be pretty dried at the first glance is planed the new wet

surface appears again and the fact that when the well dried timber absorbs moisture, after

reaching nearly the equilibrium moisture content it shows the remarkable absorption again

when it is planed, namely, hygroscopically anomalous thin layer exists at the surface of

wood. It is easily imagined that the effect of this layer on K disappears gradually with

increase of wood thickness. As to this phenomenon, however, the author can not conclude

without more detailed experiments and this may be one of the most interested problems on

drying of wood in future.

Now, in wood of below 1 cm thick the apparent value of K varies with the thickness

and decreases with the ratio of about 16.79£ / cm to the value of K of 1 cm thick timber

-100-

T. MAK U Studies on the drying of wood

and as obvious from Fig. 19 and 24, this ratio is the same as in the coefficient of surface

0

./"~

7 2ThicKness 2a

3 4em

Fig. 19 Helation of transverse coefficient ofsurf8ce evaporation to the thickness of wood

evaporation and in the longitudinal direction below 4 cm thickness. Therefore at 55°C,

40Q({ relative humidity and 0.4 - 0.5 m/s

K~ = K, {1+0.167(2a~-1)} (28)

where K: is the drying diffusion constant of 1 cm thick timber. The thicker the timber

is, the more negligible the effect of anomalous thin layer on K becomes and K shows almost

constant value for the timber of over 1 cm thick.

For the coefficient of the surface evaporation (J. also, as obvious from 222,12, the same

relation is given

(J.~ = (J.: {1 + 0.167(2a~ -I)} (29)

where (I..J is the value of 1 cm thick timber.

As for the relation between the drying time and the thickness under the same drying

condition there have been H~ = (~~r, TUOMALA and EGNER 7) gave 11. = 1.7 and MOLL7/ 1 ' a: /

and KOLLMANN 11. = 1.5.

As obvious from equation (10), (16) and etc. (use the first term approximately),

for different thickness 2 a , and 2 a~

........... , .. , ·(JO)

--- 101 --,-

WOOD HESEARCU NO. 13 Cl9fi,j i

therefore, n = 2 can exist only in the case where 011 = 01:~, that is, 2 al and 2 a~ are quite

large, and in the practical range of thickness n is somewhat smaller than 2 and below

1 cm n becomes more and more smaller by the decreasing of K. Fig. 20 shows the

AV~

V~

2.0

7.5

7 2 3 4 5 6 7 8Thickness 2a

9 70em

Fig. 20 Values of exponent n of eq. (30),from 1 cm to each thickness

O.4/ P!s-0- SC;lrrtm

--0 -- Kre;l/froxinu5(TAMO)

0.,1

c~

.::( 070i--)(:::

~ 008~---+-­R:-C)~

I:::::: 006 r----+----t--~+~~---,r_--~.c::.-_I-.-~C)

, '--V)

:i 001/ t----+-::"""...e::::--f--=--,..,..e:.::::..+--.:>.c---

~

~002 ~-~;i:::=::4::~::::!::==:::t:~

'S - 0 cf9%- -<::) 0 ~__~~_.L..-__-'--__.L-__.L-__.L-_----J

20 30 110 50 60 10 80°C 90

Tempera.ture [-

x 07;: r--------.----.-----:------.,.-------,~- c~~l:::: /Ii. R. J-/. SO %~ 0.10~--__r_--_+---~---_+_--__b,.£_-~~

S~ oIJ81-----l-------4f------f-

.s.>(f)~. 0.06 I--- ~=----+_---+_

~~ o.OLJ t---=t-----t::::::;;;;;;;;......-t-~T_-t_=:;;;;;---"'9---___i

~Cs O.0211- .1-- .1-- .!..- ...!.-__ --:::-'-~-=--o!

o 0.5 J.O 1,0 2.0 2.5 .,,-~ 3,0

Air ","Cloc ity II

Fig. 21 Relation of transverse drying diffusion constantto the drying air conditions (Fa,e:us, for timber

of over 1 cm thick)

-- 102-

T. MAKlJ Studies on the drying of wood

value of n calculated from 1 cm thickness to different thickness. The figure shows that

n is 1.3 - 1.8 in the range of 0.2 - 10 cm thick and the value of TUOMOl.A and MOLL

are all contained in above equation.

222,14 Relation of K and a to the drying air conditions

Fig. 21 and 22 show the relations of K and a to the various drying conditions for

timber of over 1 cm thick which were converted by equation (28) and (29) from the data

of veneer of Fagus (BlINA, 2 a = 1.5 mm) dried at various, steady conditions.

15,::: U.5.2

~h 0.//10/5l§0 0.4

~"" OJ~

u~ 0')l.....

:::sV)

'-t-0 0.7

:::t:~

°20'---.)30 110 50 60 'lO 80 °c 90

Te mperciture, t

-_.

R.H.50 %~----(30_----- ---- ------\ () .----

~--- IjO - .---

25 -~u

0.2~

L...:::sV)

4- 0.10

~.

())

<3 o 05 7.0 7. .5 2.0

Air velocity u2.5"'/$ 3.0

Fig. 22 Relation of transverse coefficient of surfaceevaporation to the drying air conditions(Fagus, for timber of over 1 crn thick)

Namely, the drying diffusion constant has the same inclination as the diffusion coefficient

which increases generally with increase of the abs~lute temperature and is in inverse

proportion to pressure, and as for the air velocity it its influence is slight and K seems to

increase in proportion to u;o.:;-o., in range of u = 0.5 - 2.0 m/s.

Thus, the values of K obtaineJ from the definite ha is naturally higher than those which

- - 10:3 - -

WOOD RESEARCH NO. 13 (1954)-------~---~~---~---

many researchers obtained under the condition ha = co, and so the both may not be compared,

however, for reference, calculated values of STAMM and KRiiLL were converted into those

of the same specific gravity and ploted in Figure.

222,15 Relation of K to the specific gravity

The relation between specific gravity and K converted by equation (28) from the

drying data of veneer to the plate of over 1 cm thick are shown later in Fig. 36. Drying

diffusion constant decreases linearly in inverse proportion to the increase of specific gravity,

but the difference is slight.

222,2. In longitudinal directiont~)

222,21 Drying diffusion constant K{

The drying data of Chamaecyparis (SAWARA and HINOKI), Fagus (BUNA), and

Fraxi nus (TAMO), (each initial moisture content is about 50%) give a good agreement

with the dimensionless diagram of Fig. 3 only in hygroscopic range (the moisture content

30- 10%) as similar as in 222,1 and probable ha obtained from the rate of the drying and

the moisture gradient shown in Fig. 23 are given in Table 4. According to these results,

it is concluded also in longitudinal direction that the differential equation can be applied

in hygroscopic range and the surface evapDration based on the moisture difference (us - UN!)

occupies a certain extent. From Table 4 the present author adopted hereafter the value

of ha determined from the minimum coefficient of variation of K o and showed K l

corresponded to these ha in Table.

(;ha-maecyparis (5AWARA)55°C 40% O.I/l m/

30

%

Ch..amaecypariS (HINOKI)o:-o·C. 55%. 0,47"}1:;30of/0

FdflUS (BUNA)50·C, 62 %. 0.47 "J13

30

o

Fra.x.in usrTAMO)50·C. 62% D.411J'f:;

30~o

Ue~~ 9E

251---+-+--+--+---1

o

1071p'f;~ 9E

o

;::j 20~-+---+----j,~-+-----j.....,>::~I::Clu IS I--~L--+---+__-+-----j

S J'----'-_....L.---L_-'---' 5 5 L..--.L_..L....---.L_....J-.--l

2.scm /) z.scm 0 2•.'icm 0 2.'irm 0

Thickness a Thickness a Thic;kTlP'55 a Thic.xnp.5S a.&'1.-.- __....... _._._

Fig. 23 Gradient of moisture content in longitudinal direction

--- 104--

T. MAKU ; Studies on the drying of wood

Table 4 The values of ha determined from drying process and the moisturecontent (Longitudinal direction)

Remarks

i Drying condition0.661 55', 40%, 0. 41m/s

0.457 I 50, 55, //

I0.257 50, 62,//

0.257 50, 62, //

//2'"'-'5 6(HINOKl)

Fagus 5 11(BUNA)

Fraxinus 5 7.2(TAMO)

Wood I ha

speci es 1-~c~v~--~i~~~~r;~~~~--~~-(27)--- ---------------~---~ -- ------------ ------- -------------------1--- ------------------- ---!--- ----- -- ------ --------------------------- --~----------

Chamae(ypm"is 2(SAWARA) 2.1

222,22 Relation of K l and al to the thickness of timber

Test pieces of Chamaecyparis (HINOKI) of 5, 3, 2.2, and 1.3 cm thick were dried

from about 50% to 10% moisture content. The value of K l was calculated by equation

(18) from the drying data after the moisture content of mid-plane reached 3096', K l

decreases with decreasing of thickness in plate of below 4 cm thick (ref. Fig. 24) and the

following equation similar to equation (28) is obtained at 50'C, 55% relative humidity and

0.41 m/s.

Chamaecyparis (H//\/OI1I) , 50t; 55%, 0.4775

1____ A

~~~

",0

7 234Thickness 2a

5

Fig. 24 Relation of longitudinal drying diffusion constant to the thickness of wood

K~=Kl {1+0.167(2a~-1)} ·············································(31)

where K: is the drying diffusion constant of 1 cm thick plate. For the coefficient of the

surface evaporation at, similarly

a~=a: n+O.167 (2a~-l)} .. ·· .... · .......... · ........ · .... · .......... ·(32)

where It. is rJ.' of ] em thick plate.

-- 105 --.'

WOOD RESEARCl-I NO. 13 (1954)

222,23 Relation of K~ and (1.1 to the drying air conditions

To obtain the relation of K I and (J..~ to the drying conditions, test pIeces of Fraxinus

(TAMo, thickne3s 1.3 em, the initial moisture content 50-60~?6) were dried. The values

of K~ and (J..~ obtained in hygroscopic range by equation (18) increa~,e, as the same as in

transverse direction, with increasing of absolute temperature and are inverse proportional

to the relative humidity (Fig. 25, 26), thus

70 Vc 80L/O SO 60

Te mpercdure t

'I->~.B 0.4 I------+----+---I----+_(/')

I::::303

0.6 ---------.----~--__r_--__r_--__,

~~A 0.'1-/ rnA;::.::: 0.5

R./-I. 60%

)( 60° C X.- )(

~V7

40 0 l.._.0 0 1\.)

1---

0.5 lO l5 20Air velocity u

2./i m4; 3.0

Fig, 25 Relation of longitudinal drying diffusion constant to the dryingair conditions (Praxi:ml3, for timber of 1.3 cm thick)

273+ t /III ( 1 ' r ,K r = nl( -273---) \7~-r) ., ,.. ,.. , , '" (33)

where nr and 'JJ1,1 are the experimental coefficient, H is the relative humidity, and nl ==

0.876 -4.0, 'JJ1,1 = 5.4 -9.95 in the range of the experiment (air temperature 20-90"C, relative

humidity 20-80%).

The above relation is all the same to IJ.i

273+l ·/1·'1(1 1 '; _, _11.! = 'fI't(-273--) .. -FT)··'········,············,···,······,···,········ (J4)

-- 106--

T. MAKU : Studies on the drying of wood

where n'l=O.85-4.0, m'l=4.4-8.9.

Fig. 27, 28 show the converted value for plate of over 4 cm thick.

'70 °c 8040 SO 60

Temperatu.re

<:).J

~ 0.2.4...::JCI)

~

0/C)

~~C>

<..) 00

>.l 05 r---~----r---r----r----r---'

~ if,;h. all-/ %.~

~ 0.4I..:a.~ oj I---+----+---+----j---::;l~t_-__j~ .

2.5 7n/.S 3.02.00.5

P. .H. 60%

60°Cx x

V~ x

I...... L;-O t 0 no- 0

/.0 7,S

Air velocity uRelation of longitudinal coefficient of surface evaporation to thedrying air conditions (Fraxiuus, for timber of 1. 3 cm thick)

Fig. 26

O.S~--I

0.4 7TJJ:50,8

;::::.~ 0/1 I---+---+~--t----:;~-t--: ~::-t--:::::;;....-=l:i;

;; O.7l---,.-----+---+--T---"T~~1.....,~ 0.6 1---+----l----+---+---:::J:""79----1o'-'

~ O~ l---t----l-:~;_b~~j;;;;;;;......-:=::--r-:::;;;;04

~ 02 L-----=L,....~ ~;.......~f-=::::;;;;;-1"'""=--t--__,

~ . Uii~:::t:===+--f---+-~.~ 0,7

CJ • 0 L--J----L----!-:---;;;---;;;70~crC~e()20 30 40 50 60

!nnpe fc:.tLt re

-- 107 --

WOOD RESEARCH NO. 13 (1954)

A.H. 60%

./'?

V"/

LJOC

0.5 7.0 7,5" 2.0

Air Velocity u2.5 m/s 3.

Fig. 27 Relation of longitudinal drying diffusion constant to the dryingair conditions (F'raxillus, for timber of over 4 cm thick)

0,4/ 1TYS"Q:.;:,~ 0.5 r----.---+----+----+----t~c---_l

~~ 0-4

~ O. 7 t---""'==t----t---t----t------<~----l~a

<-..J 02.!-;O:---~::---~)~'0---~rO---6.,J.o---.L----J

4 LJ 'leI co 80Tempera.ture t

2.5 TT)/s 3.07.0 75 2.0

Air ve!oc ity ~t

A.H. 50% 60°C

/ ,

/V

,L./-O-

-

Fig. 28 Relation of longitudinal coefficient of surface evaporation to thedrying air conditions (F'raxillus, for timber of uver 4 cm thick)

23. Drying of veneer)::)

--- 108--

T. MAKU Studies on the drying of wood

231 Drying in the range of high moisture content

231,1 Relation of constant rate of drying C to the drying air conditions

Test pieces of Chamaecyparis (HINoKr, 2a=1.6mm, r o=0.34), Tilia (SINA, 2a==

1.39, r o=0.43), Shorea (Lauaan 2a = 1.24-, r o=0.48), Fagus (BUNA 2a=1.54, r o=0.56),

and Betula (KABA 2a=1.40, r o=0.62; 2a=1.34, r o=0.67), (each initial moisture content

is about 50 - 60%) were used in this study. As for the drying process of veneer, as already

explained in Fig. 7 and 8 in 221, the constant rate zone and the first zone of falling rate

take place untill near the fiber saturation point, however, the gradient of the latter is so

gentle that it may be considered as a constant rate in practice.

In drying of vereer, PECK!!I) and KEYLWEI<.TH 7) establishe1 the equation~1i = - cu" in all

moisture content range (c, u : experimental coefficient) but the results of the present

author did not agree with their results. So hereafter the present author will discuss on

the range of high moisture content and on hygroscopic range, respectively.

Now, in Fig. 29 an example of drying process under various drying conditions are shown.

From these restlts

(1) The constant rate of drying (%/min) takes place until near the fiber saturation point

(2) Constant rate of drying varies with wood species and drying conditions.

Fig. :30 shows the relation between the drying conditions and the average constant

drying rate C from initial moisture content to the fiber saturation point for Fagus. C, as

similar as K, increases with increasing of temperature and decreases as the relative humidity

increases and generally

, I 273+ t '. '"" . 1'.C= n' (--273-) (-H) (35)

where nil and mil are experimental coefficient and n"=16.5-22, m!!=4.8-6.26 in the

experimented range.

The3e results are s:)mew hat different from Tuomola's experimental resulf').

As for the relation between the coefficient of heat transfer h' and the mean aIr

velocity ii, ZtJRGES 2-t) gave for rough face and u<5 m/s

h' =5.32+3.68u '" '" '" '" '" '" (36)

and KEYLWEKTH 7) gave

h' oc -u(l·"·-n.~ (37')

--- 109·-

WOOD RESEARCH NO. 13 (1954)

70 r------r---~--____r------____.% 11-0%. O.6'S60~__-+ -+- +-__---,~__........

Temperature of dryinq air30°C (/405060

~

~ 20 t----~d_-£c...-:.-.;!U:lIIIf5lIIIiar_--+_---_+_---....~

<I)

~~ /0 r----t-.=.....4oi;;;~~.b~~s~~iiiiiiOiiiii;._;;;;;;;;;_i

O'-- ~_--.L----..&----........------'o 20 40 60 80 min 100

Dryi 7lj period 9

R.H. of Dryin3 air SO °C 0.6 %

72 0/0

554025

60 ----------.------.----....,.-----~-----..

.:::s90;..,)50I::co

-t-.)

~ /J.O 1--..........-...... -~_--~o

JO~~~ 20 t---~b'-__Jlit -7f__P.n::----.,,;:..,0IIS:::""-=--_+_---_+_---_I-C)

~ 10t---i~~~~~~~~~~~~~-~

oo;;---~:__--~--~~---:f_:__---:-L-~-.J20 4060 80 700 min 720

Drytn.J period e

~-.....+---+__-_t_--I

oR0.35 ---~s...a&:::::"_=_+_--__t

0.600.'15

-I..)

~ lj() ~-..:IIt:;l'l\r-+---4-.l~C)

<..J30.-----4~~-___1

60 _---...---~---...,.---__,r------____,~o

;j 50 a-.:;:~-::=!.lIf_.,__-___+_----_+_---_f_---.,__-.-___1

~

~ 20 ~---+_:..:.JIll.1O""'i-.:>

.":1~ 10 r----t-------=F"fri6i~~~i:::2:==:t:z~--T---1

oOL----2LO----4LO----6~O----~8~0~---:1~O~O~-7Tl-:-in~120

Drying period eFig. 29 Drying process of veneer under various drying conditions

(Betula, KABA, 1.4 mm thick veneer)

--110 --

T. MAK U : Studies on the drying of wood

o

80°C gOltD SO 60 70

Te mperat().re t

l-.lF:::

7.0\\l....,\J)

I::: 0

G o 20 30

«0 ,...--~--,..---~--,.------r---r----,r

<0 mn~ 3.0 ~--T_-_-:Y:-;----+~-o-r-b-i r...l.I<-~-n-e-e-l..r,-J.-'1o-%:-o-, O....L,-6-:1'1r~i-;--t-::~"--l

~ I2 0 &'/0

~ ~,0.~ 2.0I,....

~

R.H 50%

2.5 Try"s 3.01.5 2.0

ve/oci ty u7.0

Airos

--y-- For birk veneer. SO·C.50%

BO°C 0

4.0

~.Q

in

t..:l 3.0~

F ~~20

'-r:-~i-.::)

7.0~

~-+-lV)

~

(3

Fig. 30 Relation of constant drying rate to the drying conditions

If there is a proportional relation between the coefficient of heat transfer and the

amount of moisture evaporated, above relation may be established between C and ti,

however, in the present experiment C is nearly proportional to u,r'·~-n., in the extent of

u= 0.5-2.0 and the influence of air velocity on C is smaller. This result gives the same

inclination with Kamei's experimental result which showed that in below 2 mls constant

drying rate is hardly influenced by the air velocity.

According to present experiment, it may be considered that the effect of air velocity

is remarkable in below 0.5 m/s or over 2 mis, but in the extent of 0.5-2 mls the effect

is slight.

Fig. 31 shows the amount of moisture evaporated in drying of veneer and hatched

points on curves show the time when veneer reached the fiber saturation point in mid plane.

231,2 Relation of C to specific gravity

Fig. 32 shows the relation of specific gravity and the constant rate of drying obtained

-ll~-

WOOD RESEARCH NO. ]3 (1954)

700min

8040 60Dry/n;} period 8

20

25 r------r----.,------.,-----r--~-__., fj~ t"'tj 20 1----i-----t--:::::::::;;;;;;j;;;;;;;;o;iii.J:)·--t--~·-Lf{}~ ~~ 60~ 75 1-----+----:-.stJI1ii""""""':r~~~.:::::::::~:;;:c~;;;;;;;;;;;p=50

~~ 70 1-__~oC-\.-,~C--.:..--+_----+----__+_---_;

Fig. ;·n The curve if the amount of the evaporated moisture. \ ShorM, lauaan, 1.24 mm thick veneer)

40°C, 40%/ o.67??JS

~ __ 2 3

°"-0~o~ 5.....0.......... 6

_0-.

25\j 5YV

/mlnQ)

~ 2.0J>.:.

~·b7.5"\::l'I--:l

:;::,

~ 7.0V):;::,C)

U0.5

0.3 O.t;. 05Specifc 'iJravity

0.6

10O,?

Fig. 32 Relation of constant drying rate to the specificgravity of wood (for 1 mm thick)

1 Chanlaecyparis (HINOKI)

2 Tilia (SINA)

:3 Shorea ( lauaan)4 Fagus (BUN A )

5 Bdlt/a (KABA)

(j // ( //

from' various wood speCIes and converted to veneer of 1 mm thick under the assumption

th3t in the thin plate such as veneer drying period is proportional to the thickness, that

is, drying velocity is inversely proportional to the thickness. As obvious from the

figure, .the constant drying rate decreases linearly with increasing of the specific gravity.

232. Drying in hygroscopic range

2:32,1 Relation of K and a. to the drying conditions

The drying process of veneer in hygroscopic range gave a good agreement with the

differential equation, that is, similarly as in 222,13 calculating Vall for [flit = 0.3 by

equation U8) and determing the time by means of this Va/) , from the drying data in 231

-112-

T. M AK U Studies on the dryi ng of wood

the author obtained a linear relation of vI/Ii Van- tI/ a~ diagram.

Then, as similar as in 222, 11, the most probable value of ha \vas determined as about 0.5

from minimum coefficient of variation of K. ha was inJependent on the drying conditions and

had a good agreement with one calculated by h = 6.67 which is determined by ha = 10 (i. e.h =

6.67) of Fraxinus and PrU111,f,S of 3 cm thick (for Fagus veneer a = 0.075 cm; ha = 6.67

X 0.075 = 0.51). Therefore, putting Ita = 0.5, the relation between drying diffusion constant

K and the drying conditions was obtained in Fig: 33. From the figure, K increases with

increasing of the absolute temperature and decreases in inverse proportion to the relative

humidity as similarly as the diffusion coefficient. That is

, 273+t )'111., 1 '. .,K = n (- -,')-- (-) (38 '). 27;) " ,II,'

>:::: OI)81----+------,----.------.---..---~o4K--~

<:)

(I)::E 0.06 I-----+--.....-...jl-----+-------,:;l;",.,.,..==---+-----:l:.",.,.,..==---I

~

~04

~002 ~~~~~;~~==:F::;;;~~~::t===L---~

30 40 SO 60

Temperature70 SO "C 90

2.5

R.N 50%

--0-- For birk. veneer (So"c.SO%) OOG• For bitK plywood(SO't,50%) - 8 ~'-:::"'~----l

o

~Q02

'S 'C) 0 ~O--_;:;.l.::_--~_:__--....L.---1------l.----1o 0. 5 7,0 7.5 2,0

Air velocity u

0.12 r----r----.,-----,------.------.----........cm2

,~

X' ().IO

~

~o.08>:::o~

'i:: 006 1-------4-.___--0.~C/)

::i o.of/.~~~!___-~~:::+=_--_L~~L-----J~ _0

-)(

Fig. 33 \{elation of transverse drying diffusion constant to thedrying conditions (Fagus, for veneer of 1.5 mm thick)

- 113--

WOOD RESEARCH NO. )8 (1954)

where n, m are the experimental constant, and in the experimented range n = 0.35-0.8,

m = 4.5-6.1.

As for the relation of the drying diffusion constant to the air velocity, K increases

quickly in the range of u = 0-0.5 mis, gradually in the range of 0.5-2.0 mls i. e. in

proportional to uo.~-o., and in over 2 mls seems to increase again. Fig. 34 shows the

relation between the coeffcient of surface evaporation fJ. and the drying conditions, as

same as K, the following formula is given for (J.

a= n'( 2~~tt Y"' C-k-)········· (39)

O.5r----.....----r-----,..--....,..---r----,---.

't) fmh 0.// / "Ysf:::

.<2 O.J.I.I----+----+-----4---+----+----+----'~......,

~C)

~ 031----+---+----+------+----:::/11,-:;;..---+----4~ .'V\;l)'-J~ O'2t-----+-----L...~-=:.......t---t__--= ....=--__+=:::1111"'.-:::;;.._f

l..

C5'+-

<::> 0.71-~~E==~:::=1;;.jijiIIIIIO..-r==:....--t--1--1~ I~ 0

c....J 02'="O~-J-::'O'-------'40---S-L-0--6...l...0---7..L.O---8~0-o~C---'90

Temperature t

2,5 1TJ1J 3.07.0 7,5 2.0

Air velocity u0.5

R.H.50% CO .-

~~0~~~

_0 --- ~~- 6. ~

X '1tl _ ..x- 25_ .-~-. CD •

Fig. 34 Helation of transverse coefficient of surface evaporation to thedrying conditions U;'agus, for veneer of 1.5 mm thick)

where n' = 1. 7-2. 7, m' = 5.4-5.9.

Fig. 21 and 22 show the values converted from Fig. 33 and 34 by equation (28) and

-- 114 _c

T. MAKU Studies on the drying of woo(1

(29). Fig. 35 shows the measured values of the moisture evaporated after the moisture

content of mid-plane reached the fiber saturation point (hatched point on curve in Fig.

31) and the values calculated by equation (18) and K which was obtained by the above

mentioned method.

8,---------r-----.-----r----.--,

~

50min

70 20 30.Dryin'j period B

o

40%

~ 6'\:l\\..)

1--.:1

~'J

~ 4 t-------=~~~_,~__+_---__I_---_4----'-___l\\..)

~~.~ 2~

Fig. 35 Evaporated moisture in hygroscopic range( S/lOrea, lauaan, 1.24 111m thick veneer)

< 0.06.-------------.......----

~.2 C?~~~ 40°(, J 40 %, 0) 67 ?J0:;;§ 0.05 t-----.------r-----I-----tIf)

I-:Cl\j 0.04 t----:::::.---+-"'........~~.

'2~ 0.03 t------+---~"\::i.~o.02 t-----4-----+-------4-"::.--

~~ 0.07 ~--~~--_.,~---."l-,----~

0.3 0.4 0.5 0.6 0.7SpecIfic fjral/ity Yo

Fig. 36 Relation of the drying diffusion constantto the specific gravity

1 Challlaecyparis (l-IINOK I)

2 Tilia (SlNA)

3 Shorerl (Iauaan)4 Fagus (BUNA)

:> lJetu/a (KABA)

G //

-- 115 --

WOOD .RESEARCH NO. l:i (19S4)

232,2 Relation of K to the specific gravity

According to the data of Fig. :32 the relation between the specific gravity andK are shown

in Fig. 36. K decreases linearly with increase of the specific gravity. The relation

between both for timber of over 1 cm thi.ck are calculate=! by equation (28) and shown in

Fig. 36 together.

24. Drying of plywood 11)

Urea reSIn bonded, 3 ply, Betula (Birk) and Shorea (Lauaan) plywood (thickness

3.2 and 4.6 mm respectively; initial moisture content 23-24()£) were dried under the

various drying conditions.

As S3.m·~ as in timber or veneer, VI/"/ Vo - f)/a'J diagram shows a straight line and ha

obtained from minimum value of coefficient of variation of K o are given as follows

Table 5 Values of ha

/1

/1

/1

/1

II

Drying air

conditions

, 40%, 0.4-- O. 5m/s

30'"'-'EOOC, 25'"'-'72()~

O. 1'"'-'0. 75m/s

26'"'-'90°C, 20%~80(}6

O. 4'"'-'2. 5m/s

30~60°C, 25'"'-'72~rJ

0.1 '"'-'0. 75m/s

/1

/1

//

211=4

//

0.47

1r:c;::.6.67 30'"'-'50", 20'"'-'40~(}

1. f) O. 1~0. 6m/s

1.1 #

Iza. calculated

by IL

. O. f)2

: 0.41

I·/1 i

0.4 I /1

I I·-----k=,r-;~-~--------------~---

0.32 40°, 40~;" 0.6m/si

h=6.67!0.46 . ~

; O. 4f) /11

0.4 2'"'-':i I 1. :-3'"'-'2I

0.41 6 4

0.56 ]0 1 G.G70.63 10 J0.4:i 6 4

// 2'"'-':i

// 1

/1 O. fi.-...1

. O. 34 0.2

0.43 0.5

0.48 O. fi'"'-' 1

0.56 0.5

0.63 O.fi

//

//

/1

0.14

0.46

,

iO. 133 I O. 67 i

Ii,~-1---~'"'-'2---------

1.0

O.R

0.2 'I

0.16 Ii

O. 14

I

0.124 I

I

0.154

: I

;Thicknessl

i 2a

em I3.0 I

i

Ii

~veneer '

I

i

I

!I

! I

I ---T

jPIYWOOd!

Wood

species

/1

BetulaKABA

SlNA

ShoreaLauaan

FagusBUNA

BetulaKABA

SILo/eoLauaan

ChamaecyparisHfNOKI

Chamaecyparis ISAWARA I

I// ,

HINOKI I

Fraxinus I

TAMO

P,unus fSAKLJRA Timber

Thujopsis

"limA I

Tilia

~-116 --

T. rdAK U : Studies on the llrying of wood

for lauaan plywood

for birk plywood

ha

ha

1-2

0.5-2

and the value of Ita calculated from h = 6.67 are

for lauaan plywood

for birk plywood

ha

ha

6. 67x O. 23

6.67~<O.16

1.5:3

1.07

Undoubtly. the values of Ita of both cases have a good agreement.

Table 5 shows summarily the values of Ita on timber, veneer, and plywood. As

obvious from the table, hft obtained from the minimum value of coefficient of variation

30%. 0.67 '%- Iv.."..,.~-

~)(/0

~~~ 0 Betula...

x Shorea

J 40 50

Temperature t

J SOac, 06: o/s- ~______ Ib ____ ~_

50°C. 30% I.____0-

~/

~o

20 30 1/.0

Re/~ humidity H

02 0.'1 0.6

Air velocity u

.50

m~ 08

Fig. 37 Relation of the drying diffusion constant to thedrying conditions (Betula-, Slwrea-plywoodi

-117-

WOOD H.ESEARCH NO. 13 (1954)

of K o, ha obtained from the moisture gradient and ha of veneer and plywood which

calculated from It of timber coincide well each other. From this fact it seems that in

hygroscopic range the value of h varies somewhat with wood species (ha is smaller in

light wood and larger in heavy one, so the moisture gradient becomes gentler in former

and steeper in latter) but does not vary with the thickness of wood and the drying

conditions in the extent of experiment, and even in plywood which has a few glue lines h

does not vary with above factors.

Fig. 37 shows the relation between K calculated from the above value of ha and the

drying condition and in Fig. 33 the values converted for thickness are shown, namely

the influence of the drying conditions on the drying diffusion constant in plywood is

similar to that in timber and veneer, but it seems that the absolute value of K is some­

what smaller in plywood than in timber or veneer by the presence of glue lines.

Summary

In drying of wood the differential equation similar to the heat conduction equation is not

always adaptable to explain the moisture movement through wood, however, it is often

used for the convenience that (1) it represents directly the moisture content (2) the other

equations can not be connected directly with the relative humidity and the veloci­

ty of drying air, but it can be easily connected with them (3) at least from 30- 10 .~O'

moisture content it coincides well with the drying process (4) it is convenient for the

calculation of the drying time and the moisture gradient.

At the above mentionej standpoint, the present author treated of the differential

equation and obtained the relations of the drying constant to the drying conditions.

1. Under the assumption that the coefficient of the differential equation i. e. drying

diffusion constant K is constant, the solutions were obtaine::l in steady drying condition

and in confined unsteady drying condition.

2. In high moisture range, the differential equation can not be used generally, howe­

ver, in hygroscopic range it coincides well with the drying process.

3. According to the drying process and the moisture gradient in hygroscopic range,

drying diffusion constant K and the coefficient of surface evaporation {J. are independent

upon the moisture content of wood both in the transverse direction and in the longitudi­

nal direction, and the moisture content at the wood surface is always higher a little than

the equilibrium moisture content of the drying air, and the drying proceeds under the

T. MAK U Studies on ths drying of wood

correlation between the surface evaporation by this moisture difference and the internal

diffusion.

4. In the transverse direction the value of K and a decrease somewhat with decrea­

sing of thickness of wood in the extent below 1 cm thick and in the longitudinal direction

they decrease similary in the extent below 4 cm thick. It may be caused by the existence

of the thin anomalous layer at the wood surface, but the value of the coefficient becomes

constant over the above mentioned thickness because the thin layer does not influence in

practice.

5. The relation of the drying air conditions to drying coefficent K and a was sear­

ched by the drying data of veneer and this was converted to the value of timber. The

value of K and a increase as a exponential function of absolute temperature and decreases

inverse proportionally with increase of the relative humidity as similar as the general

diffusion coefficient. The influence of the air velocity U on K and a is quite slight in the

extent of it = 0.5-2.0 mls and K and a are nearly proportional to UO.3-

O.,.

The v;alue of K thus obtained are larger a little than the value determined by the

assumption that the surface moisture content of wood conforms to the equilibrium mois­

ture content of the drying air in hygroscopic range, but, for reference, they are shown in

comparison with the value calculated by STAMM and KROLL.

6. In drying of veneer the constant rate of drying takes place until near the fiber

saturation point in practice and therefore the relation between the constant drying rate

and the drying condition was searched.

7. The drying process of plywood coincides well with the differential equation, but

the drying constant is somewhat smaller than that of veneer and timber. It may be

caused by the existence of the glue lines.

Literature cited

1) Bateman, E., Hohf, J. P. and Stamm, A. J. : Ind. and Eng. Chem. 31 (1939)

2) Egner, K. : Forsch. Ber. Holz 2 (1934)

3) Hawley, L. F. : U. S. Agric. Bull. 248 (1931)

4) KAMEl, S. : J. Soc. Chem. Ind., Japan 40, 7 (1937)

5) II 40, 9 ( II )

6) Keylwerth, R. : HQ.1z als Roh- u. Werkstoff 10, 3 (1952)

7) II 11, 1 (1953)

8) Kollmann, F. : "Technologie des Holzes" (1936)

9) "Technologie des Holzes und der Hoizwerkstoffe" Bd. 1 (1951)

-119-

WOOD RESEARCH NO. 13 (1954)

10) Kroll, K. : Holz als Roh- u. Werkstoff 9 ; 5, f) (1951 i

11) Ludwig, K. : Forsch. Bel'. Holz., 1 (1933)

12) MAKU, T : "Wood Research" 6 (1951)

13) ---: Trans. 2nd Meet. KANSAI Branch Jap. For. Soc. (1953)

14 ) Trans. 62th J\tleet. Jap. For. Soc (1953)

15) Trans. 63th Meet. .lap. For Soc. (1954)

16) This Bulletin, this Number.

17) Martley, J. F. : For. Prod. Res. Techn. Paper 2 (1926)

18) Newmann, A B. : Trans. Am. Jnst. Chern. Eng. 27 (1931)

19) Peck, R E."R T. Griffith u. Nagaraja Rao. K. : Jnd. Eng. Chern. 44,3 (1952'

20) SchlUter, R u. F. Eessel : Holz als Roh-· u. Werkstoff 2, 5 (1939)

21) Sherwood, T. K. : Ind. Eng. Chem. 21 (1929)

22) // 24, 25 (1932-33)

23) Stamm, A. J. : U. S. Agric. Techn. Bull. 929 (1946)

24) Tuttle, T : J. Franklin Jnst. 200 (1925)

25) UTlDA, S., S. KAMEl and S. HATTA : "KAGAKlJ KOGAK(]" (1951)

26) W. H. Walker, W. K. Lewis a. W. H. Mcadams : "Principles of chemical

Engineering" (1929)

27) Voigt, H., O. Krischer u. H. Schauss Holz als Roh-- unci Werkstoff 3, 10 (1940)

- 120 --..