432
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
rime /n #inufes FIG.2Cb-ADIABATIC AIR DRYING
interior. Such substances, e. g., wood, varnish, films, artificial leather coatings, etc., are dried a t high humidity so t h a t even t h e outer surface is not too dry because of the high equilibrium moisture, and a t high temperature, so diffusion will be rapid. There is a certain concentration gradient which may be maintained through t h e surface layer without straining it t o rupture. The humidity is adjusted t o get this gradient, a n d the temperature raised t o get t h e most rapid diffusion possible with this limited concentration difference. As drying proceeds t h e surface layer gets thicker so t h a t a greater total concentration difference is allowable without increasing t h e concentration gradient, i . e . , the humidity can with safety be progressively reduced. The values of the drying coefficients should where possible be determined from the measured performance of full-scale equipment. The result of plant tests can even be used t o determine the equilibrium moisture.
Vol. 13, No. 5
T h u s Fig. 19 shows t h e rate of loss of water of a porous, spongy, lumpy material, exposed a t a point in a commercial dryer where the drying conditions are substantially constant. By reading the slopes off this curve a n d plotting against t h e total water, t h e intercept of t h e line obtained gives t h e equilibrium moisture, E = 8.5, a t which evaporation ceases. One can now draw t h e logarithmic drying curve for this material (Fig. 20) from which the time required t o reduce t h e moisture content t o a n y required point can be determined. 70 The slope of this last line is t h e drying coefficient K. From 60 runs under other drying conditions t h e variations of K determine A and R. Fig. 2 1 shows t h e application of these general equations t o t h e drying of a n organic solvent from a fibrous material. 30
It is believed these facts demonstrate t h a t t h e drying of a 20 solid material represents a balance between a process of diffusion of moisture through t h e substance a n d of evaporation from its sur0 10 20 30 4 50 60 7ime in Minutes face; and t h a t these processes can be FIG.2 l - D R Y I N G OF ORGANIC SOLVENT FROM F I s R o u s MATERIAL AT CONSTANT DRYING quantitatively repre- CoNDITroNs sented by t h e differR ) , which ential equation, --dw/d8 = 8ARw/L(4A can, after modifications dependent on the material being dried, be integrated into simple a n d usable formulas which answer the question as t o drying rate.
+
The Theory of Atmospheric Evaporation-With Compartment Dryers
Special Reference to
By W. H.Carrier CARRIERENGINEERING CORPORATION, 39
I n this paper an a t t e m p t is made t o state as concisely as possible the fundamental theory involved in air dryers with particular reference t o compartment drying, although the greater part of the theory developed applies equally well t o t h e tunnel type, the continuous type, and the spray type of dryers. We have endeavored t o make t h e theory general t o apply t o the evaporation of any volatile liquid in a n y kind of atmosphere. I n this respect, we believe t h e theory is somewhat new. Moisture exists in material in two distinct forms-as free moisture, and as -hygroscopic or absorbed moisture.
CORTLANDT
Sr., NEW Y O R K , N. Y.
Evaporation is t h e term usually applied t o the converting of a liquid into a vapor in a n atmosphere whose pressure is above t h a t of the vapor pressure of t h e evaporating liquid, i. e . , causing vaporization below t h e boiling point. The heat of vaporization is usually taken entirely from t h e air itself, and this will be chiefly t h e basis of t h e theory considered. The theory will b e considered (1) with reference t o the evaporation of free moisture, a n d (2) with reference t o hygroscopic moisture. The rate of evaporation depends upon: 1-The vapor tension of the moisture in the material corresponding to its temperature.
k I a y , 1921
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
2-The vapor tension of the moisture in the air corresponding to its absolute humidity or dew point temperature. 3-The 4-The dried.
effective velocity of air over the surface. physical and chemical properties of the material being
T h e r a t e of evaporation a t any instant per unit of surface is proportional t o t h e difference in vapor pressure between t h e liquid and t h e vapor of t h a t liquid i n t h e immediate vicinity, t h a t is, dw
- = x(e’ - e ) .
433
methods, and t h e water stirred t o secure uniform cooling.l The same law was indicated by t h e evaporation experiments of Thomas With transverse flow or impact and vertical surfaces, t h e r a t e is nearly twice as great a t corresponding velocities. With t h e same frictional losses, however, t h e rate is substantially the same, regardless of t h e t y p e of air flow, as is t h e case in heat transmission. I n Fig. 1 are given t h e curves of evaporation determined experimentally by Coff ey and Horne,3 and independently by t h e writer.’
dt
( a ) This law holds only for free liquid surfaces or for vapor pressures of the liquid at the surfaces of a wet material. ( b ) It holds only when the total pressure is greater than the vapor pressure of the liquid. (c) It holds only for like conditions of relative atmospheric movement with respect to velocity and direction. ( d ) It probably holds true for any gases or any superheated vapor of a nonmiscible liquid or even for the pure superheated vapor of the liquid itself, regardless of the specific heat, specific weight, or partial pressure of the gases or superheated vapor. (e) It holds true where the liquid is above or below the temperature of the surrounding atmosphere. (f) The coefficient x in the equation is probably independent of the latent heat of evaporation,but varies directly as the molecular weight of the evaporating liquid.
It has been found t h a t t h e rate of evaporation, other conditions being constant, increases in direct proportion t o t h e velocity. Therefore, t h e rate of evaporation may be expressed by t h e following equation: dw - = (a
where a b e’ e
+
bv)(e’ - e) dt = the rate of evaporation in still air. = rate of increase with velocity. = the vapor pressure of the liquid. = the vapor pressure in the atmosphere.
For example, with water evaporating in still atmosphere R = 0.093(e’ - e ) , where R is t h e pounds of water evaporated per sq. it. per hr. If we express this i n terms of heat units, we shall have H = 97(e’ - e) B . t. u . per sq. ft. per hr. The effect of velocity ‘depends upon whether t h e flow of air is parallel t o t h e surface or transverse,* t h a t is, perpendicuJar t o t h e surface. For flow of air parallel t o a horizontal surface H = 97 W
=
(1
f
(
0.093 1
io)
(e‘-
e ) B. t. u. per sq. ft. per hr.
+,5) (e’ - e) (approximate).
= Ibs. evaporated per sq. ft. per hr. = velocity of atmosphere over surfaces in f t . per min. e’ = vapor pressure of the water corresponding to its tem-
w v
perature. e = vapor pressure in the surrounding atmosphere.
T h a t is, a t 230 f t . per min. velocity, t h e evaporation is twice t h a t in still air; a t 460 f t . per min. velocity i t is three times, etc. This law was determined by extensive experiments i n t h e rate of cooling of a body of water by evaporation i n still air and a t definite measurable velocity up t o 2000 f t . per min. Corrections for t h e radiation and convection effects were made by t h e usual calorimeter
FIG.1
Inasmuch as
dw
- is always directly proportional to dt
(e’ - e ) for all experimental ranges, i t would seem t h a t t h e evaporation is practically dependent on t h e surface tension of t h e liquid. The effect of velocity is apparently t o increase t h e rate of diffusion of t h e vapor a t t h e wetted surface. There is undoubtedly a surface film of vapor saturated a t t h e liquid temperature, and admixed with air (or gas). and this is broken up and removed in direct proportion t o t h e velocity or t o t h e square root of t h e surface frictional head effects caused by atmospheric movement. A free wetted surface unaffected by internal or external heat (apart from t h e air itself) tends t o assume a definite minimum t e m p e r a t u r e of evaporatioiz with a corresponding vapor pressure ( e ’ ) . 4 This temperature is definitely calculable for any vapor and atmosphere, and is dependent upon t h e latent heat and specific weight of t h e saturated vapor, t h e specific heat and density of t h e atmosphere and degree of initial saturation with the vapor (i. e . , t h e vapor pressure i n t h e a t mosphere). I n psychrometry, this temperature is known as t h e “wet bulb” and t h e difference between t h e atmospheric temperature and t h e wet bulb temperature, or temperature of evaporation, is termed t h e wet bulb depression. It has been shown t h a t i n becoming saturated with vapor, t h e atmosphere cools t o t h e wet bulb or t e m p e r a t u r e of e v a p o r a t i o n , and t h e latent heat of t h e water or liquid evaporated is W. H. Carrier, Proc. A m . SOL.Heat. Vent. Eng., 24 (1918),25. “A Treatise on Heat,” 1870. A m . soc. Refrigeroling Eng., 2 (1910), 6. 4 W. H. Carrier, Trans. A m . Soc. Mcch. Eng., 3s (1911). 1005.
1
2
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
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Vol. 13, No. 5
exactly equal t o t h e loss in sensible heat of t h e atmosphere. For any liquid evaporating in any atmosphere, let Wi = initial weight of vapor content per lb. of vapor free air. e = temperature of the air. Cp, = specific heat of air. Cps = specific heat of vapor. w = the lbs. of moisture in a lb. of air at an unknown temperature. r’ = the latent heat of evaporation.
T h e rate of evaporation of f r e e water i s s u b s t a n t i a l l y proportional t o the wet bulb depression w h e n t h e material i s n o t heated, and 9 5 depression is approximately equivalent t o 1 in. difference in vapor pressures i n t h e evaporation formula. Also t h e drop i n temperature of t h e air i n a dryer is proportional t o t h e rise i n vapor pressure of t h e air. If we apply t h e wet bulb depression formula t o t h e
From t h e relation, change in latent heat = change in sensible heat, we have rldw = (Cpu wlCps)d0. (1) Integrating between t h e limits w1 and W Z ,61 and 6 2 , y t ( w 2 - W) = (cpu w1cps) (e, - e,), (2) which is t h e fundamental equation for evaporation and for t h e temperature of evaporation 8’ if we substitute 8’ and w’ for O2 and we,or ~ ’ ( w’ w l ) = (cpa wlCps)(e- e’) (3) and if w = 0, then Y,W, = cpu(el - e,) (4) or if t h e superheated vapor alone is present and wl = 1 lb. then r’Z(w2 1) = cps(el - ez). (6) It will now be shown t h a t the rate of evaporation i s s u b s t a n t i a l l y proportional t o t h e wet b u l b depression 0 - 8’ as well as t o e’ - e , t h e difference of vapor pressure. Let B = barometric or total pressure. el = initial vapor pressure. e‘ = vapor pressure in the saturated air at wet bulb temperature 8‘. S = the specific weight of the vapor with reference to the molecular wt. of vapor atmosphere = (approximate). molecular wt. of atmosphere
perhr.
rate of evaporation H = 97(e‘ - e ) Then
+
+
+
-
Let R
lbs. per sq. ft. per min. 1.63 B - e‘ R=-Y’ S’r‘
=
=
(
0.0000165 1 - 2;o)
(e - e’) a t e‘
=
loo”, B
=
29.92,
and
(
0.0000166 1 - - (e - e r ) at e‘ = 60°, B = 29.92, 2;o) or the weight of evaporation is substantially the same at any temperature per degree depression.
R
=
Then by Dalton’s law, Sel
=
Gland w’
=
se’ -
B .Le’’
Substituting these values in (3) and assuming S approximately constant, we have by rearrangement
e B is one form of t h e psychrometric equation, applying t o any vapor and any atmosphere. 0.000009t (for air). Assuming B = 29.92 in., Cpa = 0.2411 Cps = 0.4423 0.00018t’ (approximate). S = 0.6620 0.00003t (approx). 8’ = looo, e’ = 1.92, e = 0.92, r’ = 1036. Then 0 - 0’ = 96’ depression = 1 in. difference. Or letting e’ = 0.92, 8‘ = 76.6’, r‘ = 1048.7, e = 0. e -e‘ Then - = 93’ depression per 1 in. difference. [NOTE:
- (scp,- cpa) is practically negligible], which
+
+
+
e’-e
From t h e above i t will be seen t h a t t h e wet bulb depression i s proportional t o t h e vapor pressure d i j e r e n c e for any given wet bulb temperature, and approximately proportional for different wet bulb temperatures, when e’ is small with reference t o B ; therefore
FIG.2
Air passing over a moist surface (as i n a drying compartment) drops in temperature toward t h e wet bulb or evaporative temperature, and its vapor pressure and (‘dew point” rise correspondingly toward t h a t of t h e “evaporative” or wet bulb temperature. I t follows t h a t t h e wet bulb temperature remains cons t a n t although t h e d r y bulb temperature drops, and also t h a t temperature of t h e material is substantially constant at t h e wet bulb temperature, if evaporating
%fay, 1921
T H E J O U R N A L OF I N D I T S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
FIQ.3-DRYINQ
freely. These facts are easily deducible from t h e preceding paragraph and they are substantiated in practice. It also. follows t h a t t h e c a p a c i t y of a i r f o r p r o d u c i n g e v a p o r a t i o n i s directly p r o p o r t i o n a l t o its wet bulb depression (and t h e actual evaporation procured is measured by t h e decrease in wet bulb depression), i. e., t h e drop in dry bulb temperature. See Fig. 2 for capacity of air for evaporating moisture. The rate of e v a p o r a t i o n a t any instant has been shown t o be proportional t o difference in vapor pressure between t h a t of t h e liquid or material, and t h a t in t h e air adjacent t o t h e material. Therefore, t h e rate of drying is proportional t o t h e difference between t h e average vapor pressure of t h e air and vapor pressure corresponding t o t h e wet bulb temperature (or temperature of evaporation),
X
(
1 - - a t €3 = 29.92 in., G = lbs. 2;o) air per rnin., a n d F = sq. f t . of surface, then GCfiad(B--St) = dh = K(B - 0’)dF (8) which by integration between t h e limits &, and 0 t o F gives = 0.0000164
el,
CHART
loge
el - e‘
KF
8 ‘= GCpa’ ez -
sq. f t . surface sq. f t . free area, G = 0.071 Av at 100’ 29.92 in. barometer.
Letf
=
F
-
A
=
+
Then from (9) log,
(-)el-e’ el (3 =
+2
. )
f at 100” and 29.92 in.
e2-,
barometer.
(10)
This evidently holds approximately for any barometric pressure and any temperature, since t h e change in air density affects t h e numerator and t h e denominator in nearly t h e same proportion. (See Equation 6.) If we let Q = cu. f t . of air per min., Q = A, and
- e‘ e2 - et R~
loge(-)
= (1
->.
+ 230
Q
(11)
The mean depression may easily be determined equal
MEAN RATE OF EVAPORATION O F F R E E MOISTURE
As t h e air passes over a wetted surface progressively, t h e dry bulb temperature drops in proportion t o t h e moisture evaporated per lb. of air, and approaches the wet bulb t e m p e r a t u r e w h i c h r e m a i n s constant throughout. The rate of evaporation constantly decreases in proportion as t h e wet bulb depression decreases. If we let h = B. t. u. absorbed per sq. f t . per min.,
438
to
This enables us t o calculate (e, - e’), t h e final depression, if t h e initial depression (& - e ’ ) is known; also t h e maximum t e m p e r a t u r e d r o p (0, - 0,) of t h e air through t h e material being dried. The weight of water in lbs. evaporated per min. is
Q(el-ez) 60500
(approx. at e’ = 1000).
(13)
436
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
T h a t is, approximately 1 grain is evaporated per cu. f t . for each 8 5 / a 0 F. drop, or 1.62 grains per lb. of air per degree drop a t 100". Theabovevalues of coefficient
(
1
+ 2;o) -
Vol. 13, N O . 5
saturation curve where 217 grains of moisture will be contained per lb. of air.
apply OlllY
t o wet material freely exposed; as t h e drying progresses t h e area of effective wet surface is reduced and t h e coefficient is correspondingly changed. Also many surfaces are complicated and impossible of determination. Therefore, i t is usual t o determine t h e factor f in Equation 9 experimentally, and t o use this experimental value in t h e design of a compartment dryer. I n other cases, however, as in t h e drying of films or sheets, t h e calculations are sufficiently accurate. A useful relation t o know is also shown by Equation 9, i. e.. for a n y given exposed surface ( S ) and air q u a n t i t y ( G ) the ratio o j the $rial d e p r e s s i o n (0, - 0,) to the i n i t i a l defiression (0, e') is constant regardless o j changes in d r y bulb t e m p e r a t u r e or m o i s t u r e content of the air.
-
D R Y I N G CHART
While all the engineering problems may be solved by t h e physical formulas, previously given, t h e results may be read directly from t h e drying chart (Fig. 3) here presented. The principal curves are t h e saturation curve, giving t h e lbs. weight of water vapor per lb. of dry air at saturation (B = 29.92 in.) and t h e corresponding vapor-pressure curve. The slanting lines represent definite wet bulb temperatures with corresponding dry bulb temperatures and weights of water vapor per lb. of air. I n using t h e chart, one merely has t o keep in mind t h a t t h e temperature drop and corresponding increase in weight of water vapor always occur along a constant wet bulb line, and t h a t , in heating air, t h e weight of water vapor remains constant.
FIG.5
The weight of moisture absorbed is the difference, or 133 grains per lb. of air. The maximum possible thermal efficiency is
-_ e' E ' = el_ _ -82 = 61
- 8,
112
73 per cent.
However, 100 per cent drying effect is both impossible and undesirable. The per cent drying effect (M) is
Fig. 4 gives t h e drying effect M for various values of
(i + +o)
FIG.4
For example, if air has a vapor pressure of 0 . 5 2 in., it has, according t o t h e chart, a dew point of 60' and contains 84 grains of moisture per lb. of dry air. If heated t o 1 7 2 O , a t t h e same moisture content, i t has a wet bulb temperature of 90. If t h e efficiency of moisture absorption were 100 per cent, t h e air would become saturated at this wet bulb temperature, t h e temperature-moisture content relation passing t o the left and upward along t h e slanting line denoting t h e cons t a n t wet bulb temperature condition of 90' t o the
j,also 1 - M.
Fig. 5 gives the maximum thermal efficiencies E and dry bulb temperature 01, various saturation temperatures 8, from 40 t o 120' corresponding t o wet bulb temperatures 8'. The actual efficiency E = ME'. The above is based on t h e assumption of all fresh air being used. T h a t , however, is not the usual or best practice. Instead, i t is customary t o use only from 50 t o 5 per cent fresh air, depending upon the wet bulb temperature and depression desired. The per cent of fresh air with a saturation 8, may be represented by the factor n and its initial temperature as en assuming t h a t i t contains all t h e heat applied t o t h e kiln. Then t h e maximum possible efficiency becomes E' = 8% -. - e' (15)
On -0,
The per cent drying effect of the fresh air admitted may be calculated from the relations. 81 - 82 = n(6n 82 - 8'
- 8,)
=I-M - 8'
81
(16)
(17)
T H E J O U R N A L OF I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
May, 1921
All values are known except 81, 82, a n d M (or On). For example: Let the wet bulb temperature 8' = 100' The max. dry bulb temp. in kiln el = 120' The saturation temperature of entering fresh air eo = 60' Ratio of depression drop in kiln determined from assumed kiln factors M = 0.30 Then, Temp. of fresh air 8% = 232', from Fig. 3 Temp. a t back of kiln e2 = 114', from Equation 17 Drying ratio Mn = 0.894, from Equation 18 Per cent fresh air R = 0.05, from Equation 16 Max. possible eff. E'
=
en- e' = 132' - = 0.77 On -8,
e' e2
= 70" = 84'
E ' = -2o = 30
E
=
t h e regain, or per cent moisture content of t h e material, and corresponds t o t h e same ratio (or per cent) of relative humidity. This ratio increases slightly with t h e temperature. The same thermal laws hold as in the evaporation of free water in unsaturated air, providing we consider t h e air t o reach its maximum possible saturation (from t h e material) not on t h e normal saturation curve b u t on a per cent saturation curve corresponding t o t h e regain. (See Fig. ti.) For example, in cotton, a regain of 6.0 parts water per hundred corresponds t o 60 per cent relative humidity a t 7 7 " F. Then t h e 60 per cent relative humidity curve on t h e drying chart corresponds t o t h e maximum air saturation in contact with cotton having 6 per cent regain.
172'
Actual efficiency E = MnE' =.0.894 X 0.77 = 0.69 Note t h e extremely small percentage of fresh air required a n d t h e high efficiency of evaporation. The efficiencies calculated are of course exclusive of radiation losses and heat required t o warm up t h e material, which are independent a n d must be calculated separately. In practice i t is found t h a t t h e average value of M is about two-thirds t h e maximum depression drop. T h a t is, M maximum would equal 0.45 if t h e average was 0.30. Now assume t h a t all fresh air were used t o obtain t h e same rate of drying, t h a t is, t h e same wet bulb depression. Assume, as before, 8, = 60', O1 - 8' = 20°, and M = 0.30
Then
437
0.67
0.30 X 0.67 = 0.20
Note t h e great decrease in possible and actual efficiency using all fresh air. In general, it may be stated t h a t t h e higher t h e temperature and greater t h e per cent of air recirculated, t h e greater t h e efficiency. EVAPORATION OF HYGROSCOPIC OR A B S O R B E D MOISTURE
I n t h e foregoing we have considered t h e theory of evaporation purely from a physical and thermodynamic standpoint a n d without reference t o t h e chemical or physical behavior of material being dried. The moisture content of a hygroscopic material depends upon t h e relative humidity a n d temperature of t h e surrounding air. This is a perfectly definite relationship for any given material, but varies widely for different materials. This content of hygroscopic moisture is termed regain, a n d is expressed in parts of water per hundred parts of dry material. I n Fig. 6 are given t h e regain curves of cotton and wool for different humidities. I n calculating the rate of evaporation of t h e hygroscopic moisture in a material, account must be taken of t h e fact t h a t t h e physical (or chemical) effect of absorption is t o reduce the effective vapor pressure of t h e contained moisture in relation t o its temperature by a definite ratio. This ratio of effective t o normal vapor pressure a t a given temperature depends upon
FIG.&-RELATION
O F RRO.4IN A N D
RELATIVE HUMIDITY
Thus, air a t 110' and 70' wet bulb (or 50" dew point} would continue t o evaporate moisture from t h e cotton and cool along the constant wet bulb temperature line until i t reached the 60 per cent saturation line a t 80.5" F., which temperature is t h e temperature of evaporation of the material in air of 7 0 " wet bulb temperature. The rate of evaporation with air a t 110" and 70" wet bulb would be proportional t o t h e difference of 60 per cent of t h e vapor pressure corresponding t o 80.5', and t h e vapor pressure (corresponding t o 50" dew point) in t h e air. This rate approaches 60 per cent of t h a t with free water. The process of absorption is t h e reverse of t h a t of evaporation and may be calculated in t h e same manner from Fig. 3. For example, saturated air a t 70", when brought in contact with cotton a t 6 per cent regain, would approach 80.5" at 60 per cent saturation, and therefore t h e absorption temperature of t h e material would be 80.5". I n short, the t e m p e r a t u r e of material h a v i n g a dejinite r e g a i n is a l w a y s $xed with reference t o t h e wet b u l b a n d i n d e p e n d e n t of t h e d r y b u l b t e m p e r a t u r e . DIFFUSION
It has already been pointed out under t h e "Theory of Evaporation" of free moisture t h a t t h e laws hold exactly only for free moisture a t the surface, t h a t is, for relatively thin materials or porous materials, in which t h e moisture flows rapidly t o t h e surface. I n thicker and denser materials, t h e rate of evaporation is limited by t h e rate of diffusion, t h a t is, b y t h e rate a t which moisture will flow from the interior t o t h e exterior. As will be appreciated, this rate varies greatly for different materials, and can only be de-
T H E J O U R N A L OF I N D U S T R I A L A N D ENGINEERING C H E M I S T R Y
438
termined b y experiment. For low rates of evaporation, t h a t is, low wet bulb depressions, t h e theory of evaporation for free moisture and hygroscopic moisture holds very exactly. For high rates of evaporation of heavier materials, such as ceramics, for example, there is a maximum rate for any temperature at which a n increase of velocity will have no appreciable effect in increasing t h e rate of drying. Under these conditions,
FIG.?-VARIATION
OF
RATEO F
EVAPORATION WITH MOISTURE CONTENT
t h e dry bulb temperature plays a n important part for t h e reason t h a t t h e temperature of the material is not at t h e wet bulb temperature, but a t a n intermediate temperature between t h e wet and dry bulbs, depending upon the evaporation determined b y diffusion. The
Vol. 13, No. 5
higher t h e temperature t h e more rapid is t h e diffusion, for t h e reason t h a t t h e vapor pressure of internal moisture increases rapidly with t h e temperature. I n such materials, t h e rate of evaporation per degree depression decreases as t h e surface of t h e material dries. This variation of rate of evaporation with moisture cont e n t is well illustrated by t h e curves in Fig. 7. These results are from actual tests of ceramic materials i n commercial dryers, and serve very well t o illustrate this practical point. The 100 per cent line indicates t h e rate of evaporation with free moisture. It will be seen t h a t this holds up fairly well until about one-half of t h e moisture is removed, and then falls off rapidly as the material is dried out. T h e average rate of evaporation is almost exactly 67 per cent or two-thirds of t h e theoretical free evaporation from a moist surface. I n Material 1 i t is about 30 per cent of the free evaporation from a moist surface. I n applying t h e foregoing theory these practical considerations must always be borne in mind, and for certain classes of materials experiments must be made on a small scale t o obtain accurate d a t a as t o t h e rate of drying as affected b y diffusion. The general theory, however, has its practical value, since i t indicates very well t h e effects of arrangement of material a n d of velocities, temperatures, a n d wet bulb depressions, SO t h a t from any known operating condition comparative results may be calculated for some other desired condition. I n this a knowledge of t h e fundamental theory is of great assistance and value.
The Compartment Dryer By W. H. Carrier and A. E. Stacey, Jr. CARRIER ENGINEERING CORPORATION, 39 CORTLANDT ST.,N e w YORK,N.Y.
T h e a r t of successful air drying, or, more properly, air processing, is coming t o be appreciated more and more as a process of chemical and physical treatment a p a r t from the mere removal of moisture. There are numerous classes of materials which require special treatment with respect t o (1) temperature, (2) relative humidity, and (3) rate of moisture removal. Most such materials are of animal or vegetable origin, and usually possess exceptional hygroscopic or absorption properties. Frequently they are of a colloidal nature. Among such materials t o which air processing is being successfully applied, the following may be mentioned: *Greenlumber Macaroni Developed films Textiles (natural and artificial) Cured tobacco Coated paper Milk Green tobacco (in curing for cigar wrappers) Tea Washed rubber Writing paper (after sizing) Photographic films Gelatin capsules Certain chemicals Chicle (for chewing gum) Certain industrial ceramics Painted and varnished surfaces, etc.
T h e optimum temperatures and humidities for t h e above vary over a wide r a n g e f r o m 75" t o 180" F. in temperatures, and from 90 per cent t o 15 per cent in relative humidities. The temperature and humidity requirements usually vary considerably in accordance with a definite established schedule. A
vigorous air circulation is usually important t o secure uniformity and maximum allowable effect. T h e time element is best regulated by controlling t h e wet bulb depression and temperature. I n some processes there are certain chemical or biochemical changes t h a t must be accurately timed with respect t o t h e percentage of moisture removed. I n these, i t must be kept in mind t h a t t h e velocity of chemical reaction a t a given moisture content of t h e material depends upon t h e temperature of t h e material (which corresponds t o t h e wet bulb temperature of the air). As chemists will appreciate, this velocity of reaction doubles approximately for every 18' F. increase in temperature. Since t h e vapor pressure also approximately doubles with each 18" F. increase in temperature, t h e velocity of chemical reaction is practically in proportion t o t h e variation in vapor pressure, as produced b y variation in wet bulb temperature. On this account, there are certain critical temperatures, as well as humidities, in t h e processing of such products as green tobacco, macaroni, etc., where certain definite chemical changes are necessary, b u t where further chemical action must be prevented. I n drying many hygroscopic substances, there are two critical points with respect t o relative humidity. The first is where the free or nonhygroscopic moisture
