is
ieleetric
C. A . RIANN, N. K. CEAGLSKE, AND A.
J
U
c. OLSON’
Unicersity of .Vfinnesota, Minneapolis, I(finn.
An investigation has been made to determine the mechanism by which sand dried when placed in a radiofrequency field. The heat required for the vaporization of the liquid was obtained from the dielectric loss of the material. The constant rate of drying increased with an increase in the potential and frequency of oscillation of the field. Raising the surrounding air temperature increased the rate of drying, while an increase i n air velocitjdecreased the rate of drying w-hen the air temperature was lower than the sand temperature. The rates of drying
obtained with the larger spherical grains of Ottawa sand were higher than those for the smaller, angular particlea of abrasive sand. Under comparable conditions, the rates of drying of different liquids from Ottawa sand increased in the order of ethyl alcohol, carbon tetrachloride, and water. The mechanism of drying was found to be the same as for air, vacuum, and radiant heat drying methods. The rates obtainable M e r e higher than those found by the other methods and were limited by the boiling point of the liquid.
HE industrial application of radio-frequency heating is
as homogeneity, nonhygroscopicity, and uniformity in size and shape. Furthermore, these same materials had been used by previous investigators, so t h a t a comparison of the data could be made. The use of a radio-frequency field t o heat nominally insulating materials is called dielectric heating, and materials which are composed of polar molecules are best suited for this action. A great deal of the fundamental theory applying to radio-frequency heating stems from Debye’s (3) work on polar molecules and on the dielectric and optical properties of molecules under the influence of an electric field. The application of this theory is given in a series of articles by Murphy and Morgan (IO), a book by Brown, Hoyler, and Bierwirth ( I ) , by Schutz s n d McMahon ( 1 4 ) , and in papers on plastic materials by Fuoss (6). The power generated in a dielectric material placed between two parallel plate electrodes may be expressed as
comparatively new, although its use was reported in 1864 by von Siemens before the Academy of Science in Berlin ( 1 9 ) . During the period betweeen 1890 and 1900, Tesla performed a number of experiments using a radio-frequency field. It was in this period that d’Arsonva1 studied the effect of the high frequency field on physiological processes and is later reported to have killed bacteria n i t h it (11). I n the late 1920’s and early 1930’6, high frequency medical diathermy was used. From 1935 to the present, the number of industrial applications have increased rapidly. The advantages of radio-frequency heating include the following ( 1 ) : The heat can be generated rapidly and uniformly throughout the material; or concentrated in portions of highest loss factor, eliminating the necessity of heating the entire body. The variation in the amount of heat is easily controlled, and the process is adaptable t o automatic control. The generating equipment presents a n economy of space and flexibility of adaptation, is simple t o operate and easy and economical to maintain, assuming a reasonable tube life. This method achieves results not possible with other processes and can increase the speed of a process, thereby decreasing labor costs. Power generated by high frequency equipment is more costly than t h a t generated by most other methods. Consequently, the advantages listed above must be very important t o the process to make i t economically feasible. The last mentioned advantage usually contributes much to the final decision. A review of the work in the field of dielectric drying by Friedman (6) tells of the applications t h a t have been made to some materials. I n many instances, the reason for using dielectric drying was the large saving in drying time and the achievement of a lower final moisture content than t h a t possible by other methods. Friedman’s accounts indicate the lack of published information concerning the underlying theory and mechanism of dielectric drying. The heat required to evaporate a liquid from a material in a drying operation may be transferred to the material by convection from hot air, by conduction from warm surfaces, by radiation from near infrared lamps, and by internal generation due to the dielectric loss in a radio-frequency field. The purpose of this investigation was t o study the mechanism of drying when using the fourth method, and to compare the results with those obtained by the other three methods. This operation is called dielectric drying. Ottawa and abrasive sands were selected for these experiments because of their physical characteristics, such 1
Present address, California Research Corporation, Richmond, Calif.
p where
= 1.41(w2)(er)(p
f.)
(113
P = power concentration, watts per cu. inch of material
f = frequency of oscillating field, megacycles E = voltage gradient, root mean square kilovolts per inch e’ = dielectric constant of material p.f. = power factor of material The product, ( e ’ ) ( p . f , ) , is known as the loss factor, e”, of the material. I n Equation 1, the role of the dielectric constant and the power factor of the material is evident. The dielectric constant decreases as the frequency increases. For polar liquids, t h e temperature coefficients of e’ are negative and fairly large. The successful explanation of this fact by the Debye theory is one of its main achievements. The dielectric constant of solid materials varies slowly with temperature, and the coefficient may be negative or positive. The power factor of dielectric materials passes through a maximum value in its variation with frequency. However, in the radio-frequency range, the variation may be either positive or negative, and the composition of the material is very important (1, 8). For many solid materials the variation is slow enough to be considered a constant for design purposes. T h e power factor of liquid dielectrics changes more rapidly than that of solid dielectrics. Schutz and McMahon ( 1 4 ) have shown t h a t for a given material of constant composition the loss factor is a function of particle size. The heating rate increases rapidly with an increase in particle size.
1686
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1949
u
AIR
I10 v. AC-DC SUPPLY
AI R HEATER
RADIO-FREQUENCY OSCl L L A T O R
"llYll , A D "
--------__--_---
UNIT
~
+ I
RADIO-FREQUENCY /I,
POWER U N I T
BALANCE
IRECORDER- CONTROLLER^ ARRANGEMENT OF APPARATUS
Figure 1
Because the power concentration in the material is proportional to the square of the voltage gradient, the best way to increase the heat generated is to raise the voltage across the electrodes. There are limits on the amount the voltage may be increased, and the factors to be considered include the spacing of the electrodes, the dielectric strength and shape of the material between the electrodes, the homogeneity and temperature of degradation of the material, and the amount of moisture present. The last item is particularly important in drying operations. If the voltage gradient is too high, the liquid will boil inside t,he material, creating vapor and exploding the solid. Aside from the loss of material, a product of reduced size may not be desirable. By an increase in the frequency, it is possible to decrease the voltage gradient and still obtain the required power concentration. This means the heating may be carried out successfully without approaching the limits set by the factors mentioned above. There is, of course, a limit on the frequency, and this is determined by the oscillating equipment and the geometry of the material. It is difficult t o generate high power concentrations at a high frequency. The final choice of voltage gradient and frequency can be made only after a careful consideration of the factors involved. The loss factors of solid dielectric materials, particularly if they are heterogeneous, have a broad maximum. This allows a band of frequencies to be used rather than a n optimum one. The selection of the voltage gradient in combination with the frequency to give a definite power concentration in the material can then best be made by taking into account the desired physical characteristics of the product. The amount of dielectric drying data in the literature is very small, and none has been found for sand. The results of experiments of different workers on the dielectric drying of compressed vegetable blocks were not in very close agreement. Since that type of material is decidedly heterogeneous, the disagreement would not be surprising. A great deal of work has been accomplished on the dielectric heating of wood, and a considerable variation in its electrical properties in a radio-frequency field has been found between samples from the same piece ( I ) . Whitehead (18) has developed a calibrated method to determine the electrical properties of a material under radio-frequency conditions. However, using identical samples of a material, as much as 5 to 10% variation in the initial values of radio-frequency current has been found. It may be expected, then, t h a t the reproducibility of results of such experiments may not be very good. Such a situation was found to be the case in this investigation. However, the effects of changing the variables on the rates of drying are well defined, and i t is possible to draw conclusions from them.
I I I
1687
The present paper is not intended to be quantitative. The work is being continued and results will be published when completed. EXPERIMENTAL INVESTIGATION
The general arrangement of the equipment is shown in Figure 1. The radio-frequency field for these experiments was generated by a Calectron unit of approximately 2-kw. capacity. The parallel plate electrodes were in a vertical plane, allowing a free passage of air upward and/or horizontally between them. T h e voltage across the electrodes could be adjusted continuously by a Variac in the power supply. The basic frequency of operation was determined by the choice of tank coils. The Ottawa and Nos. 2 and 3 abrasive sands used were obtained from the Minnesota Highway Department and Minnesota Mining & Manufacturing Company, respectively. Pyrex dishes with parallel sides, were used as containers, and sand was added t o a weighed amount of liquid, until a saturated condition existed, The sand and liquid were a t room temperature at the start of each run. The full container was placed between the electrodes of the heater, on a Mycalex sheet, supported by a Mycalex rod on one arm of a torsion balance. This balance, accurate t o 0.1 gram, was a part of an automatically recording-controlling weighing device constructed for this purpose (Figure 2 ) . The heater was turned on and adjusted t o the desired voltage, as read on a vacuum tube voltmeter built for use with this apparatus. T h e voltage was maintained constant throughout the run, and a continuous record of loss in weight of liquid against time was obtained. The dry weight was found after the sample had been in an oven a t 110" C. overnight. The temperature of the surface and of the interior of the sample was obtained to the nearest 0.5' F., from a portable Thwing otentiometer and two No. 30 copper-constantan thermocoupres. Each time the readings were made, usually every 15 or 30 minutes, the radio-frequency field voltage was reduced t o zero t o eliniinate induced e.m.f.'s in the leads, and to minimize any localized heating around the thermocouples. This procedure consumes approximately 15 seconds, so that the loss in heating time was a small percentage of the total. The effect of the radio-frequency field on the thermocouples should be very small since the loss factor is low. This was checked by taking temperature readings at intervals after the ower was shut off. There was no rapid change in temperature an$ therefore it was assumed the couple and Sample temperatures were very nearly alike. Room ajr was used for these experiments, and no attempt was made to control the humidity. However, for a greater portion of
Figure 2.
Equipment
INDUSTRIAL AND ENGINEERING CHEMISTRY
9688
Vol. 41, No. 8
desired could be calculated to determine the drying rate curve. These values weie computed with the aid of a calculating machine. I, the relative humidit) was in the neighboihood of 20YG, and the air temperature was ncar 75" F. If a forced cirrulation of air across the sample as desiied, the proper piping connectionb were made and the blovi er speed was adjusted by a rheostat The velocity of the ail acioss the surface of the sample was obtained with a hot wire anemometer. I t \vas possible to beat the air being blown across the sample by means of coil heaters in a compartment folloiiing the blower. The wet bulb and dry bulb tempeiatures of the ail, either iooin or heated, were continuously recorded on a Bnstol two pen psychrometer The wet and d i y bulb blower unit was constructed so t h a t the air passing over the bulbs was exhausted into the room. From the data recorded by the M-eighing device the drying rates could be computed at regular intervals of moisture content, without the neces.;ity of knowing the actual weight or the actual loss in weight a t any given time. A sample recorder chart 1s shown in Figure 3 The slopes of the recorded lines 1% ere measured by a Richards-Roope tangent meter, to the nearest tenth of a degree. Knowing the area of the top of the container, it was possible t o multiply the numerical value of the tangent of the slope angle by a constant and obtain the drying rate in a consistent set of units, The moisture content, a t those points at which the drying rate was determined, nas found by a simple niultiplication and a series of suhtractions from the initial \ d u e . As many points as
~
Tfie data obt.ained from each of the experimental runs were plotted on coordinate paper as drying rat'e against moisture content. Each of the drying curves could be divided into four portions: the increasing rat,e period, the constant rate period, the uniform falling rate period, and tmheaccelerated falling rate period. The last, three drying int,ervals are of the greatest import,ance in studying the mechanism of drying nonhygroscopic, granular materials. The duration of the increasing rate period depended upon the final level attained when the constant rate period began. T h e n the final level as relatively low, the increasing rate period WRS shorr; and i t was longer when a high constant rate was reached. The point a t which the constant rate period ends and the uniform falling rate begins is called the first critical moisture content. The change from the uniform falling rate period to the nccelerated falling rate period occurs a t the second critical moisture content. The results of the experiments can most appropriately be discussed by showing the effect of the variables on the value of the const,ant rate of drying. The temperature of the sample during the run gives interesting informat,ion, and is helpful in explaining the mechanism of drying and the action of the field on the sample.
0 OTTAWA SAND
3 SAND 0 NO 2 SAND FREQUENCY GIVEN A
NO
__
~
-
-3
A
O T T A W A SAND FREQUENCY I 6 8 MC. RUN NO VOLTAGE 0 43 4400 0
41
3900
I I
2 3 FIELD POTENTIAL
MOISTURE CONTENT
Figure 4.
LBS./LB.
DRY SAND
Effect of Field Potential on Rate o f Dryin::
4
5
6
r e 9 1 0
VOLTS X IO-?
Figure 5 . Effect of Field Potential Constant Rate of Drying
011
August 1949
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
1689
EFFECT O F FIELD POTENTIAL ON RATE O F DRYING
Figure 4 shows the drying curves for water from Ottawa sand a t a frequency of 16.8 mc., and three different field potentials. The value of the constant rate period increases with increasing voltage. In considering Equation 1, the assumption could be made that the rate would vary as the square of the voltage. However, there are other factors to be taken into account which make such a relation invalid. Initially the sample was a t room temperature, and according to the previous discussion, when the field was applied the temperature of the sample increased. The heat generated in the sample can be consumed by three processes-namely, raising the temperature of the sand, water, and container, evaporating the a a t e r from the sample; and losses by conduction, convection, and radiation to the surroundings. The manner in which each of these changes with an increase in temperature is important in determining the effect of voltage on the constant rate of drying. The first is relatively unimportant, especially after the heating up period. The second is constant over the small temperature range involved. Under natural convection conditions, the rate of heat loss from vertical plates due to convection is proportional to the 5/4 power of the temperature difference between the plate and the air (9). The rate of heat loss due to radiation is proportional to the difference of the fourth powers of the temperatures. Both of these losses increase with a rise in temperature; however, t h a t owing to radiation increases much more rapidly than the convection loss. When the rate of heat input is equal to the rate of heat consumption, the sample attains a n equilibrium temperature, and thr constant rate of drying period begins. The effect of inrreasing the voltage between the electrodes is to raise the equilibrium temperature of the sample, and consequently raise the constant rate. The equilibrium temperature, corresponding to a particular voltage, depends upon the heat losses, which are not a linear function of the temperature. It would, then, be difficult t o obtain a simple relation between the voltage and the constant rate of drying. Figure 5 is a log-log plot of constant rate of drying against peak voltage between the electrodes. The slopes of these lines vary from I .36 to 3.44, which shows that the combination of the effects discussed above does not allow a quantitative conclusion to be made. However, qualitatively, the effect of an increase in the field potential is to increase the constant rate of drying, and this variation is greater than linear. EFFECT O F FREQUENCY ON RATE O F DRYING
The power generated in the sample is proportional to the first power of the frequency in accordance with Equation 1. However, the same factors as were discussed in the previous section are again applicable here. It would not be expected, then, that an increase in frequency would necessarily cause a proportionate increase in the constant rate of drying. The results of the drying runs using No. 2 and No. 3 abrasive sands exhibited an increase with frequency. Drying rate curves for No. 3 sand are shown in Figure 6. The first criticnl moisture content a t the 101%frequency is higher than for the other two runs. The same was true when a voltage of 3500 was used. The specific reason for this cannot be given; however, there may be a decrease in heat input due to a peculiar combination of conditions a t that point. The variation of the constant rate of drying with frequency is shown in Figure 7 for the three sands. When using the Ottawa sand, a maximum in the constant rate was obtained a t 16.8 mc., for both 4400 and 3400 volts. An explanation of this
L B S / LB. DRY SAND Effect of Frequency on Rate of Drying
MOISTURE CONTENT
Figure 6.
apparently anomalous result must lie in the difference between the combination of Ottawa sand and water, and t h e abrasive sands and water. In order to find a complete explanation, it would be necessary to determine experimentally the dielectric constant and the power factor of the sand-water system. These measurements can be made by use of a radio-frequencv biidge, a susceptance variation resonant circuit, or a &-meter. EFFECT O F MATERIAL ON RATE O F DRYING
The drying curves of water from each of the three sands, at 11.8mC. and 4500 volts field potential, are shown in Figure 8. The size and shape of the same kind of material being dried make a differencein the value of the constant rate, The physical properties of the sands are listed in Table I.
TABLE I. PHYSICAL PROPERTIES OF THE SANDS No 2 Screen analysis % Through 20 dn 30 Through 24 on 28 Through 28 on 35 Through 35 on 4 8 Through 48 on 65 Average radius, om. Apparent density % air space Wt. yo water a t saturation Shape of particle
42 56 2 0 017 1 35 48 2 35 7 Angular
No 3
Ottawa
100
60 40
0 026 I 43 47 2 33 1 Angular
0 036 1 68
38 6 23 4 Spherical
The values of the constant rate of drying for the three sands, listed in order of decreasing rate, are given in Table 11.
-.
g3, TENTIAL G I V E N
-%32
5 e4 eo
2 I*
0
oL
1
b
I
1
,!,
7.0 I
'
LS
I
' ' ' '
yl
55
40
FREQUENCY MEGACYCLES/SECOND
Figure 7.
Effect of Frequency
0x1
Constant Rate of Drying
INDUSTRIAL AND ENGINEERING CHEMISTRY
1690
o
MOISTURE C O N T E N T
Figure 8.
LBS./LB
53
than t h a t of tlie sample, as was the case in these experiments, another effect occurs which counterbalances the beneficent action of a decrease in film thickness. Natural convection conditions no longer prevail, and the effect of increasing the velocity of the air is t o increase the value of the heat transfer coefficient. This will, in turn, increase the heat loss, thereby decreasing the temperature of the sample and lowering the rate of drying. This same action has been found in radiant heat drying of sand by Stout, Caplan, and Baird (17). The constant rates of drying ale plotted against air velocity in Figure 9 together wibh a curve for a 7/8inch-depth sample of No. 2 sand from the data of Stout, Caplan, and Baird. The similarity in the results of the influence of air velocity on the constant rate by these two methods of drying is rather clearly shown.
OTTAWA
DRY SAND
Effect of Material on Rate of Drying
Table I1 shons that the constant rates for Ottawa sand are always higher than for the abrasive sands, and that tlie order of the rates for thc latter are not consistent. Also the rate variation between the abrasive sands is small and there is a large difference between them and the Ottawa sand. This difference indicates a possible effect of particle shape and apparent density in addition to the T-ariation of particle size. EFFECT OF AIR VELOCITY O h RATE OF DRYING
The deciease in the constant rate of drying with an increase in the 'iir velocity observed in this investigation is diametrically opposite t o the variation obtained in air drying studies ( 1 1 , 1 6 ) I n the latter ease, it has been found that increasing the air velocm ity increases the constant rate of drying, which is due to a decrease of the thickness of the film above the surface of the material through which the vapor and heat must diffuse. The same diminution process holds true for these experiAIR V E L O C I T Y FT./SEC. ments. However, when the ambient temFigure 9. Effect of Air Velocity perature was lower on Constant Rate of Drying
Vol. 41, No. 8
EFFECT OF AIR TEMPERATURE QN RATE OF DRYING AND SAMPLE TEMPERATURE
When the temperature of the air and the enclosure around the sample is increased, the heat losses decrease. With the same amount of heat generated in the sample, the drying rate a t the higher ambient temperature would then be increased. This result is verified by the drying curves in Figure 10, which show an increase in the rate with air teniperature a t two field potentials. A t an air velocity of 7.5 feet per second and a field voltage of 3400, a change in air temperature from 82" to 102" F. increased the constant rate of drying from 0.92 t o 1.14 lb./(hr.)(sq. ft.). At a field strength of 1900 volt3 and an air velocity of 6 feet per second, raising the temperature of the air from 100" to 125" F. increased the rate fiom 0.47 to 0.59 1b / (hr )(sq . i t ). The air temperature in run 16 is higher than t h a t of the sample, and sensible heat is transferred into the material rather than being lost from it. The radiant heat losses still exist, however, and the resulting heat balance produces a very flat uniform falling rate curve. In both runs 16 and 17, the drying rate decreases very rapidly duiing the accelerated falling rate period, in fact, inore sharply than in any of the other drying runs. This drop is followed by a slow decrease in rate to a value of zero when the sand is dry. The critical moisture content for run 17 is out of line when compared with the other values obtained for Ottawa sand. This same phenomenon occurred in run 55 and was discussed in connection with Figure 6. The influence of air temperature on sample temperature is illustrated in Figure 11, where the temperature of the surface of
.
.
.
OTTAWA SAND FREQUENCY 2 5 5 MC. AIR AIR FIELO TEMP VELOCITY POTENTIA 82.F. 75 FTPSEC. 34OOWX IM 7.5 II 34M) I D 120 6 u 1900 DI
~
TARTJ: IT. EFFECT OF FREQIJENCY AX'D VOLTAGEO N COXSTANT RATEOF DRYISG
F20
i
Constant Rate, Constant Rate, Lb./(Hr.)(Sq. Ft.) Sand Lh /(Hr.)(Sq. Ft.) Fiequeney 11.8 MC. 4300 volts Field Potential 3500 T-oits 1.18 Ottana 2.46 Ottawa No. 3 0.98 No. 3 0.56 No. 2 0.70 No. 2 0.50
Sand
4100 volts
Ottawa so. 2
No. 3
Frequency 1 6 . 8 Me. Field Potential 3400 volts 3.44 Ottawa L37 1.28 No. 3 0.62 1.18 No. 2 0.47
Frequency 2 4 . 8 Me. 4400 ~ o l t s Field Potential 3300 volt5 Ottawa 1 14 Ottawa 2.45 1.81 h-0. 2 0 68 so. 2 h'o 3 1.71 3-0.3 0 62
0
02
04
06
OB
10
IP
14
MOISTURE CONTENT
Figure 10.
16
18
20
LBS/LB
22
34
W
28
30
DRY SAND
Effect of Air Temperature on Rate of Drying
INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1949
OTTAWA SAND F I E L D POTENTIAL I900 VOLTS FREQUENCY 255 MC RUN NO. AIR TEMP. AIR VELOCITY
2 c1
&
:
G ?I
0 0
a
15 16
200
LL(
w w
??OF.
160
125 *
n W
a
Bvj
a
+
mi A
120
," W d
t3
FJ
z>
@I-
a n
w
0 4
LA.
LL.
0
40
a
3
W I-
cn
< a
4
.M
.m
12
15
MOISTURE CONTENT LBS./LB
20
24
DRY SAND
Figure 11. Variation of Drying Kate and Sample Temperature with Air Temperature and Velocity
the sample is plotted against the moisture content for three different air temperatures. Runs 15, 16, and 17 were made a t the same field conditions, and a t each of the indifferent ambient temperatures there was a temperature gradient in the sample. In both runs 16 and 17, the temperatures decreased slightly during the falling rate period. In the accelerated falling rate period there was a sharp rise followed by a zone where the temperature was constant. The relative values of drying rates and sample temperatures shown in Figure 11 suggest the possibilities of a control of sample temperature and drying rate. The temperature of the material during run 15 was the highest of the three, and yet the rate was the lowest. The net effect of changing the air velocity and temperature in run 16 was approximately to double the drying rate of run 15 with the surface temperature of the sample remaining 18"F. lower in the constant rate period. EFFECT O F DIFFERENT LIQUIDS ON RATE OF DRYING
Several r u m were made a t the various frequencies and field potentials t o obtain the rate of drying of carbon tetrachloride and 95% ethyl alcohol from Ottawa sand. I n all the runs, the air velocity mas zero and the air temperature approximately 75' F. The drying curves in Figure 12 are for distilled water, carbon tetrachloride, and ethyl alcohol a t the same frequency and field voltage. The differences between these curves are closely related to the properties of the liquids, which are given in Table I11 (If ). The difference in drying rates exhibited in Figure 12 are the result of a combination of effects-namely, the heat input and losses, and the latent heats of vaporization. The loss factor of ethyl alcohol i s low in comparison with water. Carbon tetmchloride is a nonpolar liquid and its loss factor is very low, so that the heat input from it is the lowest of the three (7). On the basis of power generation, the drying rates should rank in the order of water, alcohol, and carbon tetrachloride. The experimental results did not verify this sequence and the discrepancy can be attributed t o the difference in latent heats of vaporisation. Alcohol and carbon tetrachloride have approximately the same boiling point; however, the latent heat of vaporization of alcohol is nearly four times that of carbon tetrachloride. The temperature of the sample during the constant rate period was nearly the same for both cases, so that the convection and radiation losses were Figure 12. almost equal. The resulting heat balances,
1691
in the range of field conditions used, gave drying rates of different liquids from Ottawa sand in the order of water, carbon tetrachloride, and ethyl alcohol. The different liquid percentages a t saturation are, of course, due to the difference in specific gravity of the three liquids. There is also a distinct difference in first critical liquid contents exhibited by the three fluids. The range for alcohol and carbon tetrachloride was 0.070 to 0.116 and 0.141 to 0.230, respectively, compared with 0.041 to 0.062 pound per pound of dry sand for water. In addition to the specific gravity, the variation may be attributable t o the different surface tensions of the liquids and the resultant capillary forces, and also to the degree to which the liquids wet the sand. This tendency was least for carbon tetrachloride, and greatest for water. The descending plane of vaporization after the second critical liquid content was reached was visible in each case. For water and carbon tetrachloride the second critical point was in the neighborhood of 0.013 to 0.020 pound per pound of dry sand, while a range from 0.040 to 0.050 was obtained for alcohol. The temperature variation of the samples during the drying runs is shown in Figure 12. When carbon tetrachloride is being evaporated, the temperature of the sample increases after the first critical point is reached. The increase is not very large and is followed by a constant temperature when the sand is nearly dry. With alcohol as the liquid, the temperature decreases a small amount after the first critical point is reached and then increases to a constant value. The point a t which the temperature of the sample, with carbon tetrachloride as the liquid, increases is not too closely allied with the first critical point, except that i t follows it. T h e heat generated in the sample arises chiefly from the sand, as pointed out above. When the drying rate has decreased sufficiently, the heat input becomes greater than the losses, and the temperature increases. In the case of alcohol, the heat input is the sum of that from the sand and the alaohol. However, according to the previous discussion, the amount of heat generated by alcohol is s o t as large as for water. Durfng the falling rate period, the heat input
TABLE 111. PROPERTIES OF LIQUIDS Water 1 Specific gravity Boiling oint ' F. 212 Latent [eat 'of vaporization at boilins; point, B.t.u./lb. 972 Surfaae tension (to air at Z O O C.),dunes/ om. 72.8 Dielectric constant 81
Carbon Tetrachloride 1.60
Ethyl Alcohol 0.79
170.2
173.1
83.6
368 24.1 24.2
26.8
2.24
,
RUN NO
LIQUID
CONTENT
110'
LIQUID
LBS./LB. DRY SAND
Effect of Liquid on Rate of Drying and Sample Temperature
INDUSTRIAL AND ENGINEERING CHEMISTRY
1692
F I E L D POTENTIAL V O L T S
-
Figure 13.
Vol. 41, No. 8
openings$begins t o recede, and air takes its place. The power generated in the air is negligible and, consequently, the total heat input is decreased, causing the temperature of both the surface and inteiior of the sample to dimnish. This is illustrated in Figure 14, which is a plot of the drying rate and temperature of the surface and the interior of the sample against moisture content for run 56, which is typical of the runs with water when the ambient temperature is lower than that of the sample. During the uniform falling rate period, the level of the water in more of the capillaries drops below the surface. This allows more air to enter the pores and further decrease the heat input. The accompanying drop in temperature and drying rate, as shown in Figure 14, is indicative of this. At the second critical moisture content, the water level in the smallest of the capillaries drops below the surface, so that the water con-
FREQUENCY MEGACYCLES/SECOND
Effect of Field Potential and Freaiienci on Constant Kate of Drying
and the rate of heat loss due t u vaporization diminish. U~.causea much greater portion of the heat comes from the sand, the input becomes larger than the losses, and the temperature rises. The variation of the constant rate of drying of alcohol arid carbon tetrachloride with frequency and field potential was found to be generally the same as with water. The curves in Figure 13 show that the constant drying rate increases with frequency and field voltage. The decrease in rate Fith frequency between 16.8 and 24.8 me. exhibited by water and Ottawa sand is not found .here. RIECH-INISM O F DIELECTKIC DRYING
'TIw determination of the mechanism oi drying of the sands
~ ~ ~~ it ~~ ~~ r ~t ~ ~i ~~~ l ~ ~ ~ ~ ~ h crease in heat input is experienced than-before. The water level in t'he capillaries recedes further into the sand, so that the evaporation of moisture must take place in the body of the sample rather than on the surface. This action could be observed during the run by noticing the level a t which the moist grains of sand touched the sides of the glass container. During the accelerated falling rate period, this level made a horizontal line around the dish, and the recession of this line away from the surface was easily discernible. This action is called the receding plane of vaporization, and has been found present in the other methods of drying sand. The greater rate of decrease in heat generated causes a corresponding faster decline in the drying rate and the temperature. These effects are evident' in Figure 14. As the moisture concentration approaches zero, the drying rate also decreases to zero. Even though the power generated in the air is negligible, the sample is obt,aiiiing some heat, from the sand. For this reason, the temperature does not decrease to that of the ambient conditions. The temperature of t,he interior is naturally higher than that a t the surface because of the difference in heat losses at the two places. For any one of t,he three sands, the level of the constant rate of drying did not. appear in general to influence the value of the critical moisture contents. I n other words, it was the net capillary forces in each sand which determined, within a small range, where each period of drving occurs, rat.her than an influence of heat input. The first critical moisture content of the sands was found t,o increase with a decrease in the size of the particle. This samz relation was observed by Ceaglske and Hougen ( 2 ) and Shepherd, Hadlock, and Brewer ( 1 5 ) . The range of first critical moisture contents for Ottawa, K O . 3, and Xo. 2 sands are 0.041 t o 0.062, 0.066 t'o 0.080, and 0.079 t o 0.090 pound of liquid per pound of dry sand, respectively. The three sands used in t'hese experiments exhibited the same type of drying curve, and t>hethermal history of the sample w a y similar in each case. Each of the sands has a different critical moisture content, depending upon the particle size. The mechanism proposed by other investigators t o explain the movement of
used i n these cxperiments vas obtained from a study of the drying curves. By changing the field potential and frequency, it was possible t o obtain a large variation in the iates of drying and some change in the shape of the curves. The first critical moisture content of the sands is of particular interest. The temperatures of the sudaice and interior of the sample throughout the run are helpful in following the drying mechanism. The amount of heat generated in the sample, as indicated by the temperature, is related to the drying rate during the run. T h e moisture distribution and mechanism of drying sand by air, vacuum, and radiant heat methods have been studied by numerous investigators ( 2 , 16,16, 1 7 ) . The mechanism proposed by these investigators is essentially based on the fact that a net capillary force controls the movement of liquid in the sand. This same mechanism call be used to explain the liquid movement and temperature variation during thc drying runs of these espeiiments. T h e moisture concentration at the surface rernains essentiallg the same during the constant rate period. The net capillary force in the smaller capillaries is sufficient to maintain the liquid a t the surface. The liquid level in the capillaries with inci easingly larger openings is slightly below the surfare. As theliquid is evaporated from the surface during the constant rate period, the level of the liquid in the largest c q i l laiies falls below the surface. HoTT-ever, the majority of the capillaries maintain their liquid a t the surface. Since the surface moisture concentration remains the same during this drying period, the heat generated at the surface is also approsimately constant, and the rate of drying does not change. The temperature of the surface and the interior of the sample is nearly constant during this period, indicating that the heat balance is maintained, even though the sample is continually losing liquid. I n order to obtain a complete history of the heat generated during &hisdrying period, and thereby fully explain the constancy of the heat balance, it would be necesaary t o know the variation of thP loss facto1 and the voltage gradient of the sand-water system. At the first critical moisture content, the level Figure 14. of thc liquid in the capillaries with the larger
200
160
I20
u. W
w
BO
40
w
IZ
I8
20
MOISTURE CONTENT L B S / L 8
24
28
32
H
DRY SAND
Rate of Drying and Sample Temperature Variation
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INDUSTRIAL AND ENGINEERING CHEMISTRY
August 1949
TABLE IV.
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COMPARISON OF DRYING METHODS
Drying Method Radiant Ais Vacuum Rates, Lb./(Hr.)(Sq. Ft.)--.KO.2 sand 0.13-1.81 1.45--1.90(17) 0.385-0.616 (8) Ottawa sand 0.14-4.92 ... 0.067-0.68 (16) Other ... ... 0.21-0.46 ( I S ) 0.03-0.2 (4) (1 1) ,-Critical Moisture for 1-Inch Layer, Lb. Liquid/Lb. Dry Sand-. No. 2 sand 0.08-0.09 0.09-0.13 ( 1 7) 0 . 1 0 ( 8 ) Ottawa sand 0.05-0.06 0.02-0.04 (16) Other ... ... 0.07-0.10 (15) a Authors’ data. Dielectrica
I
.
.
water in the sand is also applicable in these experiments. The temperature variation in the sample during the drying run further substantiates this process. COMPARISON O F DRYING BY DIFFERENT DRYING METHODS
1
,4 comparison of the ratio of drying and the critical moisture contents for the four methods of drying is given in Table IV. I n both radiant heat and dielectric drying the rates are considerU N S A T U R A T I O N OF AIR MM.OF MERCURY ably higher than in air or vacuum drying. For the No. 2 sand in dielectric drying the rates could have been increased by increasing Figure 15. Variation of Constant Rate of the power input. The rates for Ottawa sand are much higher Drying with Unsaturation of Air than for the No. 2 sand. The authors are of the opinion t h a t these high rates could not be obtained by any other method. The first critical moisture contents have been found to be almost identical by the different investigators. This point is TABLE V. SUMMARY OF DATA AND RESULTS independent of the rate of drying, the During Constant Rate Period drying conditions, and the drying method. Drying UnsaturaIt is a function of the layer thickness, the Air Relative ?Lir rate Surface tion of Field Frequency, Potential, Temp., Humidity Velocity, lb./(hr.) temp air, particle size and shape, and possibly the Run Me. Volts F. of Air, % Ft./Sec. (sq. f t . ) F.” mm. Hg degree of packing. Ottawa Sand and Distilled Water In air drying, the sample temperature 1 25.0 92 0 1.22 ... 6 25.7 is lower than that of the surroundings80 2 1.18 ... 25.7 7 82 0.90 7.5 ... .., i.e., in general i t approaches the wet bulb 8 25.7 102 1.15 7.6 . .. 10 25.5 73 0 1.72 177 35% temperature during the constant rate 13 25.5 75 0 146 0.75 163 14 25.5 period. I n radiant heat and dielectric 77 0 166 1.23 263 25.4 15 77 0 120 0 . 3 1 70 drying the sample temperature may be 16 25.5 125 0.58 6 102 37 25.5 17 100 6 0.49 95.5 27 above or below the surrounding tempera25.1 18 69 0 2.45 178.5 369 20 25.0 ture, depending upon the heat balance for 70 1.15 0 162 250 23 36.5 72 0.14 0 33 90.5 the particular conditions involved. Dur24 36.5 73 0 0.18 94 36 41 16.8 76 0 2.29 187 446 ing the two falling rate periods in air dry16.8 42 76 0 1.37 172 319 16.8 43 ing, the sample temperature changes in 74 3.44 0 191.5 494 11.8 53 77 0 2.46 181.5 395 the direction of the surrounding tempera11.8 54 75 1.18 0 254 162.5 ture. I n radiant heat and dielectric dryNO. 2 Sand and Distilled Watei ing the direction of the temperature 27 36.5 0 0.13 91 33 29 24.8 change will depend upon the ratio of heat 0 0.66 130 110 31 24.8 0 1 . 8 1 164 264 input t o the heat losses. 45 16.8 0 124 0.47 93 47 16.8 0 1.28 150 187 In air drying studies the constant rate 56 11.8 0 0.70 138 137 58 11.8 of drying is proportional to the unsatura0 0.64 134 123 61 11.8 0.50 0 127 101 tion of the air-Le., the difference in the No. 3 Sand and Distilled Water vapor pressure of the liquid a t the surface 25 36.5 1900 75 21 0 0.98 134 123 of the sample arid in the air. I n these 28 24.8 3300 69 20 0 0.62 127 104 30 24.8 studies it was possible to test this rela4400 77 19 0 1.71 158.5 232 44 16.8 4400 75 22 0 1.18 152 197 tion over a wide range. The results for 16.8 46 3500 76 22 0 0.62 137 133 11.8 55 $500 75 21 0 0.98 145 165 the three sands are shown in Figure 15, 11.8 57 d500 75 21 Q 0.56 131 113 which is a plot of the constant rate of Ottawa Sand and Ethyl Alcohol drying against the unsaturation of the 48 16.8 2000 74 0.18 74 48 air. The linearity of this relation up to 49 16.9 3400 75 0.29 80 58 51 16.9 4300 75 0.44 91 a constant rate of 1.5 lb./(hr.)(sq. ft.) is 82 59 3500 11.8 76 0.22 82 63 evident, with each of the three sands ex62 25.3 3400 75 0.49 94 89 64 25.3 4400 75 0.84 104 119 hibiting a slightly different slope. The 66 36.6 2000 75 0.24 80 58 curve for Ottawa sand increases at a rate Ottawa Sand and Carbon’Tetrachloride greater than linear after this straight line 50 17.0 3400 76 0 0.60 81 126 52 16.9 4400 portion. The reason for this nonlinearity 76 0 0.67 88 150 60 12.0 3500 76 0 0.56 80 123 is not readily apparent. One factor which 63 25.4 3500 76 ,. 0 0.71 91 16 1 65 25.4 4400 75 0 0.92 99 193 may be of significance a t high evapora67 36.6 2000 75 .. 0 0.56 79 120 tion rates is that the mass transfer coeffiI
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INDUSTRIAL AND ENGINEERING CHEMISTRY
cient is inversely proportional to the mean partial pressure of the inert gas filmthroughwhich thewater vapor is diffusing into the air. T h e results of the other investigators, together with the present study, comprise four different methods-that is, convection, conduction, radiation, and dielectric loss-by which heat is furnished to the sand. Irrespective of the manner by which the sand obtains the heat required for the vaporization of water, the mechanism of drying is the same. SUMMARY AND CONCLUSIONS
The summary of the data and results are given in Table 1’. A comparison of four drying methods for sands slion-s that the following are independent of the method of drying: shape of the drying curve; movement of liquid water in the sand; critical moisture contents; and relation between constant drying rate and the unsaturation of the air. I t is possible to obt,ain higher drying rates with dielectric drying. The effect of variables on rates of dielectric drying is that the rate increases linearly with voltage, increases v-ith the frequency with an increase in air temperature, and may increase or decrease Mith an increase in air velocity depending upon the air temperature. The rate depends upon particle size and, perhaps, shape and bulk density, and upon the electrical properties of the liquid mturating the sand. The critical moisture content depends upon the liquid being evaporated. I t is possible to control the temperature of the sample for a given drying rate by varying the air temperature, velocity, and humidity, and the heat iuput from the radio frequency field. ACKNOWLEDGRIENT
The authors wish to express their indebtcdness t:, E;. I. du Pont de Neniours 6 Company and the American Chemical Society, each of which sponsored fellomhips for one of the authors.
Vol. 41, No. 8
LITERATURE CITED
Brown, G. H., Hoyler, C. X., and Bierwirth, R. A , “Theory and Application of Radio Frequency Heating,” pp. 1, 206, New York, D. Van Nostrand Co., 1947. Ceaglske, N. H., and Hougen, 0. A., Trans. Am. Inst. Chem. Engrs., 33, 283 (1937). Debye, P., “Polar Molecules,” p. 7 , New York, Chemical Catslog Co., 1929. Ernst, R. C., Ridgway, J. W., and Tiller, F. M., IND. ENC.CIIEY., 30, 1122 (1938). Friedman, S. J., Ibid., 38, 22 (1946); 39, 20 (1947); 40, 18 (1988). Fuoss, R. M., J. A m . Chem. Soc., 59, 1’703 (1937); 60,451, 456 (1938) I 61, 2329, 2334 (1939); 63,369, 378 (1941). Gemant, A , , “Liquid Diclcctrics,” pp. 1, ’78, New York, John Wiley & Sons, 1933. Littleton, J. T., and Morey, G. W., “The Elecmical Properties of Glass,” pp. 103, 114, New York, John Wiley & Sons, 1933. McAdams, W.II., “Heat Transmission,” 2nd ed., p. 240, New York, McGraw-Hill Book Co., 1942. Murphy, E. J., and Morgan, S. O.,Ball Sustem Tech. J.,16, 493 (1937); 17, 640 (1938); 18,502 (1939). Perry, J. I$., ed., ”Chemical Engineers’ Handbook,” 2nd ed., p . 1489, New York, MoGraw-Hill Book Co., 1941. Rusca, R. A.,Teztile World, 96,No.5,118 (1946). Schsffner, R. J., and Koehler, W. A., Trans. Am. I n s t . Chem. Engrs., 39, 303 (1939). Schutz, P. W., and McMahon, E. K., IXD.ENG.CXEN.,38, 179 (1946). Shepherd, C. B., Hadlock, C., and Brewer, R. C., Ibid., 30,388 (1938). Sherwood, T.K., and Comings, E. W., Ibid., 25, 311 (1933). Stout, L. E.. CaDlan, K. J., and Bnird, W. G., Tmns. Am. Inst. Chem. Engjl.s.i41, 283 (1945). (18) Whitehead, J. B., Eke. Eng., 66, 907 (1987). (19) Zottu, P. D., Electronics, 18, No. 3, 148 (1945) RECEIVED August 9, 1948.
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J. W. BROOKS Socony-Vacuum Laboratories, Paulsboro, N . 9. Dihydroxyfluoboric acid has been used as a catalyst for the copolymerization of propene with isopentene, propene with isobutene, 1-butene with isobutene, 2-butene with isobutene, and mixed n-butenes with isobutene (refinery CCcut) a t temperatures of 0’ to 40” C. and pressures of 50 to 125 pounds per square inch. The polymers were hydrogenated, fractionated, and analyzed by infrared absorption. Copolymerization of propene with isobutene and hydrogenation of the product yielded a material containing 67vo of a heptane rut. The heptane cut was 95%
2,3-dimethyPpentane. The octane fraction of the hydrogenated propene-isopentene copolymer represented 66.4% of the total product and was composed of 54.8% 2-methyl%ethylpentanc, 4 2 . 5 7 ~ 3,S-dimethylhexane, and 2.770 unidentified hydrocarbons. The octane fraction of the hydrogenated polymer produced from 2-butene and isobutene consisted entirely of triniethylpentanes; the octane fraction of the hydrogenated 1-butene-isobutene polymer contained 3470 dimethylhexanes and 66qo trimethylpentanes.
R1
tion of the general method described by Sowa, K r o e g r , and Nieuwland ( I O ) . This method was altered by adding a saturated hydrocarbon to the boric oxide before hydrogen fluoride was added. This facilitates the cooling of the mixture and prevents the formation of solid lumps which tend to appear in the absence of hydrocarbon diluents. The liquid reaction mixture was separated from the kerosene and used as such without distillation. Hydrocarbons of the indicated purities were obtained from the Matheson Company, Inc. : propene (99%), isobutene (95%),. 1butene (99%), and 2-butene (99%). Refinery Ca cut containing 4.4y0isobutene and 14 470 n-butenes and propene mas obtained from a Thermofor catalytic cracking unit The isopentenes were prepared by the dehydration of tPrt-am,vl alcohol with 15% sulfuric acid by the method of Whitmore and co-workers (26) who reported the isopentenes to be composed of 7 parts by weight of 2-methyl-2-butene and 1 part by weight of 2-methyl-1-butene.
BKY catalysts ha\ e been proposed for the polymerization
and copolymerization of such olefins as propene, butenes, and pentenes to yield fuels of high antlknock rating. Among the most common and widely used polymerizing catalysts (12) are and copper pyrophosphosphoric acid ( I , Z), sulfuric acid (8), phate (I I). This article describes the copolymerization of olefins in the presence of dihydroxyfluoboric acid. The operating conditione employed are milder than those required with the previously mentioned catalysts. MATERIALS AKD PROCEDURE
Dihydroxyfluoboric acid (&BOzFz),was prepared by the reaccion of hydrogen fluoride with boric oxide, using a slight modifica-
