Ind. Eng. Chem. Prod. Res. Dev. 1980, 79, 617-622
817
Heat and Mass Transfer in Particle Dehydration James L. Manganaro FMC Corporation, Princeton, New Jersey 08540
Equations expressing heat and mass transfer within a particle undergoing dehydration are developed for a shell and unreacted shrinking core model. Dehydration kinetics are assumed to be rapid in comparison to heat and mass transfer rates. The governing equations are formulated as a first-order ordinary differential equation and a nonlinear algebraic equation. A computer solution for these two equations was obtained for several specific cases. For the particular fluidized bed dehydration cases studied, gas film heat transfer controlled drying rate for particle diameters 10 mesh or smaller. Thus, transport limitation through the particle dehydrated phase was not indicated until particle diameters were larger than 10 mesh. An approximate, closed form solution for the time required for particle dehydration was developed. Agreement between the approximate and exact solutions was good for the cases considered.
Introduction Design and operation of equipment for drying of hydrated materials can be facilitated by an estimate of the time required to achieve complete dehydration. In addition, prediction of particle temperature is useful when thermal sensitivity of the material is important. The present discussion will focus on fluidized bed drying. However, the equations developed should be applicable to other drying processes such as flash drying provided the representative heat and mass transfer coefficients are used and that the assumptions inherent to the analysis remain valid. This paper takes the following form: (a) general discussion of heat and mass transfer in the particle using specific parameter values; (b) formulation of governing equations using an unreacted shrinking core model; (c) computer solution, again using specific parameter values; and (d) derivation of an approximate solution and comparison with the exact solution. The unreacted shrinking core model has been discussed and employed by Shen and Smith (1965), Levenspiel (1972), and Ruether (1979). Particle Heat and Mass Transport Factors The operation of drying in a fluidized bed involves simultaneous heat and mass transfer in both a fluid film phase surrounding the particle and a particle pore phase. Therefore, in order to know in which direction it will be best to concentrate efforts we must known which mode (heat or mass transfer) and which phase are controlling. Heat and Mass Transfer Coefficients. The Froessling equations correlate heat and mass transfer data obtained from single isolated spheres suspended in an air stream. The correlations are given in eq 1 and 2. heat transfer (single sphere)
N U E=~2
+ 0.6Pr'/3Re'/2
(1)
mass transfer (single sphere) ShEx := 2
+ 0.6S~'/~Re'/~
(2)
If the spherical particles are not isolated but in the complex environment of a fluidized bed, the Froessling equations do not apply. Kunii and Levenspiel (1969) summarize data showing that considerable scatter exists and that the external Nusselt and Sherwood numbers are generally lower than those predicted by the Froessling equations in the region of interest. Kunii and Levenspiel 0196-4321/80/1219-0617$01.00/0
Table I. Particle Property Values
dehydrated material hydrate
k,
cp>
Btu/h ft "F
Btu/lb
"F
lb/ft3
ftz/h
0.15 0.5
0.15 0.27
68.7
106.0
0.0146 0.0175
p,
0 ,
(1969) suggest the following heat and mass transfer correlations in a fluidized bed. heat transfer (fluidized bed)
NuEX= 0.03Re1.3 mass transfer (fluidized bed)
(la)
ShEx = 0.374Re1.18 (2a) Equations l a and 2a were the equations used to calculate heat and mass transfer coefficients in the computer solution. Air Property Values. The following approximate equations were found to fit air properties reasonably well in the region of interest (where [7"J = O F ) air density p
= 39.5/(460
+ )'2
lb/ft3
(3)
air viscosity 1.65 X 10-*T + 1.11 X air thermal conductivity p =
k = 2.44
X
10-5T + 1.33 X
lb/(ft S) Btu/(ft h
OF)
(4) (5)
These equations were used to calculate the dimensionless groups of eq l a and 2a. Table I summarizes other pertinent property values used. External and Internal Nusselt Numbers. The following parameter values were taken as descriptive of a fluidized dryer. Tf= 198 OF D = 0.02 in. = 1.667 X = 1 ft/s
f t (35 mesh)
u
Particle Reynolds number and external Nusselt number for a single particle are determined to be R e = -PUD P @ 1980 American Chemical Society
- 6.94
618
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 4, 1980
n TEMPERATURE
Equation l a was used to evaluate NuExin a fluid bed. The subscript EX refers to the external free environment surrounding the particle. The internal Nusselt number, also called the Biot number, is next calculated.
PARTIAL PRESSURE
HYDRATE
This low value of NUIN suggests that gas film resistance is of greater significance in comparison to heat conduction within the particle. Heat Transfer Coefficient. Heat transfer coefficient in a fluidized bed is calculated for the given typical case from NUEX, kA,and D to be h = 4.02 Btu/h ft2 OF. Heat transfer coefficient for a single isolated sphere is nearly ten times this number. External and Internal Sherwood Numbers. The diffusivity of air-water gas mixtures is taken as
BEx = 0.853 ft2/h at 32 O F Using a 1.5 exponent on the temperature, the variation of diffusion coefficient at 1atm pressure with temperature is obtained. a)Ex
= 0.853(T + 460/492)’‘5
(6)
Thus at T = 198 OF we have a)Ex = 1.32 ft2/h. From eq 2a, ShEx = 3.68. The internal Sherwood number is calculated by first estimating the internal diffusion coefficient from an equation recommended by Satterfield and Sherwood (7) where 6 = porosity and T = a tortuosity factor. Assuming the porosity of the dehydrated material is the same as the weight loss, and taking a typical value, c = 0.351, and a value of T = 4 as suggested by Satterfield and Sherwood (1963), the internal diffusion coefficient is found to be BIN
= 0.116 ft2/h
ShINmay be found from
The factor of ‘I2 in the equation converts the internal Sh to a radius basis instead of a diameter. Hence, Shm = 20.8. The magnitude of this number suggests that the controlling phase for mass transport is the internal particle phase rather than the gas film. Comparison of Heat and Mass Transfer. An indication of which transport mode within the particle is controlling, i.e., heat or mass transfer, is obtained by calculating the internal Lewis number. Thus (9) or, using the internal mass diffusivity at 198 O F and the thermal diffusity for dehydrated material from Table I, we calculate LeIN= 0.126. An internal Lewis number less than unity implies that heat conduction is the controlling mode in the particle phase. For this selection of parameter values, in summary, gas phase heat transfer is overall controlling followed, in order of decreasing resistance to transport. particle phase heat
DEHYDRATED MATERIAL
’
lf
FLUID TEMPERATURE
Pf = FLUID WATER PARTIAL PRES SURE
Figure 1. Diagram of particle model.
transfer, particle phase mass transfer, and finally gas phase mass transport. Particle Model The dehydration process of a hydrate particle involves the interaction of three factors: heat transfer, mass transfer, and the kinetics of dehydration nucleation. The following assumptions are made: (1)spherical geometry; (2) nucleation kinetics not important; (3) shell and shrinking core model; (4) no volume change on dehydration, hence dehydration is a measure of porosity; (5) pseudo steady state applies. Generally a dryer will be operated at a sufficiently high temperature that nucleation kinetics are not important. Thus,it will not ordinarily be the case that an “induction” period will be required before dehydration occurs (Taylor and Taylor, 1935) or that isolated spots of dehydrated material appear. Hence, dryer temperature is expected to be great enough to justify assumptions 2 and 3. Since most of the heat supplied to the particle is typically used to vaporize the water of dehydration rather than heat up the material, the “pseudo steady state” approximation may be made. This implies that the radius of the hydrate core recedes at a sufficiently slow rate so that an approximate steady state in the shell of dehydrated material is attained. Thus, at a given instant of time it is assumed that steady state exists, and transient terms in the transport equations for the monohydrate shell may be neglected. Figure 1 is a diagram of the proposed model. Heat is transported to t h e particle surfale by convection and conducted to the shrinking core of hydrate material. Water vapor diffuses radially outward from the hydrate-dehydrate interface through the porous shell of dehydrated material and ultimately is transferred to the surrounding gas. The temperature and water vapor partial pressure gradients are illustrated in Figure 1. Analysis. The rate of heat transfer into the particle, Q, is given by Q = 4aRW2h(Tf - T,) (10) Therefore, the rate of dehydration will be rate of dehydration (mol of H20/h) = dn = (11) dd AH The moles of water contained in the hydrate core are now computed mol of H 2 0 in tetrahydrate sphere =
(4/3 dr,3pHg MH
(12)
Differentiating expression 12 with respect to time results in an equation for the rate loss of water; thus
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 4, 1980
dn -=-dtJ
4rr:P~g dr, MH de
(13)
The negative sign accounts for the decrease of hydrate radius with increasing time. Combining eq 10, 11,and 13 gives
where
and t, is the reduced radius, r/R,. Another expression for the time rate of r, decrease can also be obtained from a film mass transfer balance rate of dehydration (mol of H20/h) = dn/de = 4rRw2(pw- P f h (16) where k G is the mass transfer coefficient based on a pressure driving force. Introducing eq 13 into eq 16 yields
610
With the boundary conditions 1. at r = r, (the hydrate surface) c = c, (244 2. at r = R, (the dehydrated surface of the sphere)
Water vapor partial pressure and concentration are related by c=- P RT Integrating eq 23 and evaluating the constants of integration from the boundary conditions, an equation for the partial pressure of water vapor in the dehydrated shell is obtained -1- -1 - 1
1
ShIN
{a
The internal Sherwood number (Treybal, 1968) is defined as ~GPBMRTRW
where
=
ShIN
ptBIN
A and B are constants for a given set of operating conditions. Employing the pseudo-steady-state assumption, the thermal and material diffusion equations for a spherical shell can be readily stated and solved. The energy equation for spherical geometry is
It is assumed that the log mean partial pressure of inert, PBM, is approximately equal to the total pressure, Pt, so that kGRTRW ShIN
=BIN
A relation between pwand pais obtained by introducing t = 1 into eq 26; thus -l -
With the boundary conditions 1. at r = r, (the hydrate surface)
T = T, (20a) 2. at r = R, (the dehydrated surface of the sphere) dT @Ob) - ~ D H dr = h( T, - Tf) Integrating eq 19 subject to the boundary conditions 20a and 20b results in the following expression for the temperature profile in the spherical dehydrated shell -1_ - 1
Pf
- Pa
.
I .
-+--1 NUIN
The mass diffusion equation for a spherical shell is
-+ -1- 1 ShIN
\-.
I
l.9
The equilibrium vapor pressuretemperature relationship is now required to complete the mathematical description. Hydration vapor pressure is assumed to follow an equation of the form log p = c1 - ( c , / T ) (28) where T is absolute temperature. Other correlations such as the three-constant Antoine equation may be used if desired. Equation 28 is rearranged to give
T, =
The expression for the temperature at the outer dehydrated surface, T,,is obtained from eq 21 by letting { = t, = 1,thus
l
c2
- 460 1% Pa where the units are T, = OF,pa = atm, and c1 and c2 are appropriate constants. Tempertaure and pressure are to be evaluated at the surface of the hydrate sphere. The five dependent variables T,, T,, p,, pa,and r, are solved as the function of time, 8, by means of eq 14,17, 22, 27, and 29. If the internal resistance of the particle is small compared to the gas-film resistance then N U I N and S h I N will be small. In the limit as NUINand ShINapproach zero it is found that T, = T, and pw= pa. For the specific case previously considered, the internal Nusselt number is small while the internal Sherwood number is moderate. However, for the sake of generality the approximation of small N U I N and S h I N was not made. Equations 14 and 17 are equated to yield c1 -
620
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19, No. 4, 1980
= Pf + B(Tf - T,) (30) Solving eq 22 for T, and introducing this into eq 30 gives after rearrangement
,200
230
PW
Introducing this result for pwinto eq 27 there results I
I
3
4
DRYING T I M E , M I N .
Figure 2. Effect of air temperature on theoretical drying rate.
Equation 32 reduces, as it should, to the usual expression for the wet bulb temperature when N U I N = Shw = 0 or ls= 1. Thus eq 32 may be viewed as an expression for the “wet b u l b temperature of the surface of the shrinking core as a function of the shrinking core radius, Shm, Num and the usual parameter M k G / h and the vapor pressure relation. The term ORYING TIME. MIN.
Figure 3. Effect of air velocity on theoretical drying rate.
accounts for the effect of the shrinking core model incorporating transport of heat and mass through the dehydrated shell. Inserting the expression T, obtained from eq 22 into eq 14
MESH
I
/
-4 DRYING TIME
I
6
5
7
, MIN
Figure 4. Effect of particle radius on theoretical drying rate.
The hydrate temperature, T,, is now replaced by the water vapor pressure, p8,via eq 29, so that eq 33 becomes
Table 11. Computed Temperatures and Partial Pressures (fs = 0.3 or 97.3%of Complete Dehydration)
in Particle
“F
c
Therefore, the problem reduces to finding 5‘, and p 8 as a function of 6 from the two eq 32 and 34, where the value of T, from eq 29 has been substituted into eq 32. The time of drying is the time, 6,required for s‘, to go from unity to zero or sufficiently close to zero. Computer Solution Drying rate in a fluidized bed was studied as a function of the following parameters: surrounding air temperature, air velocity, and radius of the assumed spherical particle. The following “base case” was established. Base Case. Tf = 200 O F ; pf = 0 atm; U = 1 ft/s; R, = 8.335 X loT4f t (35 mesh); e = 0.352; r = 4; M H = 154; g = 3 (i.e., a trihydrate); AH = 23 900 Btu/lb-mol of H2O; vapor pressure given by eq 18 where c1 = 9.0992 and c2 = 5915. For these conditions the following were calculated: I.L = 1.44 X 10” lb/(ft 5); P A = 0.0598 lb/ft3; k~ = 0.0182 Btu/(h f t OF);Re = 6.93; ShEx = 3.67; ShIN = 20.9; Num = 0.0223; h 4.05 Btu/(h ft2 OF); k G = 6.06 lb-mol of
case T=190“F T = 200°Fa T = 220°F U = 0.6 ft/s U = 0.8 ftls U = 1.4 ft/s R, = 4.875 X 10-4b R, = 13.8 x 10-~ a
Base case.
atm
Tf
Tw
Ts
Pf
190 200 220 200 200 200 200
126.6 129.1 133.4 115.9 123.2 138.0 115.2
123.2 125.3 129.0 113.6 120.2 132.9 113.0
0 0 0 0 0 0 0
Pw
0.00177 0.00198 0.00243 0.00226 0.00209 0.01808 0.00226
Ps 0.0906 0.0986 0.1139 0.0612 0.0803 0.1327 0.0598
200 142.4 136.6 0 0.00171 0.1528 Units of feet.
H20/ft2h atm; B E X = 1.33 ft2/h; IN = 0.166 ft2/h. Variations from the base case were in drying air temperature (190, 220 O F ) , air velocity (0.6, 0.8, 1.4 ft/s), and particle radius (50,20 mesh). Figures 2 , 3 , and 4 illustrate the computer results for drying time. Predictions made by the model are in general agreement with results obtained for equipment operating under conditions similar to those of the model. Table I1 gives an idea of the magnitudes of temperature and water vapor pressure within the particle predicted by our model at ls = 0.3 or 97.3% of completion. The computed wall particle temperatures are in agreement with
Ind. Eng. Chem. Prod. Res. Dev., Vol. 19,No. 4, 1980 621
Table 111. Computed :Resultsfor the Base Case ss
time, rnin
1.0
0. 0.41 0.79
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 a
1.11 1.37 1.57 1.72 1.82 1.88 1.90
wt % dehydrate
% compla
T,,“F
T,, “F
P,, atm
P, , atm
0 19.4 38.2 55.4 70.2 81.9 90.5 95.9 98.8 99.8
0 27.1 48.8 65.7 78.4 87.5 93.6 97.3 99.2 99.9
54.6 75.9 87.3 95.8 103.3 110.4 117.5 125.3 134.6 147.5
54.6 76.2 87.9 96.8 104.8 112.4 120.2 129.1 140.0 156.4
0.00403 0.01153 0.01953 0.02870 0.03972 0.05365 0.07205 0.09859 0.14170 0.23058
0.00403 0.00347 0.00314 0.00289 0.00266 0.00245 0.00223 0.00198 0.00168 0.00122
In this and following tables, “compl” stands for “completion”.
particle temperatures experimentally measured in cases described by these conditions. The air velocity seems to have a relatively strong influence on drying rate; see Figure 3. This is due to the controlling nature of heat transfer and the relatively strong dependence of heat transfer coefficient on velocity; see eq la. It can be determined from Figure 4 and Table V that drying time increases nearly linearly with radius up to 10 mesh as would be predicted by considering the ratio of volume to surface area (which varies with R, to the first power). The linear dependence indicates that heat and mass transport in the dehydrated shell of the particle is not limiting for particles of 10 mesh or smaller for these heat and mass transfer fluxes; otherwise the time functionality would be more than the first power of the radius. This later phenomena has been observed for a 5-mesh particle, however. Thus, internal particle transport is a problem for particles 5 mesh (4 mm) or larger under the given conditions. Table I11 shows computed results as a function of drying time for the previousty stated base case (which is for 35 mesh particles). This table also gives an idea of the relation between reduced radius, w t % dehydrated material, and completeness of drying. The low “wet bulb” temperature of the hydrate: at {a = 1.0 relative to water results apparently from the enhanced mass transfer coefficient as compared to the heat transfer coefficient in the environment of a fluid bed. Evidently, a fluid bed tends to favor film phase mass transfer over heat transfer as compared to flow past a bluff object. Approximate Solution The following approximate solution is offered: eq 32, 29, and 33 may be cast as
Table IV. Comparison of Exact and Approximate Solutions. Effect of Tf exact e D , min 97.3%
99.2%
TS*, approxBD,
Tf,”F
compl
compl
“F
min
190 200 210 220 230
1.9 1.8 1.7 1.6 1.6
2.0 1.9 1.8 1.7 1.6
86 87 89 90 92
2.0 1.8 1.7 1.6 1.5
Table V. Comparison of Exact and Approximate Solutions. Effect of Particle Radius exact e D , min 97.3%
99.2%
TS*, approx
IO4 X R,, ft
compl
compl
“F
(50 M) (35 M) (20 M) (10 M) ( 5 M)
1.1 1.8 2.9 6.9 15.2
1.2 1.9 3.0 7.2 16.1
4.875 8.335 13.80 32.79 65.85
77 87 98 118 133
e n , min 1.1 1.8 2.9 6.9 15.0
Table VI. Comparison of Exact and Approximate Solutions. Effect of Water Vapor Partial Pressure ~
exact e D , min 97.3%
99.2%
pf,mmHg compl
compl
T$,”F
approx eD,min
1.9 2.2 3.0 4.3
87 105 130 152
1.8 2.2 2.9 4.3
0 20 80 200
1.8 2.2 2.9 4.2
Table VII. Comparison of Exact and Approximate Solutions. Effect of Drvinr! Air Velocitv exact e D , min
and dx __
A ( T f- Ta*) (37) (X + 1)4 cld ~ ~ + NuINx) ~ ( 1 where x = (l/W - 1. The asterisk denotes that a constant value is assigned to the indicated variable. Equations 35 and 36 can be solved for the constant Ts*if some average “well chosen” constant value of x in eq 35 can be selected, denoted by x * . This value of Ts* is then used in eq 37 which can then be readily integrated for x = 0 to a, As already noted, an expression of the form of eq 35 can be viewed as a relation for the “wet bulb” at the hydrate-dehydrate interface and eq 36 may be any other suitable 1
~
97.3%
99.2%
U,ft/s
compl
compl
0.6 0.8 1.0 1.4
3.2 2.3 1.8 1.3
3.3 2.4 1.9 1.3
approx
TS*, “ F e D , min 77 83 87 94
3.2 2.3 1.8 1.3
relation for the hydrate vapor pressure. The following approximation results for the drying time of a single hydrate particle gPHmRw(l O-~NUIN) 6D = (38) 3 h M ~ ( T-f T,*) where Ts* is determined from eq 35 and 36 when taking x* at some constant value. A value of x* = 0.25 (corresponding to reduced radius of 0.8) is suggested. The exact solutions vs. the approximation (using x* = 0.25) are compared in Tables IV-VII. The exact solution
Ind. Eng. Chem. Prod. R8S. Dev. 1960, 19, 622-624
622
U = superficial air velocity, ft/s
is given for completion of drying of 97.3 and 99.2%. All variations are from the previously stated base case. It is seen that this agreement is generally good for these cases. Acknowledgment The author is indebted to L. C. Cha, L. R. Darbee, and C. A. Gray of FMC Corporation for their comments and suggestions.
a = thermal diffusivity, ft2/h e
= porosity
[ = reduced radial position in the dehydrated shell, r / R w
tB= reduced radius of the hydrated core, rB/Rw 0 = time, h OD = drying time, h I.( = viscosity, lb/ft s p = density, lb/ft3 r = pore tortuosity
Nomenclature c = water concentration, mol/ft3 c = heat capacity, Btu/lb O F d = diameter of particle, f t 2l = diffusion coefficient, ft2/h g = number of moles of water in the hydrate molecule AH = heat of dehydration, Btu/lb-mol of hydrate H 2 0 h = heat transfer coefficient, Btu/ft2 O F h k = thermal conductivity, Btu/ft h O F kG = mass transfer coefficient, lb-mol of H20/h ft2 atm L e = Lewis number M = molecular weight Nu = Nusselt number NuEX= external Nusselt number, hD/kA N U I N= internal Nusselt number, hRw/kDH P B M = log mean partial pressures of stagnant species, atm p = partial pressure of water vapor, atm Pt = total pressure, atm Pr = Prandtl number Q = heat rate, Btu/h r = radial position in monohydrate shell, f t R = gas constant R , = outside radius of particle, f t Re = Reynolds number Sc = Schmidt number S h I N= Sherwood number, kJITR,/a)IN T = temperature, O F or OR
Subscripts A = air DH = dehydrated EX = external (fluid) conditions f = fluid H = hydrate IN = internal (particle) conditions s = surface of the hydrate spherical core w = exterior dehydrated material surface Superscript * = denotes variable is assigned a constant value
Literature Cited Froessiing, N. Oerlend Bekt W p h y s . 1938, 52, 170. Kunii, D.; Levenspiel, 0. “Fluidization Engineering”, Wiiey: New York, 1969. Levenspiel. 0. “Chemical Reactlon Engineering”, 2nd ed.; Wlley: New York, 1972. Rank, W. E.;Marshall, W. R., Jr. Chem. Eng. hog. 1952. 48(4), 173. Ruether, J. A. Can. J. Chem. Eng. 1979, 57, 242. Satterfleld, C. N.; Sherwood, T. K. “The Role of Diffusion in Catalysis”, AddC son-Wesley: Reading, Mass., 1963. Shen, J.; Smith, J. M. Id. Eng. Chem. Fundam. 1965, 4 , 293. Taylor, T. L.; Taylor, G. G. Ind. Eng. Chem. 1935, 27, 672. Treybal, R. E. “MassTransfer Operations”, 2nd ed.; McGrawHiii: New York, 1968.
Receiued for review November 26, 1979 Accepted June 16,1980
Surface Properties of Plasma Polymers from Diethylaminotrimethylsilane and Hexamethyldisilazane Toshlhlro Hlrotsu Research Institute for Po&mers and Textiles, Tsukuba, Ibaraki 305, Japan
Plasma polymers of some silyl amines were produced and investigated on their surface properties. The polymers formed from diethylaminotrimethylsilane and hexamethyldisilazane were found to be as hydrophobic as those of tetramethylsihne. The hydrophobicity can be attributed to the loss of nitrogen (which will form the more hydrophilic functional groups in other nitrogen monomers) in the course of polymerization. Orientational behavior of some liquid crystals was investigated on these polymer layers and it was found that the layers gave orientation of the biphenyl-type liquid crystal with good heat resistance.
Ltd. The polymer is hydrophobic, but hydrophilicity is sometimes preferable. Some attempts have been made for effecting this property on the surface by graft polymerization of the monomelg with hydrophilic functional groups under irradiation of y-rays (Ratner et al., 1978), and ultraviolet light (Tazuke and Kimura, 1978). One of the unique methods is the plasma surface modification by ammonia and nitrogen (Hoollahan et al., 1969). Nitrogen functional groups such as amines which are more hydrophilic can be incorporated onto the surfaces by exposure to plasmas.
Introduction Silyl compounds are the easily polymerizable monomers in glow discharges to give highly cross-linked products. The reactivity is attributed mainly to the Si-Si couplings. The products whose hydrophobicity is one of the interesting characteristics have been investigated for practical purposes, i.e., for medical use, anti-fogging, soil repellant, and so on. Nowadays, the silyl polymers or the silicon rubbers are popular and valuable in many fields. One of the best known plastics is Silastic available from Dow Corning Co. 0196-4321/80/ 1219-0622$01 .OO/O
0
1980 American Chemical Society
