Ind. Eng. Chem. Res. 1987,26, 1999-2007
1999
Effect of Reactant Mixing on Fine Particle Production in a Tubular Flow Reactor Toivo T. Kodast and Sheldon K. Friedlander* Department of Chemical Engineering, University of California at Los Angeles, Los Angeles, California 90024
S o t i r i s E.Pratsinis Department of Chemical and Nuclear Engineering, University of Cincinnati, Cincinnati, Ohio 45221
Ammonia and nitric acid were combined in a tubular flow reactor using single- and multiple-jet mixing heads to form ammonium nitrate aerosol. Particle concentrations from 10 to 107/cm3,number-average particle diameters from 0.05 to 0.3 pm, and mass loadings to 10 mg/m3 were studied. Experiments and theories indicated that the system behaved like a well-mixed reactor followed by a laminar flow reactor. Above a critical saturation ratio, particle formation and growth took place in the reactant-mixing region; as a result, the aerosol dynamics were controlled by reactant mixing. Below the critical saturation ratio, the aerosol dynamics were not influenced by mixing since particle formation and growth took place mainly in the laminar flow region. Seeding the reactant gas streams narrowed the particle-size distribution and increased aerosol yields. 1. Introduction
Aerosol flow reactors (AFR) are used for production of pigments and reinforcing agents (Ulrich and Subramanian, 1977), carbon black (Medallia and Rivin, 1976), optical fibers (Miller et al., 1984), and ceramic powders (Bowen, 1980; Heberlein, 1984). Frequently, two or more reactant streams must be mixed in an AFR to produce the product particles. A common example is the formation of ammonium chloride aerosol from the chemical reaction of ammonia and hydrochloric acid vapors (Henry et al., 1983). Several investigators have found that reactant mixing influences the product particle size distribution. Kat0 et al. (1981) mixed gaseous metal compounds with ammonia and hydrocarbons to form nitride and carbide particles. The rate of mixing of reactant gases in their tubular AFR significantly affected product particle-size distributions. Canteloup et al. (1979) formed silica powders doped with alumina by reacting silicon and aluminum vapors with oxygen in a plasma AFR. The reactants had to be well mixed to get a homogeneous particle composition. Two types of mixing geometries have been used in tubular AFR studies: single jet (coaxial) and multiple inlet. Single-jet mixing heads have been used to study the formation and growth of environmentally (Vance and Peters, 1976; Countess and Heicklen, 1973) and industrially important particles (Kato et al., 1981; Prochazka and Greskovich, 1978; Lay and Iya, 1981). Multiple-inlet mixing heads have been used by Henry et al. (1983) and Countess and Heicklen (1973) to study ammonium chloride particle formation and growth. The purpose of this work was to investigate the effect of reactant gas mixing on the operation of tubular aerosol flow reactors. In this study, both single- and multiple-jet mixing heads were used, to compare their effects on aerosol reactor operation. An isothermal system was studied to allow reactant mass-transfer effects to be separated from heat-transfer effects. Production of ammonium nitrate aerosol from ammonia and nitric acid was used as a case study. Ammonium nitrate particle formation probably occurs by reaction of ammonia and nitric acid on the surface of clusters (Olszyna et al., 1974; Brandner et al., 1962; Kodas et al., 1986); similar formation pathways are
* To whom correspondence should be addressed.
+Presentaddress: IBM Almaden Research Center, ML K91801, 650 Harry Road, San Jose, CA 95120. 0888-5885/87/2626-1999$01.50/0
encountered in the production of ceramic particles such as AlN, Sic, and TiB, and pigments such as SiO, (Rutner et al., 1964; Katz and Donohue, 1982). Reactor operation was described in terms of moments of the particle-size distribution. Theories were developed for the limiting cases of slow and fast reactant mixing compared to particle formation and growth. The conditions required for production of monodisperse particles at high yields were examined. Monodisperse powders are desirable for production of pigments with improved optical properties (Herrmann, 1976),carbon black with increased tensile strength and abrasion resistance (Medallia and Rivin, 1976; Dannenberg, 1971), and ceramic parts with increased strength and toughness (Kingery, 1960; Bowen, 1980). Theory Friedlander (1983) derived a closed set of equations for the moments of the particle-size distribution in an analysis of the behavior of batch and stirred-tank aerosol reactors. Kodas et al. (1986) and Pratsinis et al. (1986a) extended this approach to describe tubular AFR operation accounting for radial diffusion of the condensing species and the reactor residence-time distribution. In this work, the approach of Kodas et al. (1986) for ammonium nitrate particle formation and growth is extended to describe the effects of reactant mixing on AFR operation. 2.1. Kinetically Controlled Operation: Infinitely Fast Mixing Theory. For sufficiently low reactant concentrations, reactant mixing is rapid relative to particle formation and growth; the aerosol dynamics are not influenced by the mixing process and are controlled by the kinetics of particle formation and growth. The following theory is proposed for this limiting case. Ammonia and nitric acid are instantly mixed at x = 0. As the gas mixture flows down the tube, ammonium nitrate particle formation and growth and wall losses of ammonia and nitric acid deplete the reactant concentrations. Sufficiently far down the reactor, equilibrium is reached between the solid and gas phases and particle formation and growth no longer occur. The assumptions of the theory are as follows: ammonia and nitric acid are instantly mixed at the reactor inlet so that their concentration profiles are uniform across the reactor; diffusivities of ammonia and nitric acid are constant throughout the reactor; the gas mixture is in plug 2.
0 1987 American Chemical Society
2000 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
flow or fully developed laminar flow; particle formation takes place according to the modified form of classical nucleation theory presented by Kodas et al. (1986)in which particle formation occurs by direct reaction of ammonia and nitric acid on the surface of ammonium nitrate clusters; particle growth takes place at a rate determined by kinetic theory (molecular bombardment) (Friedlander, 1977) and occurs by direct reaction of ammonia and nitric acid on the surface of ammonium nitrate particles (Kodas et al., 1986);the accommodation coefficient for the limiting reactant is unity; coagulation, subcritical cluster scavenging, and the Kelvin effect for stable particles are not important; particles do not diffuse radially during their residence in the reactor; the wall is coated with ammonium nitrate so that S = 1 at r = 1. For these conditions, the reactant mass balances and aerosol moment equations in dimensionless form describing the aerosol dynamics are nitric acid balance
ammonia balance
zeroth moment dN
2f(r) - = pZ a01
first moment
dM1
Y
2f(r) - = pIk*1/3+ -N 861 3
second moment
third moment
av
2f(r) - =
pZk*
+ ?A
for particle formation and growth, depending on the operating conditions. initial conditions at 0 = 0
CN = CN,O
CAO A=Ao
CA
N=No V = Vo
=Mlo (8)
boundary conditions at r = 0 -~ =C- =N-~=C- -A- dN dr dr dr
dMi - -dA = - dV = 0 dr
dr
dr
(9)
boundary conditions at r = 1
Table I lists the dimensionless variables, parameters, and auxiliary functions in the equations above. The saturation ratio and the moments of the particle-size distribution are determined by the initial conditions and the five dimensionless groups, EA,I, E N , I , 2, r, and 6,. By use of orthogonal collocation, eq 2-6 were transformed into a set of coupled ordinary differential equations which were solved by the Adams-Moulton method in the subroutine DGEAR (IMSL, 1980). Ammonia and nitric acid are consumed a t equal rates by nucleation and growth according to stoichiometry. Thus, if the initial concentrations of nitric acid and ammonia are equal and if EA,I= EN,I,their concentration profiles are identical and only one of eq 1 and 2 need be solved. Roughly equimolar concentrations were used in all the experiments. It was found experimentally and theoretically that radial diffusion of ammonia and nitric acid was not important for sufficiently high saturation ratios in agreement with Pratsinis et al. (1986a). For lower saturation ratios where radial diffusion of the reactants was important, the validity of using only one equation was checked by using both eq 1 and 2 in the calculations. Nearly identical particle concentrations, average particle diameters, and yields were calculated with either the ammonia or the nitric acid balance equations. Cup-mixing particle concentrations and number-average particle diameters were calculated from radial profiles of moments of the particle-size distribution. The yield, defined as V/Col, and the polydispersity index
a01
where f ( r ) = 1 - r2 for a parabolic velocity profile
=
y2
for a uniform velocity profile
and
The functions, /3 and y, account for the possibility that either ammonia or nitric acid may be the limiting reactant
were calculated from cup-mixing averages of the moments. The assumption of infinitely fast mixing was valid when particle formation and growth occurred over a much longer time than that required for complete reactant mixing. The parameter space in which this occurred was determined experimentally. Turbulence caused by the reactant mixing process may have influenced the aerosol dynamics by increasing rates of ammonia and nitric acid transport to the reactor walls. This effect was studied by solving the time-averaged versions of eq 2-6, neglecting the effect of turbulence on the particle formation and growth terms and assuming a constant eddy diffusivity. Calculations showed that turbulent mass transport of ammonia and nitric acid had a negligible effect on the total particle concentration and only a small effect on the other output parameters. Calculations were done with both laminar and plug-flow velocity profiles. No significant difference was observed between the two cases, in agreement with the results of
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2001 Table I. List of Dimensionless Variables, Parameters, and Auxiliary Functions for Infinitely Fast and Lamellar Mixing Theories
saturation ratio
t-
x= o
ammonia concentration
I
t = o
x=
1
nitric acid concentration surface tension group I
I
x=
x=o
nucleation rate
1
>o Figure 1. Coordinate system for lamellar mixing theory. At t = 0, ammonia and nitric acid are completely segregated into lamellae of width L. For t > 0, diffusion of reactant gases and particle formation and growth occur until equilibrium is achieved. t
av residence time for infinitely fast mixing theory av residence time for lamellar mixing theory ammonia diffusion group for infinitely fast mixing theory nitric acid diffusion group for infinitely fast mixing theory ammonia diffusion group for lamellar mixing model nitric acid diffusion group for lamellar mixing theory aerosol surface area first aerosol moment aerosol number density
r = r'/b Y = Y'IL
radial coordinate Cartesian coordinate perpendicular to reactor axis no. of monomers in the critical size particle time constant for infinitely fast and lamellar mixing theories
reactant mixing occur simultaneously (Ottino, 1981; Mao and Toor, 1970; Belevi et al., 1981;Jenson, 1983; N a m a n n and Buffham, 1983). In this work, this approach was extended to include particle formation and growth. The theory is as follows. Ammonia and nitric acid are introduced into the reactor through a mixing head, resulting in the formation of segregated fluid elements containing ammonia and nitric acid vapors. Ammonia and nitric acid then diffuse into neighboring elements of the other reactant while particle formation and growth occur. Wall losses of ammonia and nitric acid are negligible because the diffusing ammonia and nitric acid are rapidly consumed by particle formation and growth. Particle formation and growth cease when equilibrium is reached between the solid and gas phases. The assumptions of the theory are as follows: the lamellae containing the ammonia and nitric acid vapors have equal width L, are oriented along the axis of the reactor, and are totally segregated at t = 0 (Figure 1);deformation of the lamellae is not important; no losses of gases or particles occur; the remaining assumptions concerning the aerosol dynamics are as stated for the infinitely fast mixing theory. The reactant mass balance equations in dimensionless form are ammonia balance
nitric acid balance aerosol volume
Pratsinis et al. (1986a). Coagulation was unimportant since particle concentrations were less than 5 X 106/cm3and the residence time was 25 s. A discussion of the validity of the other assumptions is given by Kodas et al. (1986). 2.2. Mixing Controlled Operation: Lamellar Mixing Theory. For sufficiently high reactant concentrations, reactant mixing and particle formation and growth occur simultaneously. In this case the aerosol dynamics are no longer controlled by the kinetics of particle formation and growth but are also influenced by the reactant mixing process. Lamellar mixing theories are commonly used to describe the behavior of reactors in which chemical reaction and
The moment equations can be obtained from eq 3-6 by setting f ( r ) = 1/2 and 0, = OL. initial conditions at 0 = 0 C A = ~ C A OC N = O N = N o Mi = M I 0 A = A.
V = Vo for 0 I y 5 0 . 5
C A = o CN=2CNo N = N o h f l = M , o A = A.
V = V , for 0.5 I y I 1.0
(13)
The factor of 2 is introduced for the initial concentrations
2002 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
B
Mass
FIOW
Controller
0 Rotameter
N 19-rr.J fi
Vent
HN03/H20
Figure 2. Experimental system. Ammonia and nitric acid vapors in nitrogen are mixed using single- and multiple-jet mixing heads to produce ammonium nitrate aerosol. Seed particles are generated by reaction of ammonia with the nitric acid gas stream outside the reactor.
of ammonia and nitric acid to make the cup-mixing concentrations of ammonia and nitric acid equal to C,, and CNO,respectively. boundary conditions at x = 0 and x = 1
~ - =C- =N-~- C AaN - - MI aY aY aY aY
- -aA =--
aY
av - 0 aY
(14)
Table I lists the dimensionless variables, parameters, and auxiliary functions in the equations above. The ammonia and nitric acid concentrations and moments of the particle-size distribution are determined by the initial conditions and the five dimensionless groups, EA,L,EN,L, E, BL, and x. Equations 11 and 12 along with eq 3-6 were solved by using the same numerical procedure as for the infinitely fast mixing theory. Mixing models with lamellae of equal widths have also been proposed by Mao and Toor (1970) and Angst et al. (1982). Jenson (1983) and Belevi et al. (1981) have discussed the standard assumption of total segregation a t t = 0. Negligible lamellae deformation has been assumed by numerous investigators (Mao and Toor, 1970; Jenson, 1983; Belevi et al., 1981). A mass balance on the reactor showed wall losses of ammonia and nitric acid were negligible for sufficiently high saturation ratios. This showed that radial diffusion of reactants and wall losses of particles were negligible. 3. Experimental Measurements
The experimental system is shown in Figure 2. Nitrogen was saturated with 70 wt % nitric acid and then diluted to provide the nitric acid reactant stream. Bottled ammonia in nitrogen was diluted to provide the ammonia reactant stream. The ammonia was a certified standard gas with an accuracy of 2% obtained from Matheson. Gas flows were controlled by using mass flow controllers (Tylan) and measured with calibrated rotameters. Teflon filters were used to remove any foreign particles in the reactant streams. The effectiveness of the filters was confirmed by measuring background particle concentrations before and after experiments. Two mixing heads were used. The single-jet mixing head, M-1, consisted of a 1.6-cm-i.d. glass inner tube in a 5-cm-i.d.glass tube. One reactant was introduced through the inner tube and the other through the annular region. The multiple-jet mixing head, M-19, consisted of 19 0.3-
cm-i.d. stainless steel jets spaced approximately 1-cm apart in a hexagonal array. Ammonia was introduced through 10 and nitric acid through 9 jets. The flow patterns in the reactor were visualized by passing titania and cigarette smoke through the center jet of the single-jet mixing head and through alternating jets of the 19-jet mixing head. Flow visualization indicated that fluid entering the reactor was divided into relatively even-sized elements with dimensions on the order of the jet size or spacing. The reactor was a 5-cm-i.d., 230-cm-long Pyrex tube. The longest residence time studied was 25 s. A movable sampling tube allowed measurements at various axial and radial locations, keeping the total flow rate fixed. Particle-size distributions were measured a t various reactant concentrations. Particle-size distributions were measured by using an electrical aerosol analyzer (EAA) (TSI 3030) over the equivalent mobility size range, 0.01-1.0 pm, and an optical particle counter (OPC) (LAS-X, PMS) over the optical diameter range, 0.09-3.0 pm. The total concentration of particles larger than approximately 0.01 pm was measured with a condensation nuclei counter (CNC) (TSI 3020). All runs were made at 1-atm pressure and approximately 23 " C . Three or more duplicate runs were made for each set of conditions. The total gas flow rate was kept at 10 L/min for all experiments, corresponding to a reactor Reynolds number of 274, except when the effect of total flow rate was being studied. Reactor residence-time distributions were measured with the two mixing heads for total gas flow rates of 5, 10, and 20 L/min. A step input of carbon monoxide tracer gas was introduced into the mixing head and the reactor output monitored with a CO analyzer (Energetics Science, 2106) to obtain the residence-time distribution. Seed particles were formed by adding ammonia to the nitric acid gas stream before the entrance to the mixing head. Seed particle-size distributions were measured as follows. The seed particles in the nitric acid gas stream were introduced into the reactor through the mixing heads. The ammonia reactant stream was replaced by nitrogen, thereby eliminating particle formation and growth in the reactor. The reactor contents were then sampled with the OPC, CNC, and EAA. Seed particle diameters ranged from 0.01 to 0.04 pm with W values of 0.5-1.0. 4. Results
For the single-jet mixing head, experiments were done with nitric acid in the inner tube and ammonia in the annular region and with the streams reversed. Experiments with nitric acid on the inside gave slightly lower particle concentrations and yields than experiments with ammonia on the inside. The diffusivity of ammonia is roughly twice that of nitric acid. Thus, placing nitric acid on the outside increased wall losses, thereby reducing the saturation ratio and the nucleation rate. Most experiments were done with equal flow rates of the NH3 and HN03 reactant gas streams. Some experiments were also done with 9 L/min nitric acid and 1L/min ammonia in nitrogen and vice versa, keeping the reactant cup-mixing concentrations constant. Some differences in the particle-size distributions were observed between these cases. However, all experiments with the same total flow rate and cupmixing reactant concentrations were treated as identical conditions. This was done since the infinitely fast mixing model could not differentiate between conditions with the same cup-mixing reactant concentrations. This resulted in larger error bars for M-1 than for M-19. Total particle concentrations, aerosol yields, numberaverage particle diameters, and polydispersity indexes were
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2003 calculated from measured particle-size distributions. Sampling at different axial positions indicated that particle formation and growth were complete before 25 s at most. All measurements were made at this point. This allowed an accurate comparison of measured and calculated aerosol yields and eliminated errors resulting from reaction in the sampling line or quenching of the reaction by diluting the sampled gas stream. Error bars on the following graphs indicate the range of measurements for duplicate runs performed on different days. Error bars for the cup-mixing saturation ratio reflect the possible range of reactant flows due to inaccuracies in the flow controllers and rotameters. 4.1. Comparison of Experiment and Theory. To compare theory and experiment, values of the dimensionless groups were required. The average residence time, reactor diameter, temperature, and reactant concentrations were measured. The equilibrium relationship between ammonia and nitric acid vapors and the solid was obtained from Stelson et al. (1979) and Brandner et al. (1962). Molecular diffusivities of ammonia and nitric acid were calculated by using the Chapman-Enskog relationship. For the 19-jet mixing head, the lamellae thickness, L, was taken as the jet spacing, 1cm, as suggested by flow visualization. The only unknown parameter, the surface tension of ammonium nitrate, was obtained by fitting theory to experiment. The infiiitely fast mixing model, applicable when mixing was rapid with respect to particle formation and growth, was compared to the M-19 data at small saturation ratios. The lamellar mixing model, which applied when radial diffusion of reactant gases was negligible, was compared to experiments with the 19-jet mixing head for inlet saturation ratios greater than 1.5 X 105where vapor wall losses were negligible. Calculated and measured center-line particle concentrations for the 19-jet mixing head were compared as a function of cup-mixing inlet saturation ratio (Figure 3a). The best fit was obtained with Z = 5.8, somewhat higher than the results of Kodas et al. (1986) where values of Z between 5.0 and 5.5 fitted the data best. The infinitely fast mixing theory underpredicted the total particle concentration for values of Z greater than 5.8. For values of Z less than 5.8, the value of the lamellae thickness required to fit the data was larger than the jet spacing for the 19-jet mixing head and larger than the diameter of the inner jet of the single-jet mixing head. Figure 3b shows the aerosol yields as a function of the inlet cup-mixing saturation ratio, So. Wall losses were negligible for So> 1.5 X lo5 for M-19 and So > 5 X lo5for M-1. For these cases, particle formation and growth occurred rapidly relative to radial diffusion of ammonia and nitric acid. Diffusing ammonia and nitric acid were preferentially consumed by the large aerosol surface area, resulting in negligible wall losses. As the saturation ratio was decreased, the yield dropped almost to zero for a critical saturation ratio of 5 x IO4 for both the single- and 19-jet mixing heads (Figure 3b). Near the critical saturation ratio, particle formation and growth took place slowly relative to diffusion of ammonia and nitric acid to the reactor wall. The small resulting aerosol surface area was not sufficient to consume the diffusing ammonia and nitric acid entirely. Similar results were found by Kodas et al. (1986) for ammonium nitrate particle formation and growth in a constant-rate AFR. The infinitely fast mixing theory (with I: = 5.8) with the molecular diffusion coefficient of ammonia overpredicted the yield for So = 5 X lo4 (Figure 3b). The mixing heads produced turbulence near the reactor entrance which increased ammonia and nitric acid wall losses. This effect
0 19 let mixing
head
Infinitely Mixing
Cup-mixing Inlet S a t u r a t i o n R a t i o So
1
Ti
'1
04 4
0.24 I
0 0
1x:05
5:1o4
3x'105
5x'1O5
C u p - M i x i n g Inlet Saturation R a t i o So
INFINITELY F A S T
n
2 1 4 U
e Y >
\
o.li
LAMELLAR MIXING
4
b
1i105 CUP-MIXING
,,'lo5 ,1105 5J105 I N L E T S A T U R A T I O N R A T I O So
Figure 3. (a, top) Center-line particle concentration as a function of inlet cup-mixing saturation ratio. Predictions of infinitely fast mixing and lamellar mixing theories are shown for best fit value of Z = 5.8. All other parameters were either measured or calculated. The lamellar mixing theory is applicable in the region So > 1.5 X lo5 where wall losses of reactant gases were negligible (part b). Infinitely fast mixing theory is applicable for approximately So < 1.0 X los where reactant mixing was rapid relative to particle formation and growth. (b, middle) Aerosol yield as function of inlet cup-mixing saturation ratio. Predictions of infinitely fast mixing theory are shown for best fit value of Z = 5.8. Infinitely fast mixing theory overpredicted the yield for So = 5 X lo4 due to enhanced radial reactant diffusion resulting from the mixing process. Doubling the value of the eddy diffusivity used in the calculations gave good agreement. This indicated that turbulent reactant transport decreased aerosol yields slightly for So = 5 X lo4 but did not influence results for higher S,. (c, bottom) Number-average particle diameter as function of inlet mixing cup saturation ratio. Experimental data for 19-jet mixing head are shown. Predictions of infinitely fast mixing and lamellar mixing theories are shown for best fit value of Z = 5.8. For low saturation ratios, infinitely fast mixing model overpredicted the yield so that average particle diameters were overpredicted. Both theories also overpredicted d,, since measured particle-size distributions were polydisperse, while calculated particle-size distributions were nearly monodisperse. For the same aerosol volume (part b) and particle concentration (part a), a polydisperse aerosol has a smaller average particle diameter.
2004 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
was studied by solving the time-averaged version of eq 2-6, neglecting the effect of turbulence on the particle formation and growth terms and assuming a constant eddy diffusivity. The experimentally observed yield as a function of the initial cup-mixing saturation ratio was bounded by calculations with values of the eddy diffusivity corresponding to the molecular diffusivity of ammonia and twice the molecular diffusivity of ammonia (Figure 3b). Total particle concentrations were influenced only slightly by reactant diffusion to the walls. This occurred since particle formation began immediately at t = 0 and ceased after a short time relative to the time required for the reactants to diffuse to the walls. The average particle diameter and yield, however, were decreased significantly because particle growth occurred over a longer length than particle formation; sufficient residence time was available for the walls to consume reactants that would have gone into particle growth. Figure 3c shows measured and calculated number-average particle diameters as a function of the inlet cupmixing saturation ratio for the 19-jet mixing head. Theory overpredicted the average particle diameter by a factor as great as 3. The discrepancy may be due to differences in the spread of calculated and measured particle-size distributions; theory predicted nearly monodisperse particles, while experiment gave a polydisperse aerosol. For equivalent aerosol concentrations and volumes (parts a and b of Figure 3), a polydisperse aerosol has a lower average particle diameter (Warren and Seinfeld, 1984). Continuum effects for particle growth were not included in the theories. Calculations showed that particle formation ceased while the particles were still in the free-molecule regime. Thus, for high saturation ratios where reactant wall losses were negligible, the only effect of neglecting continuum effects was to decrease the time required for the particles to grow to their final size. Since all measurements were taken at 25-s residence time where particle formation and growth had ceased, this effect was unimportant for high saturation ratios. For low saturation ratios, neglecting continuum effects may have caused the theory to underpredict reactant wall losses since theory overpredicted rates of particle growth. 4.2. Effect of Mixing on Aerosol Concentration and Average Diameter. The predictions of the lamellar mixing theory for .Z = 5.8 were compared to total particle concentrations obtained with the two mixing heads (Figure 4). Experiments showed that faster mixing produced more particles; particle concentrations with M-19 were an order of magnitude higher than with M-1 for all values of S,. This occurred since particle formation and growth took place at the interface between ammonia and nitric acid gas streams. Diffusing ammonia and nitric acid were scavenged by aerosol particles formed at the interface. More diffusing ammonia and nitric acid molecules were lost as L was increased, resulting in fewer particles. Figure 4 shows that a theory neglecting mixing effects (the infinitely fast mixing theory) could overpredict the total particle concentration by 1 or 2 orders of magnitude for large saturation ratios. Average particle diameters for M-1 were up to 3 times as large as for M-19. More particles were produced for faster mixing (M-19, L = 1 cm) than for slower mixing (M-1,L = 2 cm) (Figure 4). Thus, faster mixing produced smaller particles since the amount of condensable material was the same for both cases. Similar results were obtained by Liu and Levi (1980), who studied formation of sulfuric acid aerosol by mixing a hot sulfuric acid vapor stream with an ambient temperature gas stream. In their system, more
8 10-
Infinitely Fast
o single j e t m
.
7
10-
;Y
z C
0
:6
-
10-
u a, 0
0 a, -
-2 2
5 10-
a
a,
-5
.. L
a,
C
a , 4
0 10-
I& I Cup-mixing Inlet Saturation Ratio So
Figure 4. Effect of mixing geometry on total particle concentration. Experiment and theories with 2 = 5.8 show that faster mixing (smaller L ) produces higher particle concentrations. Neglecting the effects of reactant mixing ( L < 0.1 cm, infinitely fast mixing theory) overpredicted particle concentration by up to 2 orders of magnitude.
rapid mixing also produced a greater number of particles, resulting in a decrease in the mean particle size. These results show that a theory neglecting the effects of reactant mixing can underpredict the particle diameter. A desirable characteristic for powders is for the average particle diameter to be large enough to allow convenient collection of the particles (Heberlein, 1984). The theories and experiments indicated that larger particles are favored by slower mixing and lower initial saturation ratios. Larger particles, however, are obtained at the cost of lower particle concentrations (Figure 3a) and yields (Figure 3b). 4.3. Effect of Reactor Residence-Time Distribution on Particle-Size Distribution. For sufficiently high saturation ratios, the mixing theories predicted narrower particle-size distributions than those observed experimentally. Measured particle-size distributions for the single-jet mixing head were nearly monodisperse (W < 0.3) for So 5 1 X lo5 (Figure 5) and polydisperse (W = 0.8-2.2) for So 2 1 x lo5. The 19-jet mixing head produced polydisperse aerosol for all saturation ratios studied (Figure 6). Theory, however, predicted nearly monodisperse aerosol (W < 0.3) for both mixing heads and all saturation ratios. Polydispersity probably resulted from broad residence-time distributions, resulting from fluid recirculation (Naumann and Buffiam, 1983) with the single-confined-jet (Iribarne et al., 1972) and multiple-jet mixing heads (McKelvey et al., 1975). Flow visualization indicated that recirculation occurred over roughly the first 10 cm or 1 s of residence time for both mixing heads. Measured residence-time distributions for M-1 and M-19 were approximately exponential for the total flow rate of 10 L/min used in the experiments. Pratsinis et al. (1986b) have shown that extensive recirculation resulting in well-mixed conditions produces a broad particle-size distribution with an exponential dependence on the particle diameter. Figure 7 shows that a particle-size distribution for M-19 with So = 5.2 x lo5 is approximately exponential. Par-
Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987 2005 I 05.
7
10-
4 10 '
; *
*
E .
6 10-
s
-
-
1
n P 0 0
-
.
z n
-a
z
5
10-
lo3
4 10
-
102
-0
0.1
I
1 .o
PARTICLE DIAMETER dp urn
103-0
0.2
0.4
0.6
PARTICLE DIAMETER
Figure 5. Particle size distribution for single-jet mixing head measured with OPC for initial saturation ratio of 5 X lo4. Electrical aerosol analyzer detected no particles below 0.1 pm. 1 06
Io5
m
; Q Pn
-00 5
. 4 10
io3 0.01
PARTICLE DIAMETER d p um
Figure 6. Particle-size distribution for 19-jet mixing head measured with EAA for initial saturation ratio of 2.6 X lo5.
ticle-size distributions for M-1 were bimodal for So = 2.6 X lo5 and 5.2 x lo5. Recirculation can produce bimodal particle-size distributions by seeding the reactor inlet streams. These results suggest that the reactor behaved as a well-mixed reactor followed by a laminar flow reactor. For saturation ratios greater than approximately 1 x lo5,the lamellar mixing theory with L = 2 cm (single-jet mixing head) indicated that the time required for complete particle formation and growth was on the order of or less than the residence time in the mixing region (approximately 1 s). As a result, particle formation and growth were rapid and confined to the mixing region and the aerosol dynamics were influenced by the reactant mixing process. For saturation ratios less than 1 x IO5, the lamellar mixing
0.8
1.0
dp
Figure 7. Particle-sizedistribution obtained with 19-jet mixing head for So = 5.2 X lo5. Approximately linear slope indicates exponential particle-size distribution resulting from recirculation at the reactor entrance.
theory with L = 2 cm showed that complete particle formation and growth required on the order of 10 s, a time longer than the residence time in the mixing region. As a result, the aerosol dynamics occurred mainly in the laminar flow portion of the reactor, resulting in monodisperse particles for the single-jet mixing head as predicted by the theories. This infinitely fast mixing mode of reactor behavior has also been studied by Okuyama et al. (1984) using a nonisothermal system. Okuyama et al. mixed a hot gas stream containing a condensable vapor with a cold gas stream. The time for complete mixing was much shorter than that for particle formation and growth. Thus, the infinitely fast mixing theory should also be valid for nonisothermal systems with sufficiently fast mixing. The lamellar mixing theory with L = 1 cm (multiple-jet mixing head) predicted that particle formation and growth were complete after a few seconds or less for all saturation ratios studied. As a result, particle formation and growth occurred in the mixing region, and measured size distributions were polydisperse for all the saturation ratios studied. The effect of fluid recirculation on the polydispersity index was examined by varying the total flow rate, keeping the cup-mixing reactant concentrations constant at So = 2.6 X lo5. For a 10 L/min flow rate, W for M-1 ranged from 0.85 to 1.5; RTDs were approximately exponential. Decreasing the total flow rate to 5 L/min narrowed the particle-size distribution to W = 0.5-0.8; RTDs approximated that for fully developed laminar flow. Thus, narrowing the residence-time distribution by reducing recirculation narrowed the particle-size distribution for the single-jet mixing head. The spread of the particle-size distribution for the 19-jet mixing head did not depend on the total gas flow rate for So = 2.6 X lo5. These results also indicate that particle-size distributions obtained with the single- and multiple-jet mixing heads for large saturation ratios were dominated by recirculation at the reactor entrance. Polydispersity can also be caused by a distribution of lamellae thicknesses resulting from the mixing process or by lamellae deformation by the nonuniform velocity pro-
2006 Ind. Eng. Chem. Res., Vol. 26, No. 10, 1987
file. Particle-size distributions calculated with a distribution of lamellae thicknesses would be broader than those calculated with a single lamellae thickness since the average particle size depends strongly on the lamellae thickness. Therefore, the incorporation of a distribution of lamellae thicknesses into the lamellar model is expected to result in better agreement of theory with experiment. Incorporation of a distribution of lamellae thicknesses into the lamellar model, however, adds an adjustable parameter to the model and is not expected to add significant physical insight to the problem. 4.4. Effect of Seeding on Particle Size Distribution. Pratsinis et al. (1986a) have shown theoretically that seeding laminar-flow tubular AFRs can narrow the product particle-size distribution. Experiments were done to determine if seeding could narrow the particle-size distribution. Ammonium nitrate seed particles with W values of 0.5-1.0 and number-average particle diameters of 0.01-0.04 pm were introduced into the reactor through the center nitric acid jet of the single-jet mixing head. The inlet saturation ratio was 2.6 X lo5. Seeding with an aerosol surface area of lo3 pm2/cm3 narrowed the particle-size distribution from W = 1-2 to W = 0.5-1.0. Seed particles acted as sinks for condensing ammonia and nitric acid. This reduced the saturation ratio, eliminating the production of small particles at longer residence times. Pratsinis et al. (1986a) have shown that new particle formation must be suppressed by seed particles to obtain monodisperse aerosol. Measurements confirmed that seed particle concentrations were the same as product particle concentrations for conditions under which seeding was effective in narrowing the particle-size distribution. Appreciable new particle formation was observed for conditions under which seeding was ineffective in narrowing the particle-size distribution. For the single-jet mixing head, the addition of seed particles increased yields from 0.4 (Figure 3b) to near unity for So = 2.6 X lo5. Reactants lost to the walls without seeding were consumed by the seed particles.
5. Summary and Conclusions The parameters of importance for the design of AFRs with multiple-jet reactant mixing were identified. Reactor and jet Reynolds numbers, jet spacing, radial diffusion of reactants, reactant concentrations, and extent of seeding controlled reactor behavior. Operation of multiple-jet reactors under conditions producing high aerosol yields does not depend on reactor diameter since radial diffusion of reactant gases is not important. Reactor operation, however, depends strongly on jet Reynolds number and spacing since these quantities determine the importance of recirculation between the jets which, in turn, controls the spread of the particle-size distribution. Operation of single-jet reactors depends on both reactor and jet Reynolds numbers since these quantities determine the extent of fluid recirculation in the reactor. Two limiting cases for AFR operation with reactant mixing were observed. In the limit of low reactant concentrations, reactor operation was not influenced by reactant mixing; particle formation and growth were slow relative to reactant mixing and occurred mainly in the laminar flow portion of the reactor. The laminar flow gave a narrow residence-time distribution, resulting in monodisperse aerosol. This type of reactor behavior can also be obtained in nonisothermal systems with fast mixing relative to particle formation and growth. Large wall losses of reactants were observed for the lowest reactant concentrations studied. In the limit of high reactant con-
centrations, reactor operation was controlled by the mixing process; particle formation and growth were rapid relative to mixing and were confined to the mixing region near the reactor entrance. Recirculation in the mixing region produced a broad residence-time distribution, resulting in a polydisperse aerosol. Narrowing the residence-time distribution by reducing recirculation at the reactor entrance narrowed the particle-size distribution. Wall losses of reactants were negligible for sufficiently high reactant concentrations. Seeding one of the reactant gas streams with ammonium nitrate particles narrowed the particle-sizedistribution and increased yields. Seed particles prevented the formation of new particles a t long residence times by consuming reactants and lowering the saturation ratio. Design guidelines were developed for reactors intended for production of monodisperse particles at high yields by reactant mixing. Although the experiments and calculations were performed for an isothermal system, the guidelines should also be valid qualitatively for nonisothermal systems. High yields of monodisperse particles are favored by reducing recirculation (narrowing RTD), increasing the speed of mixing, and seeding the reactant gas streams. Larger particles can be obtained at the expense of broader particle-size distributions by increasing recirculation (broadening the RTD) and decreasing the speed of reactant mixing relative to particle formation and growth. Large particles can also be obtained at the expense of lower yields and particle concentrations by decreasing the reactant concentrations. The aerosol production rate can be increased by increasing reactant concentrations and total flow rate. Increasing the reactant concentrations increases the particle concentration. Thus, the upper limits for the reactant concentrations are determined by the effects of coagulation, a mechanism that can broaden the particle-size distribution. Operation at higher flow rates, corresponding to higher Reynolds numbers and turbulent flow, should improve reactor performance; turbulence results in faster reactant mixing which favors narrower particle-size distributions.
Acknowledgment This work was supported in part by the National Science Foundation, Grant CPE-81-17288.
Nomenclature A’ = aerosol surface area, cm2/cm3 b = radius of reactor, cm CA‘ = concentration of ammonia, no./cm3 CN’ = concentration of nitric acid, no./cm3 d, = particle diameter, cm a , = monomer diameter, cm D = molecular diffusivity, cm2/s E = diffusion group f = 1 - r2 for parabolic velocity profile, = for flat velocity profile Z = nucleation rate Kq = equilibrium constant for the reaction HN03(g)+ NH3(g) = NH4NO3(s),no./cm6 k* = number of molecules in a particle of critical size k B = Boltzmann’s constant L = width of a lamella in lamellar mixing model, cm mA = ammonia molecule mass, g mN = nitric acid molecule mass, g m, = monomer mass, g MI’ = first aerosol moment, cm/cm3 M2’ = second aerosol moment, cm2/cm3 N’= aerosol number density, no./cm3 r‘ = radial coordinate, cm
Ind. Eng. Chem. Res. 1987,26, 2007-2011 Re = reactor Reynolds number S = saturation ratio s1 = monomer surface area, cm2 t = residence time, s T = temperature, K u = fluid velocity, cm/s u1 = monomer volume, cm3 V‘ = aerosol volume density, cm3/cm3 x ’ = axial coordinate, cm W = polydispersity index Y = aerosol yield y’ = Cartesian coordinate perpendicular to x axis, cm Greek Symbols
0 = dimensionless average residence time = aerosol surface tension, dyn/cm Z = dimensionless surface tension group T
= time constant for infinitely fast and lamellar mixing
theories, s Superscripts -’ = dimensional = average Subscripts s = seed particle A = ammonia N = nitric acid AN = ammonium nitrate 0 = inlet
I = infinitely fast mixing theory L = lamellar mixing theory 1 = limiting reactant Registry No. NH3, 7664-41-7; H N 0 3 , 7697-37-2; NH4NO3, 6484-52-2.
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Henry, J. F.; Gonzales, A.; Peters, L. K. Aerosol Sci. Technol. 1983, 2, 321. Herrmann, E. Characterizationof Powder Surfaces; Parfitt, G . D., Sing, K. S. W., Eds.; Academic: New York, 1976. IMSL IMSL Contents Document, 8th ed.; International Mathematical and Statistical Libraries: Houston, 1980. Iribarne, A.; Frantisak, F.; Hummell, R. L.; Smith, J. W. AZChE J. 1972, 18, 689. Jenson, V. G. Chem. Eng. Sci. 1983, 38, 1151. Kato, A.; Hojo, J.; Okabe, Y. Mem. Fac. Eng. Kyushu Uniu. 1981, 41, 319. Katz, J. L.; Donohue, M. D. J. Colloid Interface Sci. 1982,85, 267. Kingery, W. D. Introduction to Ceramics;Wiley: New York, 1960. Kodas, T. T.; Pratsinis, S. E.; Friedlander, S. K. J . Colloid Interface Sci. 1986, 111 , 102. Kodas, T. T. “Aerosol Dynamics In Tubular Flow Reactors”, Ph.D. Dissertation, University of California, Los Angeles, 1986. Lay, J. R.; Iya, S. K. ZEEE Photovoltaic Spec. Conf., 15th 1981,565. Liu, B. Y. H.; Levi, J. In Generation of Aerosols and Facilities for Exposure Experiments; Willeke, K., Ed.; Ann Arbor Science: Ann Arbor, MI, 1980. Mao, K. W.; Toor, H. L. AIChE J . 1970, 16,49. McKelvey, K. N.; Yieh, H.; Zakanycz, S.; Brodkey, R. S. AIChE J. 1975, 21, 1165. Medallia, A. I.; Rivin, D. In Characterization of Powder Surfaces; Parfitt, G. D., Sing, K. S. W., Eds.; Academic: New York, 1976. Miller, T. J.; Potkay, E.; Yuen, M. J. “Review of Chemistry and Mechanism of Deposition for Optical Waveguide Fabrication by Vapor Deposition from a Combustion Flame”, AIChE Meeting, Anaheim, CA, 1984. Naumann, E. B.; Buffham, B. A. Mixing in Continuous Flow Systems; Wiley Interscience: New York, 1983. Okuyama, K.; Kousaka, Y.; Motouchi, T. Aerosol Sci. Technol. 1984, 3, 353. Olszyna, K. J.; DePena, R. G.; Heicklen, J. J . Aerosol Sci. 1974,5, 421. Ottino, J. M. AIChE J . 1981, 27, 184. Pratsinis, S. E.; Kodas, T. T.; Dudukovic, M. P.; Friedlander, S. K. Ind. Eng. Chem. Process Des. Deu. 1986a, 25, 634. Pratsinis, S. E.; Kodas, T. T.; Dudukovic, M. P.; Friedlander, S. K. Chem. Eng. Sci. 1986b,41, 693. Prochazka, S.; Greskovich, C. Cer. Bull. 1978, 57, 579. Rutner, E.; Goldfinger, P.; Hirth, J. P. Condensation and Euaporation of Solids; Gordon and Breach: New Yorli, 1964. Stelson, A. W.; Friedlander, S. K.; Seinfeld, J. H. Atmos. Enuiron. 1979, 13, 369. Ulrich, G. D.; Subramanian, N. S. Combust. Sci. Technol. 1977, 17, 119. Vance, J. L.; Peters, L. K. Ind. Eng. Chem. Fundam. 1976,15,202. Warren, D.; Seinfeld, J. H. J. Colloid Interface Sci. 1984, 3, 135.
Received for review May 6, 1986 Revised manuscript received April 9, 1987 Accepted June 10, 1987
An Internally Heated Weighed Reactor Thermobalance for Gas-Solid Reaction Studies Michael H. Treptau and Dennis J. Miller* Department of Chemical Engineering, Michigan State University, East Lansing, Michigan 48824-1226
A novel thennobalance apparatus is described which alleviates some problems traditionally associated with thermogravimetric reaction studies. The new design provides direct measurement of sample temperature, elimination of external mass-transfer resistances via gas flow directly through the sample bed, and added safety using a cold-wall vessel design. The sensitivity of the balance is approximately f10 mg for a 2-g carbon sample. The apparatus consists of a pressure vessel, a counterweighted balance arm, and a top-loading electronic balance. The pressure vessel is internally heated and insulated; the solid sample is a fixed or fluidized bed through which reactant gas flows directly. Results from gasification with C02and O2 show that the balance adequately measures sample weight during reaction. Thermogravimetric analysis has long been recognized as a useful and straightforward method for ‘measuring 0888-5885/87/2626-2007$01.50/0
gas-solid reaction rates and adsorption phenomena. Thermobalance apparatus of many different configurations 0 1987 American Chemical Society
