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Breakup of Latex Doublets byImpactionWalter John a & Virendra Sethi aa Air and Industrial Hygiene Laboratory, CaliforniaDepartment of Health Services , Berkeley Way, Berkeley,CA, 94704Published online: 11 Jun 2007.

To cite this article: Walter John & Virendra Sethi (1993) Breakup of Latex Doublets byImpaction, Aerosol Science and Technology, 19:1, 57-68, DOI: 10.1080/02786829308959621

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Breakup of Latex Doublets by Impaction

Walter John* and Virendra Sethit Air and Industrial Hygiene Laboratoly, California Depavtment of Health Services, 2151 Berkelq Way, Berkeley, C A 94704

The breakup by impaction of a simple agglomerate consisting of two identical spherical particles has been studied. The agglomerates were doublets produced by nebulizing suspensions of latex particles. The doublet concentrations before and after impaction were deter- mined from the particle size spectra obtained with an optical particle counter. Preliminary experiments showed that the latex doublets did not break up in the acceleration nozzle of the impactor. The doublet frac- tion (DF) is defined as the doublet/singlet concentra- tion ratio after impaction to that before impaction. The DF of 2.99-pm Dow latex measured at ,/Stk= 1.62 decreased by about a factor of 2 as the relative humid- ity (RH) was varied from 8% to 85%. The remaining experiments were made at low RH with seven different

surfactant-free suspensions of polystyrene latex stabi- lized by the addition of charged surface functional groups. All of the data, for particle sizes ranging from 1.62 to 4.07 p m and impact velocities from 10 to 80 m/s, could be fitted by the expression, DF = 18.2

-0.5SD -1.60 , where the impact velocity v is in m/s and the particle diameter D is in pm. The van der Waals adhesion energy is calculated to be less than 1/3000 of the kinetic energy needed to break up half of the doublets. The repulsive electrostatic energy of the surface functional groups is estimated to be about 1.25 times larger than the van der Waals adhesion energy. It is concluded that the doublets are probably bound by bridges of residue left after droplet evapora- tion.

INTRODUCTION

The strong cohesive forces between parti- cles cause the formation of agglomerates when particles come into contact. Thus bulk powders and soil particles are invari- ably agglomerated. When agglomerates collide with other particles or impact on a surface, constituent particles are released. Sehmel (1978) observed up to 10 million particles produced from single soil parti- cles, 130-400 pm in diameter, when they were dropped onto a plate. The produc- tion of soil aerosols by wind erosion is attributed to the disintegration of agglom- erates (Gillette, 1974). Davies et al. (1951) reported the breakup of coal dust aggre-

* To whom correspondence should be addressed. 'Present address: Department of Civil and Envi-

ronmental Engineering, University of Cincinnati, Cincinnati, OH 45221.

gates during passage of the aerosol through slits. They also observed the frac- ture of quartz dust by impaction. John et al. (1991b) found that the deagglomera- tion of soil particles on the impaction plate of a PM-10 sampler caused over- sampling. The generation of aerosols in a fluidized bed involves the deagglomera- tion of the feed particles from the bed particles (Guichard, 1976). Thus, deag- glomeration is important in a variety of aerosol processes.

There are relatively few studies that yield information on the mechanisms in- volved in deagglomeration. Rosinski and Langer (1974) concluded that the shed- ding of particles by large soil particles was not due to breakup of loose aggregates but that large numbers of small particles were present in the interstices of the par- ent particle. After shedding, the parent particle was practically unchanged. Kou-

Aerosol Science and Technology 19:57-68 (1993) Q 1993 Elsevier Science Publishing Co., Inc.

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58 W. John and V. Sethi

saka et al. (1979) found that powders were more effectively dispersed by impaction than by shear flows. It was pointed out (Kousaka et al., 1980) that, if the cohesive forces within the aggregate are weaker than the adhesion force to a surface, reentrainment by air flow can break the agglomerate. Gillette et al. (1972) showed that the particle size distribution of soil samples suspended in water agree with the size distributions of airborne soil. When detergent was added to the water, an excess of submicrometer particles was observed compared to the soil aerosol, indicating that submicrometer particles are not released during the aerosol pro- duction. Al-Chalabi et al. (1990) found that 3-pm silica spheres were better dis- persed from a fluidized bed when the sur- faces were treated to make them hy- drophobic. This prevented the absorption of water with consequent formation of water bridges between particles.

There are no theories available with which to predict deagglomeration phe- nomena. Experimental measurements of simplified agglomerated systems are needed to guide the formulation of the- ory. We have undertaken an exploratory study of the simplest agglomerate possi- ble, two identical spherical particles. Such doublets are easily generated by nebuliz- ing suspensions of latex particles. The la- tex doublets were impacted on a surface at various velocities and the fraction un- dergoing breakup observed. The effect of varying particle size was investigated. Sev- eral types of latex suspensions were used to study possible surface effects.

EXPERIMENTAL METHODS

Generation of Latex Doublets

It is well known that when a suspension of latex particles is atomized, the droplets contain varying numbers of particles, de- pending on the concentration. The proba-

bility P(x) of having x particles in a ran- domly chosen droplet is governed by the Poisson distribution, but an integration must be performed over the droplet size distribution (Raabe, 1968):

Here the droplet size distribution has been taken to be lognormal with count median diameter CMD and geometric standard deviation ag. d is the droplet diameter. n is defined by:

where F is the volume fraction of parti- cles in the stock solution, y is the dilution ratio, and D is the particle diameter. The substitution, d = eY, enables the writing of Eq. 1 in a form which can be numerically integrated by a personal computer appli- cation such as MATHCAD'.

(In CMD - y)2

2 1n2%

Equation 3 can be used as a guide for the design of the experiment; however, the nebulizer parameters must be specified. For this work, the DeVilbiss No. 40 nebu- lizer was chosen for three reasons: (1) the small droplet size, 4.2-pm MMD (a, = 1.8)

' The mention of commercial products does not imply an endorsement of such products.

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Breakup of Latex Doublets by Impaction

at 10 psi (Mercer et al., 1968), minimizes the amount of dissolved residue which will deposit on the particles when the droplet evaporates, (2) the small volume of the nebulizer permits efficient use of the ex- pensive latex solution. The dead volume is about 1 mL; a 5-min run consumes about 1 mL, (3) the glass construction facilitates cleaning between runs. Even when the particle size is not changed, the solution must be changed because the concentra- tion increases as the solution is nebulized.

The evaluation of Eq. 3 for D = 2.5 pm, F = 0.04, and y = 20 gives an illustra- tive result: 99.8% of the droplets gener- ated have no particles, 0.19% contain a singlet, 0.003% contain a doublet, and 0.0002% contain a triplet. The doublet/ singlet ratio is predicted to be 1.5%. For these operating parameters, the doublet/ singlet ratio observed by experiment was 3%. Thus Eq. 3 underestimated the dou- blets by a factor of 2. Two reasons may be advanced for the discrepancy. First, the calculation is sensitive to the droplet size distribution; the assumed parameters may not have been accurate for our experi- ment. Secondly, we note that the esti- mated CMD droplet diameter, 1.5 pm, is smaller than the latex particles. This may cause a deviation from the simple theory.

For the above example, the triplet/ doublet ratio is predicted to be 6.7%. This shows that the doublet/singlet ratio has to be held below about 10% to avoid significant errors from the breakup of triplets to form doublets. The triplet/ doublet ratio was estimated for the oper- ating conditions actually used by adjusting y in Eq. 3 to match the calculated to the observed doublet/ singlet ratios and then calculating the triplet/ doublet ratio. The ratios are listed in Table 1. During the experiment, the absence of a triplet peak confirmed that no detectable error oc- curred from triplets. For the measure- ments, the dilution factors ranged from 2 to 40.

Identification of Doublets

The latex particles were sized and counted by a Climet 208 optical particle counter (OPC). The doublets appeared as a peak in higher channels of the pulse height analyzer than the singles peak (Figure 1). However, as the peak marked Singlet B illustrates, some of the latex suspensions contained traces of singles at slightly larger particle size than the main singles size. The contaminant singles were pre- sent in the latex suspension as received from the manufacturer. The concentra- tion of contaminant singles was so small that it had no effect on the measure- ments, but the contaminant singlet peak (Singlet B) had to be distinguished from the doublet peak (Doublet A) formed from the main singles (Singlet A). The doublet peak was identified by running solutions at different dilutions; the doublet/singlet ratio decreases with dilution whereas the contaminant singlets maintain a constant ratio with the main singlets. Another test was the observation of a decrease in the doublet/singlet ratio after impaction on a surface (Figure 1). Incidentally, total count rates were below 2,000-3000 counts/min so that false doublet counts produced by two single particles traversing the OPC's viewing volume simultaneously were neg- ligible.

An attempt was made to predict the optical size of a doublet. In the particle size range above 2 pm in diameter, the Climet 208 produces a pulse with a height that varies as the square of the particle diameter, ix., as the projected area. The projected area of a doublet, averaged over all orientations, can be calculated analyti- cally. Our result (unpublished) is 1.85 times the projected area of a singlet. The experimental result we obtained was 1.42 + 0.06, averaged over all of the latex sus- pensions. This may indicate a degree of alignment of the doublet in the Climet, produced by shear flow in the inlet. While

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TABLE 1. Measured Doublet/Singlet Ratio, Estimated Triplet/Doublet Ratio

Estimated Doublet/singlet triplet/doublet

Latex suspension (%I (%I

1.62-pm sulfate 8 20 2.54-pm sulfate 3 11 3.06-pm sulfate 1 4 4.07-pm sulfate 6 3 2.51-pm amidine 3 10 2.51-pm AML 3 10 2.80-pm CML 5 15

I Singlet A 1 .

t- Doublet A 1. : lab:

I - ! !

Singlet A+ I i I :: i . I . I: +Singlet B

W. John and V. Sethi

the calculated size could not be used to identify the doublets, the constancy of the ratio of the optical size of the doublet to the singlet for the various latex suspen- sions indicates a consistent identification.

Latex Suspensions

Latex suspensions are commonly stabi- lized against coagulation by the addition of surfactant. We used such a latex in the preliminary setup work because of the availability of an old supply of Dow latex.

0 FIGURE 1. Optical particle coun- ter spectra of 2.54-pm sulfate latex aerosol. Top panel: before im- paction, bottom panel: after im-

200 paction. Note expanded scale on the right.

Channel Number

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Breakup of Latex Doublets by Impaction

However, when the droplets dry, the sur- factant is deposited on the particles. To avoid this complication, we conducted most of the experiment with surfactant- free latex. Such latexes are stabilized by surface coatings of charged functional groups. Several different types of sur- face-coated latexes were used to look for possible differences in doublet bonding produced by the surface coatings. The characteristics of the latex suspensions used in the experiments are listed in Table 2.

Experimental Arrangement Figure 2 shows the arrangement of the apparatus. Aerosol from the DeVilbiss No. 40 nebulizer was diluted with extremely dry air. The aerosol was then neutralized with a Kr-85 radioactive source. To pro- vide additional drying, the aerosol was passed through a diffusion dryer and then to a plenum. The excess from the plenum

TABLE 2. Characteristics of Latex Suspensions"

Surface Particle charge diameter Particles/rnL density

Typeb ( prn) x 1 0 - V pc/crn2)

Sulfatec 1.62 + 0.02 39.8 4.68 Sulfate 2.54 f 0.11 9.37 4.36 Sulfate 3.06 & 0.10 5.36 4.29 Sulfate 4.07 & 0.27 2.25 0.39 Amidine 2.51 k 0.12 5.03 31.2 A M L ~ 2.51 + 0.12 4.66 17.68 C M F 2.80 i 0.31 4.09 43.7

a Data from manufacturer, Interfacial Dynamics Corp., Porkland, OR 97220.

Polystyrene latex with surface charge groups listed. "Surface functional groups are sulfate and hydroxyl. d ~ l d e h y d e modified latex produccd by reacting 40% of

amidine groups with glutaraldchyde. " Carboxylte modified latex, aurfacc groups predomi-

nately carhoxyl. Only hydrophilic latcx in table; all othcrs are hydrophobic.

passed over a probe for the monitoring of the relative humidity and temperature.

The test chamber has been described previously (John et al. 1991b). It is equip-

1 PLENUM

A I R -- -- TEST

CHAMBER MANOMETER

I M P A C T I O N D E V I L B I S S SURFACE D I L U T I O N A I R N E B U L I Z E R

__*

COUNTER

FIGURE 2. Experimental arrangement.

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62 W. John and V. Sethi

ped with a circular nozzle impactor. Most of the measurements were made with a 0.08-cm diameter nozzle. The impaction surface was a polished aluminum SEM stub which was machined down to a 5-mm diameter to minimize retention of parti- cles after impaction. The impaction sur- face can be retracted to permit particle counting without impaction. The ratio of singles counts with the impaction surface retracted to counts with the surface in place averaged 1.04 f 0.10 over the exper- imental runs. Thus losses in the chamber including deposition on the impaction sur- face were about 4%. This is consistent with a previous determination of 5% par- ticle losses in the chamber (John et al., 1991a). The impactor is pumped by a Climet 208 OPC. Flow through the im- pactor nozzle can be varied by the addi- tion of bypass air, the total flow through the OPC being maintained at 5 L/min. The nozzle flow was measured by the pressure drop indicted by a precision manometer. The pressure drop was cali- brated in terms of flow rate with a bubble meter.

Pulses from the OPC were counted and sorted in a multichannel analyzer, then stored in a personal computer. Sample particle spectra are shown in Figure 1. The doublet peak is well resolved from the much larger singlet peak. To elimi- nate any effects from concentration varia- tions, each doublet count (area under the doublet peak) was divided by the corre- sponding singlet count. A measurement consisted of taking a 5-min count with the impaction surface retracted and then a 5-min count with the impaction surface under the nozzle. The "doublet fraction," the proportion of latex doublet particles which undergo impaction without breakup, is defined here by:

( ND )after impaction Doublet fraction =

( N~ )before impaction

where ND = (number of doublets)/(num- ber of singlets).

MEASUREMENTS AND RESULTS

Investigation of Breakup in the Nozzle

Davies et al. (1951) reported that coal dust particles were deagglomerated in passing through nozzles. This was at- tributed to the lagging of the particles in the accelerating flow, resulting in a high relative velocity between the air and the particles. The possibility of impaction on nozzle walls was also mentioned. We therefore began the present study by in- vestigating whether the latex doublets breakup in the nozzle.

Aerosol was nebulized from a diluted solution of 2.68-pm Dow latex (presuma- bly containing surfactant) and accelerated through a 0.159-cm diameter nozzle with- out the impaction plate. For various flow rates, JStk for doublets was calculated from:

where pp is the particle density, 1.055 g/cm3, C is the slip factor, u is the air flow velocity, p is the viscosity of air, dj is the nozzle diameter, D, is the singlet particle diameter, and f 2 is the ratio of the aerodynamic diameter of a doublet to that of a singlet. Since we have no knowl- edge of the orientation of the doublets at impaction, we choose f, for random ori- entation, which is f, = 1.20, based on the- ory (Happel and Brenner, 1973) or experi- ment (Cheng, et al., 1988).

The percentage of doublets leaving the nozzle was measured over a range of JStk. If doublet breakup occurs in the nozzle, the percentage of doublets would be ex- pected to decrease with increasing JStk. The data points were fitted with a regres- sion line which was then used to calculate the change in the percentage of doublets over the range of JStk. Results are listed

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Breakup of Latex Doublets by Impaction

in Table 3. Also listed are counts taken with the 0.159-cm diameter nozzle re- moved, leaving a straight pipe with a 0.79- cm inside diameter. Similar data are listed for the surfactant-free latexes. These data were obtained during the impaction runs because each run included a measure- ment with the 0.08-cm diameter nozzle and no impaction plate.

For only one case in Table 3, 2.51-pm AML (aldehyde modified latex), was the change in percent doublets negative, indi- cating the possibility of breakup. Even this case is marginal. The consistent posi- tive change for all the other latexes shows a small experimental bias for an unknown reason. It is also noteworthy that the data on the last line in the table, for measure- ments with a relatively large pipe, shows no difference from the data on the pre- ceding line taken with the nozzle at higher JStk. We conclude that breakup did not occur in the nozzle. Evidently, the latex doublets are more tightly bound than were the coal dust particles studied by Davies et al. (1951).

Effect of Relative Humidity on Breakup

A series of measurements of the doublet fraction (defined in Eq. 4) were made at various relative humidity (RH) levels to determine the sensitivity of breakup to RH. For all of the measurements, 2.99-pm Dow latex doublets were impacted at JStk = 1.63. The air temperature was 22°C. To

reach the higher RH values, the diffusion dryer was removed and the dilution air humidified.

The data are plotted in Figure 3. The slope of the regression line is - 0.0022 f 0.0011. In going from 17% to 85% RH, the doublet fraction decreased by nearly a factor of two, but the uncertainty is rela- tively large. It is somewhat surprising that humidity apparently facilitates breakup.

Doublet Breakup by Impaction

For each of the available latexes, the dou- blet fraction was measured as a function of Stokes number. With the diffusion dryer in place, the RH was typically 7% or 8% at the beginning of a run and increased by 1% or 2% by the end of the 5-min run. Thus the RH was relatively low and rela- tively constant for most of the runs. An exception was the measurement using 4.07-pm sulfate. The diffusion dryer could not be used because the large particle size resulted in prohibitive losses. For this la- tex, the RH ranged between 24% and 31%.

For each latex type, the doublet frac- tion vs. Stokes number was plotted on log-log scales. As illustrated in Figure 4 for 2.80-pm CML (carboxylate-modified latex), the data were found to be fit rea- sonably well by a straight line. Each data set can then be represented by the slope of the line and the Stokes number for a doublet fraction of 0.5. These parameters

TABLE 3. Data on Possible Doublet Breakup in Nozzle

Mean percent Changea in Latex dstkmm ds%,, doublets percent doublets

2.54-pm sulfate 1.0 2.1 3.0 + 0.4 + 0.3 + 0.4 2.52-pm amidine 0.9 2.5 2.4 + 0.2 + 0.4 k 0.2 2.51-pm AML 1.0 2.3 2.8 + 0.5 - 0.9 1 0.4 2.80-pm CML 1.2 2.8 3.7 + 0.4 + 0.5 0.3 2.68-pm Dow 0.8 1.8 2.2 + 0.3 + 0.4 k 0.3 2.68-pm D O W ~ 0.4 0.8 2.1 + 0.3 + 0.5 k 0.3

"Change over the range of JStk, calculated from regression analysis. Negative sign indicates breakup. b Data taken with 0.79-cm diameter pipe, no nozzle.

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0.0 L 0 20 40 60 80 100

RH. %

FIGURE 3. Doublet fraction vs. relative humid- ity for 2.99-pm Dow latex aerosol after im- paction at JStk = 1.63.

are listed in Table 4 where the Stokes number for a doublet fraction of 0.5 has been converted to the corresponding ve- locity and called u,,. The correlation co- efficients are also listed; the relatively high values indicate that a straight line is a good fit. The average slope from the data in Table 4 is - 0.58 ) 0.17. Therefore, the

1

Stakes Number

FIGURE 4. Doublet fraction of 2.80-pm CML latex aerosol vs. Stokes number. The regression line is shown.

W. John and V. Sethi

TABLE 4. Regression Parameters for Doublet Fraction vs. Stokes Number

u,, Correlation Latex Slope (m/s) coefficient

1.62-pm sulfate 2.54-pm sulfate 2.54-pm sulfateb 3.06-pm sulfate 4.07-pm sulfate 2.51-pm amidine 2.51-pm AML 2.80-pm CML

"Extrapolated value; lowest doublet fraction was 0.65. This run was not included in the data analysis.

doublet fraction can be written: DF = K ~ ~ . ~ ~ (6) where K is independent of velocity.

To obtain the dependence of the dou- blet fraction on particle diameter, us, was plotted vs. particle diameter on a log-log scale. Figure 5 shows that the data points lie very close to a straight line. The tight fit must be considered somewhat fortu- itous. The data point at the smallest diam- eter, 1.62-pm sulfate, involved an extrapo- lation down to 0.5 from 0.65. the smallest

- Ragremmion Une 0 1.62 urn Sulfate-PSL A 2.54 urn " " 0 3.08 urn " "

(A) 0 4 . 0 7 u r n " " rn 2.51 urn AML-PSL A 2.52 urn Amidino-PSL

2.80 urn CML-PSL

1 10

Particle Diameter, um

FIGURE 5. Particle velocity producing 50% doublet breakup vs. particle diameter. The re- gression line is shown; the point in parentheses was not included in the analysis.

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Breakup of Latex Doublets by Impaction

doublet fraction which could be measured with the apparatus. The data point at the largest diameter, 4.07-pm sulfate, was taken at a somewhat higher RH, was dis- cussed above. However, on the basis of Figure 3, a correction to lower RH would increase u5, by only about 12%. The point in parentheses in Figure 5 was not in- cluded in the regression analysis since it is clearly anomalous. We have no explana- tion for this discrepancy. The equation of the regression line is:

where u,, is in m/s and D is the particle diameter in pm. Since u,, is the velocity giving DF = 0.5, Eq. 6 can be written:

Equations 6, 7, and 8 can be combined to give:

DF = 18.2u-0.58f 0.171)-1.60f 0.48 (9)

According to Eq. 9, the data for all the different particle sizes can be plotted to- gether against impact velocity by dividing

DF by D-'.~', This has been done in Figure 6. The line is 1 8 . 2 ~ - O . ~ ~ from Eq. 9. The line is a good fit to the data. For comparison, from regression analysis, the expression would be 1 3 . 7 ~ - ~ . ~ ' , with a cor- relation coefficient of 0.77. Thus Eq. 9 accounts for both the particle size and impact velocity dependence of the doublet fraction, within statistical error.

DISCUSSION

Equation 9 could also be written in terms of particle mass, m:

DF = constant X u-0.58m-".53 ( 10)

The two exponents are equal within error; using the mean, the doublet fraction can be expressed in terms of prticle momen- tum:

DF = constant X (mu) -0.55 (11)

There are no theories available with which to compare this empirical equation. How- ever, by comparing the kinetic energy to the particle adhesion energy, we can in-

-0.58 . - 1 8 . 2 V ' o 1.62 urn Sulfate-PSL

A 2.54 urn " o 3.06 urn " o 4.07 urn " ,I

2.51 urn AML-PSL A 2.51 urn Amidine-PSL

2.80 urn CML-PSL

FIGURE 6. Comparison of the data for all particle sizes and impact 'velocities to the line based on Eq. 9.

Impact Velocity, m/s

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66 W. John and V. Sethi

vestigate the nature of the binding of the particles.

We will choose the 2.54-pm sulfate la- tex as an example. The kinetic energy necessary to break up half of the doublets will be calculated. From Eq. 7, u,, = 37.7 m/s. The actual impact velocity is slightly less because of slowing down in the boundary layer. From Marple (1970), the jet velocity should be multiplied by a fac- tor of about 0.85, giving 32 m/s. The density of the polystyrene latex is 1.055 g/cm3 (from manufacturer, listed in Table 2). The calculated kinetic energy of a dou- blet for 50% breakup is 9.3. 10-I' J.

The adhesion energy between two polystyrene latex spheres from van der Waals forces can be calculated from Johnson-Kendall-Roberts theory (John- son et al., 1971). The adhesion energy, Eadheslon depends on the radius, a, of the contact circle:

where y is the adhesion energy parameter and a is given by:

For polystyrene, the dispersion surface energy parameter is 0.0426 ~ / m ~ (Wu, 1982). For two identical particles, y is twice the dispersion surface energy, or 0.085 ~/rn' . R is the particle radius. K is a function of the elastic properties of the material:

K = - k=- 3rrk ' ~ E Y ( 14)

where v, Poisson's ratio, is 0.33 and Ey , Young's modulus for polystyrene, is 3.2. lo9 ~ / m ' . The result for the adhesion energy is E ,, = 2.8. 10-l5 J. The ratio of the kinetic energy to the adhesion en- ergy is 3300. Thus, the doublets are bound together much more strongly than could

be accounted for by the van der Waals forces.

The binding between particles will be further reduced by the electrostatic repul- sion between the charged surface func- tional groups. The repulsive electrostatic energy will be calculated for the two cir- cular contact areas separated by a dis- tance d, taken to be of the order of mag- nitude m (10 &. The surface charge density, u , is, from Table 2,4.36 pC/cm2. The electrostatic energy, E ,,,,,, o,ta,ie, is given by:

The constant E , is 8.85. 10-l2 C 2 / ~ m 2 . The result for the electrostatic energy is Eelectrostdtlc = 3.5. J. The calculated repulsive electrostatic energy is 1.25 times larger than the adhesion energy. This is consistent with the fact that suspensions of these latexes do not need surfactants to prevent coagulation. The electrostatic en- ergy is 2700 times smaller than the kinetic energy.

A likely possible explanation of the ob- served strong binding of the doublets is the formation of a bridge between parti- cles by residue left by the evaporation of the solution droplet. The latexes used are manufactured to be "ultraclean" and are suspended in reagent-free distilled water. In the experiments, the suspensions were diluted with our laboratory distilled water, which is filtered. The concentration of total dissolved residue in our laboratory water was once estimated to be of the order of 1 ppm, based on the sizing of particles left after the evaporation of droplets of known size. We note that even this high level of purity in the nebulized droplet can leave a monolayer of residue on an area of the size of the contact area calculated above, and, of course, even thicker layers over smaller contact areas. The actual contact area is not known; the

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Breakup of Latex Doublets by Impaction 67

van der Waals contact area is presumably not applicable. Reasonable care was taken to avoid additional contamination in the performance of the experiments, but the exercise of extraordinary care was beyond the scope of these exploratory experi- ments.

Bridges of residue between particles could consist of solids requiring consider- able forces to break. This is consistent with the lack of any observable effect of varying surface charge densities among the latexes used (Table 2). It is also con- sistent with measurements made using old solutions of Dow latex. The results for doublet breakup vs. velocity were of the same order of magnitude as for the other latexes. The Dow solutions undoubtedly contained surfactant and would be ex- pected to leave residue. We noted above that doublet breakup increased with in- creasing relative humidity. This might be the indication of the weakening of solid bridges of soluble material by the addition of water.

From the foregoing discussion, the pre- sent experiment apparently did not yield information on van der Waals adhesion or the effects of surface functional groups. However, particle binding by residues is also of interest. For example, it would be expected to be present in particles aerosolized from soils, where the material is exposed to moisture in the presence of soluble chemicals.

SUMMARY AND CONCLUSIONS

Doublet particles were produced by nebu- lizing suspensions of polystyrene latex. The commercial surfactant-free latex sus- pensions used were stabilized by surface functional groups on the particles. The observed doublet/singlet ratios in the aerosol were higher than calculated from theory. Under the operating conditions, triplet concentrations were insignificant. The observed ratio of the optical diameter

of the doublets to that of the singlets was 1.42 0.06, while the calculated projected area ratio is 1.85, indicating some degree of alignment in the OPC.

Preliminary experiments showed that there was no significant breakup of dou- blets in an acceleration nozzle. Latex aerosol was then impacted on an alu- minum surface at various velocities and the doublet fractions measured. Measure- ments at relative humidities ranging from 8 to 85% using Dow latex showed the doublet fraction to decrease by nearly a factor of 2. Subsequent measurements were made at relatively low humidities.

The doublet fraction vs. Stokes number plotted on log-log scales was well fitted by a straight line. From the average of the slopes, the doublet fraction was propor- tional to u-' '8. Also, from a plot of u,,, the velocity to break up half of the dou- blets, vs. particle diameter, it was found that u,, was proportional to D-' 757.

These functional dependencies were com- bined to produce an expression for the doublet fraction, DF = 18.2 u-0.58 D - ~ . ~ ~ ( U in m/s, D in pm). This equation was shown to fit all the data, for particles from 1.62 to 4.07 p m (singlet diameter) and velocities from 10 to 80 m/s.

The surface adhesion energy from van der Waals forces between two polystyrene latex spheres was found to be less than 1/3000 of the kinetic energy needed to break up half of the doublets; moreover, the repulsive electrostatic energy of the charged surface groups was estimated to be about 1.25 times larger than the sur- face adhesion energy. Therefore it was concluded that the doublet binding was probably due to the formation of bridges between particles by residue left after droplet evaporation.

To our knowledge, the present experi- ment is the first of its kind. Various exten- sions of the measurements could be made readily. Measurements over a wider parti- cle size range, particularly to smaller sizes,

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68 W. John and V. Sethi

would be desirable. Determination of the size of the bridges between particles, per- haps by microscopy, would be helpful, as well as determination of the chemical nature of the bridges. The reduction of residues to insignificant levels would re- quire extraordinary measures; it may be impractical. Perhaps the opposite tactic, the addition of dissolved substances to the suspensions to increase the bridging would be productive. Finally, theoretical model- ing is needed to calculate the forces on the bridges. A mechanistic understanding of the present simple system would be useful for the study of more complicated agglomerates such as encountered in practical situations.

This work was supported by Grant No. CTS-8821902 from the US. National Science Foundation.

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Received August 10,1992; accepted December 21,1992.

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