Heterogeneous nucleation of bubbles at solid surfaces in gas-supersaturated aqueous solutions

Heterogeneous Nucleation of Bubbles at Solid Surfaces in Gas-Supersaturated Aqueous Solutions 1 WAYNE A. GERTH AND EDVARD A. H E M M I N G S E N Physiological Research Laboratory, Scripps Institution o f Oceanography, University o f California, San Diego, La Jolla, California 92093 Received February 21, 1979; accepted July 18, 1979 CH4, Ar, and N2 supersaturation thresholds for cavitation in saturated aqueous solutions of succinic acid, potassium nitrate, and potassium chloride were determined at room temperature in the presence and absence of crystalline precipitates. To avoid the introduction and interference of preformed gaseous nuclei, crystals were formed in situ by cooling prior to decompression, after the solutions had been equilibrated with gas at elevated pressure and temperature. In the succinic acid and potassium nitrate systems, bubbles first occurred during decompressions in exclusive association with crystals. At ambient pressure, such cavitation occurred with supersaturations below 10 atm, while cavitation without crystals required supersaturations over 100 atm. In contrast, cavitation with potassium chloride crystals required supersaturations exceeding 100 atm. It is concluded that thresholds with succinic acid and potassium chloride crystals accurately reflected particular properties of the crystal-liquid interfaces, while the low thresholds observed with potassium nitrate crystals may also have reflected certain effects of the preceding crystallization processes per se. Results may be of particular biological significance because thresholds with succinic acid crystals at atmospheric pressure were within 5 atm of the supersaturations which elicit bubble-induced trauma in animals and man. INTRODUCTION

been limited largely to empirical results obtained with distilled water and certain aqueous solutions contained in glass tubes (1-4). In these systems, thresholds for nucleation at the glass surface were moderately below those for homogeneous nucleation; yet they exceeded by over 100 atm the supersaturations at which bubbles are most commonly encountered, particularly in living organisms (7-9). Qualitative evidence (10, 11) however, has suggested that bubbles may nucleate spontaneously at other solid surfaces at substantially lower supersaturations. The possible significance of these latter results for elucidation of the critical conditions for bubble formation in animals and man apparently has not been fully appreciated because of more recent evidence (12, 13) indicating preformed gaseous nuclei (14-17) may exist in certain tissues. Continued interest in factors which limit the

Bubbles nucleate spontaneously in gassupersaturated liquids when the supersaturations exceed certain threshold values (1-4). While thresholds for homogeneous nucleation in bulk liquid are conditioned only by the nature of molecular interactions between dissolved gas and liquid, those for heterogeneous nucleation at solid surfaces are affected additionally by conditions unique to solid-liquid interfaces (5, 6), Accordingly, nucleation thresholds at solid surfaces should often differ significantly from those in bulk liquid. Quantitative knowledge of nucleation thresholds in gas-supersaturated liquids has 1 The work was supported by grant No. HL 16855 from the U. S. National Institutes of Health (Department of Health, Education and Welfare) and a Biomedical Institutional Grant. 80 0021-9797/80/030080-10502.00/0 Copyright© 1980by AcademicPress,Inc. All rightsof reproductionin any formreserved.

Journal of Colloidand Interface Science, Vol. 74, No. 1, March 1980

BUBBLE NUCLEATION AT SOLID SURFACES ability of living tissues to sustain gassupersaturations metastably motivated the following experimental investigation of spontaneous bubble nucleation at selected solid-liquid interfaces. To avoid the introduction and interference of preformed gaseous nuclei, the solids were crystallized in situ by cooling concentrated aqueous solutions, after they had been equilibrated with gas at pressures up to 240 atm. Apparent cavitation threshold supersaturations were then obtained from the minimum decompressions required to observe bubbles. Gas solubility changes induced by cooling and crystallization caused dissolved gas tensions to deviate from the equilibration pressures. These deviations were measured with a separate technique and were used to correct the apparent cavitation thresholds. Corrected thresholds were then compared to thresholds obtained from similar solutions which lacked crystals. EXPERIMENTAL

The apparatus (1) consisted of a pressure chamber with a straight Pyrex glass capillary (0.10 cm i.d., 0.60 cm o.d.) extending through the lid. The capillary was sealed at the end of a visible section 11 cm long with a gasket secured by a piston and screw. The screw could be loosened to release liquid from a 10-ml glass sample bowl in the chamber. The visible column of solution was separated from the chamber volume by a liquid column 6 cm long. This diffusion barrier allowed the hydrostatic pressures and dissolved gas concentrations of the observed solutions to vary practically independently. The concentrated aqueous solutions had the following approximate compositions: 2.0 molal succinic acid (C4H~O4), or 6.2 molal potassium nitrate (KNO,), or 5.9 molal potassium chloride (KC1). These solutions were undersaturated with respect to these solutes at 65°C, the temperature chosen for gas equilibrations, and each produced crystalline precipitates at room temperature (20-25°C) in the capillary. All

81

solutions were prepared with reagent grade chemicals and distilled water. Each was heated, when necessary, to dissolve all solute and passed through a Millipore filter of 0.45/xm pore size at least once before use. Capillaries were periodically cleaned in dichromate-sulfuric acid and rinsed with distilled water. CH4, At, and N2 of better than 99.9% purity were used. After the sample bowl was filled with a heated concentrated solution, the apparatus was assembled and immersed upright in a 65 ___0.1°C water bath. Gas pressure to at least 205 atm was then applied for 15 min to force dissolution of most gaseous nuclei (2). Following equilibration with gas at the desired pressure for over 1.5 hr, assured by stirring at 200 rpm with a magnetic stirrer, the solution was transferred under pressure into the capillary. The apparatus was removed from the water bath, positioned horizontally, and cooled to room temperature while the pressure was maintained at the equilibration value. Crystallization did not readily occur, so it was induced either by applying acetone over the entire capillary while ventilating it with a fan, or by quickly cooling about 1 cm of the capillary at the gasket seal end with a short burst of Freon 12 (CC12F2). After waiting for the solution to equilibrate with its precipitate at room temperature, the system was decompressed, either directly to ambient pressure in about 2 - 5 sec, or in 3 atm steps with 2 - 5 min at each stop, while the capillary was visually scanned for bubbles through a 15× binocular microscope. Apparent cavitation threshold supersaturations at a given hydrostatic pressure were each defined as the smallest difference between the gas equilibration pressure and the hydrostatic pressure required to observe bubbles. Cavitation thresholds at ambient pressure in the absence of C4H604 and KNO3 crystals were determined by conducting similar experiments entirely at room temperature with saturated solutions. Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980

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GERTH AND HEMMINGSEN

CORRECTIONS FOR EFFECTS OF COOLING AND CRYSTALLIZATION

Cavitation thresholds for the room temperature saturated solutions needed no correction because before bubbles formed, gas supersaturations were given directly by the differences between corresponding equilibration and decompression pressures. Thresholds for the other systems required correction because gas solubility changes induced by cooling and crystallization caused the dissolved gas tensions to deviate considerably from the equilibration pressures before decompression. Quantitation of these gas tension changes required determination of: (i) the dissolved gas concentrations in the liquids remaining after the concentrated solutions, gas saturated at various pressures and 65°C, had been reequilibrated at 25°C; and (ii) the gas solubilities of the saturated solutions at 25°C. A method similar in principle to that used by Wiebe etal. (18) and Schrrder (19) was developed (20) to measure the required gas solubilities. Gas volumes evolved from decompressed liquid samples which precipitated solute could also be measured. The 2.0-

apparatus consisted of a magnetically stirred equilibration chamber (25 ml capacity) connected by stainless-steel tubing (0.08 cm i.d., 0.16 cm o.d.) to the sample inlet valve of a degassing vial and volumetric gas measuring assembly. These assemblies were thermostated by immersion in water baths. The gas equilibration assembly with connecting tubing was maintained at 65 ___0. I°C for the concentrated solutions and at 25 ___0.01°C for the 25°C-saturated solutions. The other assembly was always at 25 _+ 0.01°C. After gas equilibration at the desired pressure, set to within 0.5 atm, 0.5- to 3.0-ml samples of gas saturated liquid were successively admitted to the degassing vial and reequilibrated at ambient barometric pressure. The weight of each liquid sample was determined following measurement of the combined liquid plus evolved gas volume. Liquid volumes were calculated from the sample weights and densities at 25°C, and evolved gas volumes were determined from the differences between the measured volumes and the corresponding liquid volumes. Gas remaining in solution at ambient pressure was not included in these evolved gas volumes.

B

A

C CH4

N2

a Ar

].5a

E I--

1.0-

i

0

50

I00 150 0 50 I00 P P Gas Equilibration Pressure (Atm)

b

i

150 0

50

I00

150

FIG. l. Gas solubility coefficients (ml gas (STP) dissolved per ml liquid) as functions of pressure in aqueous KNOz solutions. (a) Cs(P,25°C); gas solubilities of the saturated solution at 25°C. (b) Cs(P,65°C); saturation curves for the concentrated solution, gas equilibrated at 65°C, uncorrected for precipitate volumes. (c) C ' ( P ) ; same data as in (b) corrected for precipitate volumes. (A) is labeled for description of calculations used to correct apparent cavitation thresholds for effects of cooling and crystallization. Journal of Colloid and Interface Science, Vol.74, No. 1, March 1980

83

BUBBLE NUCLEATION AT SOLID SURFACES

A

B

o

N2

3,0.

2.5

2.0 c

8

(D

L5

m

0.5 ,

i

b

I

i

i

,

o.c

o

so ~o ~o o 50 too Cos Equilibration Pressure (Arm)

1so

FIG. 2. Gas solubility coefficients as functions of p r e s s u r e in a q u e o u s C4H604 solutions. Notation as in Fig. 1.

Solubility coefficients of N 2 , CH4, and Ar in KNO~ solutions (Fig. 1) and of N2 and Ar in C 4 H 0 0 4 solutions (Fig. 2) were determined with gas equilibration pressures ranging from 17 to 170 atm. Most coefficients were determined to within a standard deviation of 1%. In each sample of the concentrated solutions, crystallization occurred after admis-

sion to the degassing vial. Accordingly, evolved gas volumes were determined from "liquid" volumes calculated from densities of the precipitate-liquid slurries. Solubility coefficients labeled C ' ( P , 65°C) in Figs. 1 and 2 were calculated with these volumes. Because the precipitated crystals had negligible gas solubilities, however, gas displaced from solution as the actual liquid volumes diminished during crystallization (14) was included in the measured gas volumes, while the "liquid" volumes incorrectly included the precipitate volume fractions. Coefficients corrected for the latter effect were given by C ' ( P ) = Q / ( V - V x (1 - x)), where P = the gas equilibration pressure, Q = the evolved gas volume (corrected to STP), V = (sample weight/p0 and pl = the density of the precipitate-liquid slurry at 25°C. The precipitate volume fractions, (1 - x), were obtained after solving x = (pl - p3)/(P2 - p3) for each solution, where x = the liquid volume fraction, P2 = the density of the saturated solution at 25°C, and P3 = the density of the solid. Density data and calculated volume fractions are shown in Table I. Gas tension changes associated with cooling and crystallization were approximated by linear interpolation of the gas solubility curves labeled C ' ( P ) and C~(P, 25°C) in the figures. Variations of dissolved gas tensions with hydrostatic pressure (21) and any over-

TABLE I Densities and Calculated Volume Fractions U s e d to Determine Gas Solubility Coefficients Concentrated solution equilibrated at 25°C

Aqueous

C4H604

A q u e o u s KNOa

Pl (g/ml)

P2 (glml)

pa (g/ml)

Calculated liquid volume fraction (x)

Calculated precipitate volume fraction (I - x)

1.063 1.268

1.011 1.185

1.572 2.109

0.908 0.910

0.092 0.090

p~ = density of precipitate-liquid slurry at 25°C; Pz = density of saturated solution at of solid. 02 for C4H604 was obtained from "International Critical T a b l e s " (E. W. W a s h b u r n , McGraw-Hill, N e w York, 1928. P3 values were obtained from " H a n d b o o k of C h e m i s t r y and pp. B-125 and C-495. C.R.C. Press, Cleveland, 1971. Other values were determined C o n c e n t r a t e d solutions were: 2.01 molal C4H604 and 6.18 molal KNO~.

25°C; P3 = density Ed.), Vol. 7, p. 68. P h y s i c s , " 51st ed., in our laboratory.

Journal of Colloid and Interface Science, VoL 74, No. I, March 1980

84

GERTH AND HEMMINGSEN

all volume changes associated with cooling and crystallization were ignored. As a graphic example of the interpolations, Fig. 1A is labeled for the concentrated solution which had been isobarically reequilibrated at 25°C in isolation from a gas phase, following N2 equilibration at pressure P and 65°C. The dissolved gas concentration in the remaining liquid was C'(P), provided gas displaced during crystallization was uniformly distributed and the precipitate volume fraction was invariant with pressure. Because the remaining liquid was a 25°C saturated solution, it had a gas solubility of C+(P, 25°C). Thus the final dissolved gas tension equaled P ' , the equilibration pressure required to saturate this solution at 25°C with gas at concentration C'(P). Results were similar between each set of solubility data. Dissolved gas tensions following cooling and crystallization were always lower than the original equilibration pressures. The corresponding undersaturations (P - P') increased systematically with equilibration pressure. Apparent cavitation thresholds obtained with crystals in these systems were corrected by subtracting the appropriate values of (P - P'). CAVITATION THRESHOLDS

Crystals Present In the KC1 system, bubbles were only rarely observed at ambient pressure after decompressions from equilibration pressures below 100 atm. When decompressed from higher equilibration pressures, bubbles formed as readily at the glass-liquid interface as on the crystals. Few bubbles were observed after decompressions from N2 equilibration pressures up to 150 atm. Because cavitation appeared unaffected by the presence of this precipitate, no further investigation of this system was attempted. Figure 3 shows cavitation thresholds in the KNO3 and C 4 H 6 0 4 systems as functions of the hydrostatic pressures during decompression at which bubbles were first obJournal of Colloid and Interface Science, Vol. 74, No. 1, March 1980

45 A) KNO3

40-

351 30-

esi 2O ~g

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I

N

35

~

30

CH4 Ar

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--~ 5 I

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I

~

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o

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• i

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Hydrostatic Pressure (Atmg) FIG. 3. Gas supersaturations with crystals in (A) a q u e o u s KNO3 and (B) a q u e o u s C4H604 solutions vs p r e s s u r e s during d e c o m p r e s s i o n s at which bubbles were first observed. E a c h point represents a single experiment.

served. With increasing hydrostatic pressures to greater than 120 atm, bubbles always formed among crystals at supersaturations less than 40 arm. Far greater supersaturations were required for bubbles in bulk liquids or at the glass-liquid interfaces. Bubbles in either system rarely formed on seemingly planar crystal surfaces until the supersaturations were substantially increased. At ambient pressure, cavitation was always profuse moments after decompressions which produced the threshold supersaturations. With threshold supersaturations at higher hydrostatic pressures, more than 20 bubbles were visible throughout the capillary a few minutes after decompression; other bubbles were probably obscured by crystals. The number of bubbles and the number of nucleation sites on crystals increased with increasing supersaturations.

B U B B L E N U C L E A T I O N AT S O L I D S U R F A C E S

Bubble formation with C4H604 crystals was always profuse before supersaturations reached 35 atm. In contrast, with K N Q crystals, profuse cavitation at higher hydrostatic pressures often required supersaturations approaching 100 atm. Thresholds for a given gas were consistently lower in the C4H604 system than in the KNO3 system. For example, at ambient pressure, thresholds for all gases were less than 5 arm in the C4H604 system and between 5 and 10 atm in the KNO3 system. Cavitation thresholds tended to increase as the systems were decompressed from greater equilibration pressures. This tendency was most pronounced in the K N Q system. Thresholds at a given hydrostatic pressure in the latter system differed among the gases if the decompression stops were 2-5 min. Cavitation thresholds for N2 under these conditions were lower than those for the more soluble Ar. In the C4H604 system, no systematic difference was ever apparent between the thresholds for these gases. If decompression stops at higher pressures were prolonged to 30 rain or more, a few bubbles (<10) would often form on some crystals at supersaturations lower than the indicated thresholds. The incidental occurrence of these bubbles appeared unrelated to either the gas solubility or the degree of supersaturation, implicating the interference of nucleating factors other than the crystals; e.g., background radiation (22-24). Applications of hydrostatic pressures exceeding the gas equilibration pressures by as much as 200 arm in either system, during and continuing for as much as 2 hr after crystallization, did not affect either the cavitation thresholds or the apparent number of bubbles. Data for the KNO3 system were obtained for crystals initiated by cooling the entire capillary with acetone. In these cases, separate crystals propagated rapidly (0.52 rain) from many sites throughout the capil-

85

lary. However, when crystallization was initiated with a burst of freon at one end of the capillary, continuous intertwined spicular crystals propagated down the capillary only from the cooled end in from 2 to 4 min. At ambient pressure, cavitation associated with these crystals required N2 supersaturations of about 35 atm. This was at least 25 atm greater than the corresponding threshold for the more rapidly crystallized precipitate. The manner in which crystallization was induced in the other systems did not affect either the appearance of the crystals or the cavitation behavior. However, crystallization in these systems was much slower; more than 1 hr was required to reach equilibrium once crystallization had been initiated. If the crystals in either system were redissolved before decompression by warming the capillary, bubbles formed at decompression pressures similar to those observed when crystallization had not yet occurred. With Nz, these supersaturations exceeded 100 atm at ambient pressure (uncorrected for gas solubility changes). When either system was decompressed after crystallization, recompressed to the equilibration pressure, and the crystals then redissolved, large numbers of bubbles often occurred upon decompressions to ambient pressure when the initial decompressions produced supersaturations which were too small to observe bubbles with the crystals.

Crystals Absent Cavitation behaviors of room temperature saturated C 4 H 6 0 4 and KNOa solutions lacking precipitates are shown in Fig. 4. In all cases, supersaturations at ambient pressure had to exceed 100 atm before bubbles would occur within 2-3 min of decompression. Cavitation profusion increased with supersaturation. Light to moderate cavitation appeared to nucleate at the glass-liquid interface, whereas massive cavitation, occurring in each system above certain Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980

86

GERTH AND HEMMINGSEN

supersaturations, was clearly associated with widespread nucleation in bulk liquid. As in distilled water (1-3), thresholds in both solutions decreased with increasing gas solubility. In the C4H604 solution, cavitation thresholds both in bulk liquid and at the glass surface were somewhat lower (20-30 atm) than those for distilled water. Thresholds in the KNOa solution, however, were practically the same as those for distilled water. DISCUSSION

In the absence of crystals, cavitation thresholds in the saturated aqueous solutions did not dramatically differ from those which have been established for distilled water. However, in the presence of crystals, cavitation thresholds in the KNOa and C4H004 systems were dramatically lower, while thresholds in the KC1 system appeared unaffected. Bubbles on these crystal surfaces must have nucleated spontaneously because the in situ precipitations obviated the introduction of preformed gaseous nuclei. Thus, thresholds with crystals reflected particular properties of the crystal-liquid interfaces and/or effects related to the accumulation of dissolved gas at advancing crystal surfaces during the preceding crystallizations (14). The latter possibility may be excluded if such displaced gas accumulated and dissipated without nucleating bubbles before decompression. Transient accumulations of high gas tensions during crystallization were indicated when rapid crystallization was induced after certain decompressions. For example, after the KNO3 solution had been stably N2-supersaturated with 4 - 6 atm at ambient pressure, crystallization induced by acetone cooling was accompanied by profuse bubble formation. In contrast, no bubbles occurred when the experiment was performed by completing crystallization before decompression. These results indicated considerable gas tensions accumulated and readily dissipated by diffusion or convection in the Journal of Colloid and Interface Science, V o l . 7 4 , N o . 1, M a r c h 1980

Noz o o i

gr o m [I •

no cavitation l light cavitation moderate cavitation massive cavitalion

I

oo

C4H604

o o

o

oooo

ooom~

•

8

o o°og ~"

° o

8 g • g ~

KNO 3 t

r

r

50 I00 150 200 Gas Equilibration Pressure (Atrng)

FIG. 4. Cavitation behavior of saturated aqueous C4H604 and KNO3 solutions lacking crystals when decompressed directly to ambient pressure, after gas equilibration at the indicated pressures. Each point represents the cavitation profusion observed in a given experiment within about 2 min of decompression. periods usually allowed before decompression. The practically complete dissipation of gas tension accumulations during these periods was indicated in other experiments by the fact that thresholds were nearly the same when decompression was delayed by over 12 hr. Other results indicated maximal accumulated gas tensions decreased with crystallization rate. The slightly slower propagation of the spicular KNO3 crystals did not generate bubbles even if the solution was N2-supersaturated by as much as 50 atm. In these cases, if the final supersaturation exceeded about 35 atm at ambient pressure, bubbles were not observed until a given crystal had apparently stopped growing. Additionally, following crystallization in the KC1 solution, thresholds were still comparable to those in distilled water. These observations suggest that gas tensions which accumulated during the slow KC1 crystallizations were much smaller and thus of lesser consequence, than those which accumulated in the KNO3 system. This suggestion should extend to the comparably slow crystallizations in the C4H604 system, though differences in crystal geometries, gas solubility changes, and quantities of displaced gas were probably also important.

BUBBLE NUCLEATION AT SOLID SURFACES Any momentary supersaturations which might have been generated in either system during crystallizations before decompression were evidently insufficient to nucleate bubbles, either in bulk liquid or at crystal surfaces. First, results indicated no gaseous nuclei remained after the crystals were redissolved before decompression. Second, results in either system were not discernibly affected when the hydrostatic pressures were increased during crystallizations up to 200 atm over the equilibrium pressures. Displaced gas accumulations still could have affected the threshold determinations if liquid pockets were trapped in crystals during crystallization before locally accumulated gas tensions had completely dissipated. Because the threshold determinations required that gas was uniformly distributed throughout the liquids during decompression, displaced gas retained in such pockets might have caused gas-supersaturations to differ from the calculated values. For example, bubbles might have nucleated in such pockets during decompression before a supersaturation sufficient to nucleate bubbles was attained elsewhere in the system. The KC1 and C4H604 crystallizations appeared too slow to have allowed the entrainment of liquid with substantial amounts of displaced gas, but this effect could not be excluded from consideration of the KNOa data. With crystals in this system, both thresholds and threshold differences among the gases increased with hydrostatic pressure. At most pressures, thresholds were higher the more soluble the gas: N2 < CH4 < Ar. This relationship was opposite that for thresholds in bulk liquid at ambient pressure. With crystals in the C4H604 system, no systematic differences were apparent between the gases, though thresholds also tended to increase with hydrostatic pressure. In experiments where the KNO3 or C4H604 crystals were dissolved following a decompression- recompression sequence,

87

some results suggested that at higher hydrostatic pressures, bubbles may have nucleated on the crystals at lower supersaturations than those which were ordinarily required to observe them with the crystals. This in turn suggested an explanation for the observed threshold increases with hydrostatic pressure. Bubbles expand to smaller equilibrium sizes at slower rates with increasing pressure at a given supersaturation tension (25). Thus, at higher hydrostatic pressures and given supersaturations, bubbles which might have exceeded the critical size may not have reached visible size in the periods allotted and would have escaped detection until the supersaturations were increased by further decompression. The generally lower gas solubilities in the KNQ system would have caused such bubble growth rate or size limitations to be more important than in the C4H604 system. Indeed, thresholds increased more rapidly with pressure with KN03 crystals than with C4H6O4 crystals. However, with KN03 crystals at higher hydrostatic pressures, the threshold-solubility relationship among the different gases was not consistent with the involvement of bubble growth rate or size limitations, indicating other factors contributed to the threshold differences among the gases. One such factor might have been trapped liquid pockets which retained varying amounts of displaced gas depending on the solubility of the gas and its concentration during crystallization. We conclude that thresholds with K N Q crystals may not have been conditioned only by properties of the crystal-liquid interfaces because displaced gas which accumulated during crystallization might have failed to dissipate completely before decompression. On the other hand, thresholds with crystals in the KC1 and C4H604 systems were evidently not affected by such consequences of the preceding crystallization processes and must have accurately reflected particular properties of the crystal-liquid interfaces. Some of these properties may Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980

88

GERTH AND HEMMINGSEN

be inferred by considering the results in the context of nucleation theory. The degree to which the liquid wets the solid, given quantitatively by the value of the contact angle, 0, and the solid surface geometry are theoretically the principal properties which determine the relative ease of nucleation from solid surfaces (5, 6). Heterogeneous nucleation is thermodynamically favored over homogeneous nucleation at any solid surface which is not perfectly wetted by the liquid, i.e., where 0 > 0°, and should occur at lower supersaturations in systems exhibiting poor wetting characteristics, i.e., those with large 0, than in well-wetted systems with small 0 and identical solid surface geometries (5, 6). Nucleation at planar crystal surfaces could not account for the great difference between homogeneous and heterogeneous thresholds in the succinic acid system unless the contact angle was improbably high. For a contact angle of 90°, a value characteristic of poorly wetted solids such as paraffin wax in water (0 = 95 to 105°), the heterogeneous nucleation threshold at a planar surface is theoretically only about 30% lower than the homogeneous threshold (5, 26). In comparison, the observed difference in the C4H604 system was over 97%. Theory indicates that for a given non-zero contact angle, nucleation from surface cavities should occur at lower supersaturations than nucleation from plane surfaces or from surface projections (5, 6, 26). Because nucleation from surface cavities should occur at lower supersaturations as the cavity walls form more acute angles, bubbles from C4H604 crystals probably nucleated in acuteangled cavities formed at grain boundaries, cracks, or crevices on the crystal surfaces. As similar surface features were probably present on the KC1 crystals, the relatively high thresholds with these crystals indicated they were more easily wetted by their host solution than were the C 4 H 6 0 4 crystals. Contact angles and crystal surface geometries at the nucleation sites which must Journal of Colloid and Interface Science, Vol. 74, No. 1, March 1980

be known to make more quantitative evaluations could not be characterized. Moreover, rigorous application of the theory here was discouraged by the failure yet to achieve satisfactory agreement between theory and experiment for water or aqueous liquids; homogeneous nucleation theory has been successfully extended to account for observed effects of dissolved gases on nucleation thresholds only in certain organic liquids (27, 28). Nevertheless, these empirical results with crystals may be of particular biological significance. With C 4 H 6 0 4 crystals, thresholds were within 5 atm of the supersaturations which elicit bubbles in living animals (7-9), while the higher thresholds with KC1 crystals were comparable to those for homogeneous nucleation or for nucleation at the glassliquid interface. Further study is warranted to determine whether solid-liquid interfaces in certain tissues promote the spontaneous nucleation of bubbles which occur at low gas-supersaturations in animals. REFERENCES 1. Hemmingsen, E. A.,J. Appl. Phys. 46, 213 (1975). 2. Gerth, W. A., and Hemmingsen, E. A.,Z. Naturforsch. 31a, 1711 (1976). 3. Hemmingsen, E. A., Nature (London) 267, 141 (1977). 4. Hemmingsen, E. A., Z. Naturforsch. 33a, 164 (1978). 5. Cole, R., Adv. Heat Transfer 10, 85 (1974). 6. Blander, M., Adv. Colloid Interface Sci. 10, 1 (1979). 7. Nebeker, A. V., and Brett, J. R., Trans. Amer. Fish. Soc. 105, 338 (1976). 8. Nebeker, A. V., J. Fish. Res. Board Canad. 33, 1208 (1976). 9. Hills, B. A . , " Decompression Sickness, Vol. 1,The Biophysical Basis of Prevention and Treatment." John Wiley, New York, 1977. 10. Farncomb, F. J., Trans. Roy. Soc. Canada III 19, 32 (1925). 11. Pease, D. C., and Blinks, L. R., J. Phys. Colloid Chem. 51,556 (1947). 12. Evans, A., and Walder, D. N., Nature (London) 222, 251 (1969). 13. Albano, G., and Columba, M., in "Underwater Physiology" (C. J. Lambertsen, Ed.), Vol. 4, p. 193. Academic Press, New York, 1971.

BUBBLE NUCLEATION AT SOLID SURFACES 14. Harvey, E. N., Whiteley, A. H., McElroy, W. D., Pease, D. C., and Barnes, D. K.,J. Cell. Comp. Physiol. 24, 23 (1944). 15. Holl, J. W., J. Basic Engineering 92, 681 (1970). 16. Apfel, R. E., J. Acoust. Soc. Amer. 48, 1179 (1970). 17. Yount, D. E., Aviation. Space Environ. Med. 48, 185 (1977). 18. Wiebe, R., Gaddy, V. L., and Heins, C. Jr., J. Amer. Chem. Soc. 55, 947 (1933). 19. Schr6der, W., Z. Naturforsch. 24b, 500 (1969). 20. Gerth, W. A., and Hemmiugsen, E. A. (unpublished). 21. Enns, T., Scholander, P. F., and Bradstreet, E. D., J. Phys. Chem. 69, 389 (1965).

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22. Greenspan, M., and Tschiegg, C. E., J. Res. Nat. Bur. Standards, 71C, 299 (1967). 23. Walder, D. N., and Evans, A., Nature (London) 252, 696 (1974). 24. Sette, D., in "Underwater Acoustics" (V. M. Albers, Ed.), Vol. 2, p. 139. Plenum, New York, 1967. 25. Epstein, P. S., and Plessett, M. S., J. Chem. Phys. 18, 1505 (1950). 26. Fisher, J. C., J. Appl. Phys. 19, 1062 (1948). 27. Mori, Y., Hijikata, K., and Nagatani, T., Int. J. Heat Mass Transfer 19, 1153 (1976). 28. Forest, T. W., and Ward, C. A., J. Chem. Phys. 66, 2322 (1977).

Journal of Colloidand Interface Science, Vol.74. No. 1. March 1980