Force exerted on a single spherical particle by a freezing interface: Experiments

Force Exerted on a Single Spherical Particle by a Freezing Interface: Experiments GIRISH GUPTA, 1 RICHARD F. RICE, 2 AND WILLIAM R. WILCOX Department o f Chemical Engineering, Clarkson College o f Technology, Potsdam, New York 13676 Received October 7, 1980; accepted January 12, 1981 Freezing naphthalene, salol, camphor, and succinonitrile exerted forces on the order of 10-5 N on glass beads fixed on the end of tungsten wire. The force increased with decreasing freezing rate and with increased bead size. Impurity additions increased the force exerted by naphthalene, but reduced that produced by succinonitrile. Purified camphene produced no detectable force.

INTRODUCTION

EXPERIMENTAL METHODS

In a previous paper theoretical relations were developed for the maximum force F that a freezing melt can exert on a fixed spherical particle (1). The starting point was the steady-state equations of Chernov et al. (2), which take into account the hydrodynamic force pushing the particle into the interface and the disjoining pressure pushing the particle away from the interface, both corrected for the curvature of the solidliquid interface under the particle. It was predicted that F should vary with the freezing rate V as I/V, 1/V1% or 1/V z, and with the particle radius R as 1/R or 1 / g 1"73. In a similar treatment Gilpin (3) found F to be proportional to h~/VR 2 for small freezing rates, where he is the characteristic thickness of the film of melt between the particle and the freezing solid. For a chemical potential change that varies with film thickness h according to a power law relationship, h-~, the force is proportional to R ~I~/VR 2. The present paper reports on experimental tests of these and other theoretical predictions. Present address: 44 Kuppu Muthu Mudali St., Madras, India. Present address: Allied Chemical, Syracuse, New York.

The experiments are described in detail elsewhere (4, 5). Gupta first performed experiments on naphthalene, salol, and camphor (4). Later Rice worked with camphene and succinonitrile (5). In each experiment an organic compound was contained in a sealed Pyrex tube, 2.5 cm (1 in.) in outside diameter. From the wall projected a 50-t~m (2 mil) tungsten wire, which was bent downward near the center of the tube. To the bottom of the wire was fused a Pyrex glass ball, ranging from 0.43 to 1.67 mm in diameter. During an experiment the tube was lowered slowly through a heater, causing upward solidification to occur. As the freezing interface reached and passed the glass bead the cantilever was deflected. The deflection 6 of the end of the cantilever ranged from 4 tzm to 2.3 mm, and was measured by means of a calibrated Filar eyepiece on a microscope at 87.5×. Gupta frequently measured both the maximum deflection during freezing and the movement back down upon melting, and encountered some problems with movement of the microscope on its stand. Thus the data exhibit some scatter. An elastic modulus E of 4 × 107 lb/in. 2 was used in the equation

458 0021-9797/81/080458-07502.00/0 Copyright© 1981by AcademicPress, Inc. All rightsof reproductionin any formreserved.

Journal of Colloidand InterfaceScience, Vol.82, No. 2, August 1981

459

F O R C E AT A F R E E Z I N G I N T E R F A C E TABLE I S u m m a r y of Results a

Host Naphthalene Naphthalene Naphthalene Naphthalene Zone-refined naphthalene Zone-refined naphthalene Zone-refined naphthalene Zone-refined naphthalene Zone-refined naphthalene Zone-refined naphthalene Zone-refined naphthalene Salol Camphor Camphor Camphor Camphene Succinonitrile Succinonitrile Succinonitrile

Least squaresfit to lnF=ao+a~lnV

Bead diameter (ram)

Freezing rate (mm/hr)

ao

a,

r2

n

(FV)a¢,

Srv

0.43 0.70 1.10 1.67

0.59-5,18 0.74-7.68 0.67-5.64 0.58-6,35

0,87 1.67 1.75 2.80

-0.91 -0.95 -1.25 -1.05

0.97 0.996 0.91 0.93

6 6 8 8

2.6 5.4 4.9 16.8

0.33 0.35 1.61 4.19

1.38

0.72-7.61

0.89

-1.09

0.64

7

2.2

1.20

0.2% w B z O H

1.38

0.55-9.09

1.69

-0.77

0.90

9

7.1

2.46

0.4% w B z O H

1.38

0,85-7.69

2.09

-1.18

0.90

8

7.0

2.42

0.2% w2nap

1.38

0.57-8.12

1.08

-1.00

0,87

I0

3.1

1.11

0.4% w2nap

1.38

0.89-5.80

3.8

- 1.6

0.90

3

32

17.8

0.2% wAnth

1.38

2.08-3.85

4

-2

--

2

17

9.6

0.02% wMB

1.38 1.38 1.40 1.40 1.40 1.12-1.39 1.12 1.12 1.4

0.98-4.18 0,70-6.99 1.78-8.8 2.55-4.62 1.66-4.14 0.10-4.03 0.05-1.42 0.06-1.24 0.04-1.49

3.1 -----2.3 1.1 2.0

-0.4 -m ----0.6 -0.3 -0.2

0.27 ~0 --0 ---0.76 0.17 0.30

3 8 5 2 2 13 13 5 12

Impurity

0.3% w2nap 0.015% wMB

0.48% wCamp 0.034% wMB

F = 3 ~ E I / U to convert from deflection to force. Here I is the moment inertia of the wire (3.27 x 10-11 cm 4) and / is the length of the cantilever (0.7 to 1.3 cm). Forces so computed ranged from 0.08 to 59 x 10-5 N. Gupta measured the freezing rate V just prior to contacting the bead by measuring the distance travelled in 5 to 20 min. Rice measured the distance moved after several hours during which time the bead was engulfed. Some interface fluctuations were observed, presumably due to drafts in the laboratory, even though an external glass tube was used as a shield. Freezing rates were varied from 0.04 to 9.09 mm/hr. The organic materials investigated included naphthalene, phenyl salicylate (salol), d-camphor, camphene, and succinonitrile.

39 5 9 7 6 0 8.8 0.9 4

20.7 4 6 2.4 4 0 3.4 0.4 2.3

Fay,

sF

1.6 1.5 1.9 2.1 0 1.5 0.56 1.0

0.56 1.3 0.11 0.08 0 1.4 0,24 0,33

Benzoic acid (BzOH)2-naphthol (2nap), anthracene (Anth), methylene blue (MB), and d-camphor (Camp) were used as added impurities. For some experiments the naphthalene was zone refined prior to use, with eight tipward passes at 25 mm/hr and two at 11 mm/hr in 1.8-cm-o.d. Pyrex tubes. The camphene was purified by vacuum distilling four times with argon bubbling through the melt, and then zone refining in 18-mm-o.d. Pyrex tubes at 2.58 cm/hr for 51 zone passes. The succinonitrile had been treated in a similar fashion by Professor Glicksman's group at Rensselaer Polytechnic Institute. These materials were sufficiently pure that dendrites were not observed during the force measurements. The solid-liquid interfaces were facetted only in the salol experiments. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981

460

GUPTA, RICE, A N D W I L C O X RESULTS

The experimental results are summarized in the tables and the figures. Only the purified camphene never yielded any measurable deflection of the cantilever, i.e., the force was less than 8 x 10.7 N and was probably zero. Nearly all of the naphthalene results show a clear proportionality of F on 1IV. The salol and camphor results show too much scatter to yield any evidence of a velocity dependence. The succinonitrile F data also exhibit a good deal of scatter, but do show a clear trend lower as V increases. The first four naphthalene groups in Table I yield the dependence of F on bead diameter. In contrast to the theoretical predictions, F increases with increasing bead diameter. Figure 1 shows a plot of the 95% confidence limits (6) on F V for each bead diameter. The results for 0.7 and 1.1 mm diameters overlap sufficiently that one cannot say that they are contrary to the overall trend with diameter. Probably the radius of curvature on the bottom differed somewhat from half the bead diameters, which were 30

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BEAD DIAMETER (tam) Fro. 1. Average values of'force x freezing rate vs bead diameter for as-supplied naphthalene. Error bars represent 95% confidence limits (6). Line is based on average value of ( F V / d i a m e t e r ) a v g = 7.1. Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981

100

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IMPURITY

FIG. 2. Influence of impurities on F V product for zone-refined naphthalene with 1.38-mm bead diameter. It is assumed that the basic zone refined material contains less than 0.05% of unremoved impurities. N, No impurities added; 0 , benzoic acid added; ©, 2-naphthol added; [3, methylene blue added; II, anthracene added; ..... , as-supplied naphthalene from line in Fig. 1 for 1.38-mm diameter.

measured with a micrometer. Linear regression analysis of all these data yields F = 0.00243RHsV -1.°7 N

[1]

where R is the bead radius in mm and V is freezing rate in mm/hr. The fraction of the variation in F that has been explained by this equation is r ~ = 0.89. As shown in the table and in Fig. 2, the naphthalene results all show that impurity additions increase the force that freezing naphthalene can apply to a glass bead. The effect is particularly marked for methylene blue additives. On the other hand impurities produce no detectable effect on F for camphor and reduce F for succinonitrile. Using the Student's t statistical test (6) these differences were found to be significant at the 0.87 to 0.9999 level for naphthalene and at the 0.9998 and 0.999999 level for succinonitrile. Two related experiments were also performed. In one, the glass bead was siliconized by heating in dimethylpolysiloxane for

461

FORCE AT A FREEZING INTERFACE TABLE II Data v (ram/In')

Deflection (rnm)

Force (N) × 105

V (rnm/hr)

N a p h t h a l e n e - - n o impurity added (0.43-ram bead; 1.2-cm cantilever)

Deflection (ram)

Force (N) × 10s

Zone-refined naphthalene (1.38-mm bead; 1.2-cm cantilever)

0.59 1.09 1.50 1.97 3.08

0.132 0.128 0.074 0.064 0.042

2.58 2.50 1.45 1.25 0.81

0.72 1.07 2.22 3.01

0.091 0.117 0.090 0.062

1.77 2.28 1.75 1.21

4.43 4.78 5.18

0.011 0.034 0.025

0.20 0.66 0.50

3.54

10.025 [0.037

0.49 / 0.71 l

5.09

/0.012 /0,016

0.25 / 0.31J

6.43 7.61

0.044 0.004

0.87 0.08

N a p h t h a l e n e - - n o impurity added (0.70-ram bead; 1.25-cm cantilever) 0.74 1.37 2.15 3.05 4.51 4.83 7.06 7.68

0.404 0.592 0.143 0.100 0.070 0.066 0.050 0.033

6.99 10.24 2.47 1.71 1.15 1.14 0.86 0.58

N a p h t h a l e n e - - n o impurity added (1.10-mm bead; 1.0-cm cantilever) 0.67 1.15 1.43 2.32 2.59 4.25 4.88 5.64

0.216 0.142 0.112 0.101 0.054 0.035 0.022 0.012

7.28 4.81 3.78 3.41 1.83 1.19 0.74 0.41

N a p h t h a l e n e - - n o impurity added (1.67-ram bead; 0.75-cm cantilever) 0.58

0.412

32.99

0.77 0.91 1.34

0.388 0.221 0.114

31.07 17.67 9.15

1.84

10.050 ~0.094

3.16 4.81 5.59 6.35

0.0065 0.050 0.244 0.032

3.99 l 7.55J 5.18 4.02 19.54 2.55

Zone-refined naphthalene (l.38-mm silicone-treated bead; 1.2-cm cantilever) 0.88

-0.262

-5.12

1.41

0.344 0.294

6.72 / 5.76J

2.51

0.086 0.049

1.68 l 0.96J

3.36

0.629 0.633

12.30/ 12.38/

5.22

-0.009 -0.042

- 0.19 / -0.83J

6.54

-0.0061 -0.0073

- 1.20 / - 1.42J

8.80

-0.034 -0.074

-0.67 / - 1.45J

Zone-refined naphthalene + 0.2% BzOH (l.38-mm bead; 1.2-cm cantilever) 0.55

0.466

9.10

0.82

/0.452 [0.47l

8.84 / 9.20J

1.32

10.178 [0.217

3.49 / 4.23J

1.74

/0.138 t0.123

2.69 l 2.41]

1.99

" /0.091 [0.123

1.77 l 2.41]

Journal o f Colloid and Interface Science,

Vol. 82, No. 2, August 1981

462

GUPTA, RICE, AND WILCOX TABLE II (Continued)

V (mm/hr)

Deflection (ram)

Force (N) × 105

5.85

/0.060 [0.163 I0.049 [0.069

1.18 l 3.18J 0.98 / 1.34J

6.40

/ 0"071 [0.109

1"39l 2.13J

9.09

/0.034 [0.070

0.67 / 1.37]

4.35

Zone-refined naphthalene + 0.4% BzOH (1.38-mm bead; 1.2-cm cantilever)

V (mm/hr)

Deflection (ram)

Force (N) x 105

Zone-refined naphthalene + 0.4% 2-naphthol 0.89 3.00 5.80

j2.240 [2.430 0.842 o. 101

43.90 l 47.60J 14.50 1.97

Zone-refined naphthalene + 0.2% anthracene 2.08

0.582 0.600

11.40 11.70

3.85

0.120 0.163

2.34 3.18

0.85

10.650 [0.610

12.70 / 11.90J

1.40

0.275

5.37

0.98

0.85

2.05

10.080 [0.130

1.56 / 2.50J

1.74

/1.982 [1.379

38.801 26.90J

3.28

jo.154 [o.15o

3.Ol / 2.93/

4.18

0.529

10.30

3.79

J0.088 [0.089

1.711 1.75J

4.27

J0,059 [0.057

1.14] 1.12J

0.70 0.94

0.060 0.101

1.17 1.96

6.55 7.69

0.043 0.044

0.83 0.86

1.38

/0.152 [0.108

2.97 / 2.11[

1.66

10.046 [0.037

0.91 / 0.73J

3.33

0.058

1;13

4.40

J0.073 [0.084

1.43[ 1.65[

5.86

)0.076 /0.086

1.49 I 1.67]

6.99

0.083

1.63

Zone-refined naphthalene + 0.2% 2-naphthol (1.38-ram bead; 1.2-cm cantilever) 0.57

10.233 [0.199

4.56 / 3.88J

0.91

0.158

3.09

Zone-refined naphthalene + 0.02% methylene blue

Salol (1.38-mmbead; 1.2-cmcantilever)

1.12

/0.104 [0.098

2.02[ 1.92]

2.23

l 0"094 [0.102

1"83/ 1.99J

2.50 3.22 3.85 5.24

0.066 0.073 0.068 0.026

1.28 1.41 1.32 0.50 0.27 / 0.35[

3.57

6.62

10.014 [0.018

8.12

0.013

0.25

3.99

Journal of Colloid and Interface Science, Vol. 82, No. 2, August 1981

16.6

Camphor--no impurity added (1.40-mm bead; 1.3-cm cantilever) 1.78

10.031 [0.074

/0.113

0.48[ 1.14]

1.75 /

[0.038

0.59~

J0.216 [0.263

3.32 l 4.04J

463

FORCE AT A FREEZING INTERFACE TABLE II ( C o n t i n u e d ) V (mm/hr)

Deflection (mm)

Force (N) × 105

7.90

0.117

1.80

8.80

/ 0.057 [0.106

0'87 / 1.63/

V (mm/hr) 0.85 1.01 1.24 1.42 1.54

Deflection (ram)

Force (N) × 105

0.174 0.126 0.088 0.056 0.078

17.l 12.4 8.6 5.5 7.7

Camphor + 0.3% 2-naphthol 2.55

/0.132 ~0.127

2.02 / 1.961

4.62

0.119

1.83

Camphor + 0.015% methylene blue 1.66

/0.083 [0.184

1.27 l 2.83J

4.14

/0.156 ~0.127

2.39 / 1.95j

Purified succinonitrile (1.12-ram bead; 0.7-cm cantilever) 0.05 0.15 0,16 0,22 0,26 0,38 0.44 0.46 0.47 0.69 0.70 0.74 0.74 0.82

0.596 0.751 0,097 0.097 0.609 0.166 0.426 0.185 0.023 0.156 0.069 0.146 0.079 0.094

58.6 73,8 9,6 9.6 59.9 16.3 41.9 18.2 2.2 15.4 6.7 14.4 7.7 9.2

2.5 hr at 160°C. This treatment was reported by Omenyi and Neumann (7) to reduce to zero the critical velocity3 V~ for pushing of free particles, although we found no influence on engulfment (8). It has been suggested that our naphthalene was less pure than Omenyi's, which was zone refined. In the present force experiments using zonerefined naphthalene, very erratic results were produced. Two experiments yielded a Vc is the freezing rate above which an unrestrained particle is eventually trapped (engulfed) and below which it is pushed indefinitely.

Succinonitrile + 0.48% camphor (l.12-mm bead; 0.7-cm cantilever) 0.06 0.15 0.15 0.16 0.19 0.19 0.41

0.044 0.093 0.282 0.064 0.058 0.022 0.026

4.4 9.1 27.7 6.3 5.8 2.1 2.6

Succinonitrile + 0.034% methylene blue (1.40 mm bead; l.l-cm cantilever) 0.04 0.14 0.14 0.15 0.16 0.23 0.32 0.33 0.38 0.44 0.48 0.5l 0.54 0.59 0.68 1.44 1.49

0.502 0.542 2.41 0.164 0.087 0.335 0.363 0.344 0.585 0.466 0.528 0.367 0.237 0.216 0.629 0.237 0.071

12.7 13.0 61.1 4.2 2.2 8.5 9.2 8.7 14.8 11.8 13.4 9.3 6.0 5.5 16.0 6.0 1.8

much larger forces than with an untreated bead, one the same value, and three actually gave negative values for the force (the cantilever moved down as the freezing interface approached the bead and up when meltback occurred). In still another related experiment the influence of 2-naphthol additions on the critical trapping velocity V~ of naphthalene was determined. A mass of 0.132 g of -230 + 270 mesh glass beads was used. As shown in Fig. 3, impurity additions do appear to increase slightly the critical velocity, alJournal of Colloid and Interface Science, Vol. 82, No. 2, August 1981

464

GUPTA, RICE, AND WILCOX ti ,~

2.5

I

E E v I--

~D2.0 .M W .,J ~- 1.5 U

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WEIGHT PERCENT 2-NAPTHOL

FIG. 3. Influence of 2-naphthol additions on engulfment velocity for glass beads in zone-refined naphthalene. Points show limits between which V~ lay.

though beyond 0.1 wt% 2-naphthol no additional effect was noted. (The points in Fig. 3 are the limits within which V~ lay.) DISCUSSION

The observed dependence of force F on freezing rate V agrees well both with Wilcox's theory (1) and with Gilpin's theory (2), especially for the naphthalene data. On the other hand, Wilcox predicts that F should decrease with decreasing particle diameter, while Gilpin predicts the reverse for ct < 3/2. Indeed the naphthalene data corresponds to c t - 1, although for ice - 2 (2). Transient effects may also be important (9). For naphthalene we have found a critical freezing rate Vc for engulfment of groups o f - 0 . 1 - m m beads o f - 2 mm/hr (4), and - 1.6 mm/hr for -0.23-mm beads (10). Since Vc decreases as particle size increases, this indicates that most of our force measurements on naphthalene were made at freezing rates above the critical. Thus engulfment would eventually have occurred in most cases even if an external force had not been applied, i.e., we most certainly measured transient forces rather than maximum steady-state values. If one considers the diffusion required when a segregating impurity is present in the melt, then one predicts that the critical velocity Vo for engulfment of an unrestrained particle is reduced (11, 12). SimiJournal of Colloid and Interface Science, Vol. 82, No. 2, August 1981

larly one would expect the maximum force F on a restrained particle to be reduced. Experimentally we found that all impurities increased both F and Vc for naphthalene, had little influence on F for camphor, and decreased F for succinonitrile. With aromatic impurities it made little difference whether the distribution coefficient was less than 1 (benzoic acid and anthracene) or greater than 1 (2-naphthol). However the methylene blue dye had a potent effect both for naphthalene and for succinonitrile. It seems clear that these impurities are acting by means of changes in the surface properties of the particle-melt-interface systems. Such changes were neglected entirely in the theoretical treatment (11, 12), and can apparently completely overwhelm diffusional effects. ACKNOWLEDGMENT This research was supported by grant ENG 7600701 from the National Science Foundation and by Clarkson College of Technology via computer and secretarial services furnished. REFERENCES 1. Wilcox, W. R., J. Colloid Interface Sci. 77, 213 (1980). 2. Chernov, A. A., Temkin, D. E., and Mel'nikova, A. M., Sov. Phys. Crystallogr. 21, 369 (1977). 3. Gilpin, R. R.,J. ColloidlnterfaceSci. 74, 44(1980). 4. Gupta, G., M.S. Thesis, Clarkson College of Technology, Potsdam, New York, 1977. 5. Rice, R. F., M.S. Thesis, Clarkson College of Technology, Potsdam, New York, 1980. 6. Bennett, C, A., and Franklin, N. L., "Statistical Analysis in Chemistry and the Chemical Industry." Wiley, New York, 1954. 7. Omenyi, S. N., and Neumann, A. W., J. Appl. Phys. 47, 3956 (1976). 8. Fedich, R. B., and Wilcox, W. R., Separation Sci. Technol. 15, 31 (1980). 9. Temkin, D. E., and Chernov, A. A., Sov. Phys. Crystallogr. 22, 534 (1978). 10. Fedich, R. B., M.S. Thesis, Clarkson College of Technology, Potsdam, New York, 1977. 11, Chernov, A. A., and Temkin, D, E., in "1976 Crystal Growth and Materials" (E. Kaldis and H. J. Scheel, Eds.). North-Holland, New York, 1977. 12. Temkin, D. E., Chernov, A. A., and Mel'nikova, A. M., Soy. Phys. C~stallogr. 22, 13 (1977).