The contact angle of water on coal

Colloids and Surfaces, 22 (1987) 21-35 Elsevier Science Publishers B.V., Amsterdam -

21 Printed in The Netherlands

The Contact Angle of Water on Coal D.V. KELLER, Jr Otisca Industries Ltd, P.O. Box 127, Syracuse, NY 13208 (U.S.A.) (Received 21 April 1986; accepted in final form 8 July 1986)

ABSTRACT The value of the contact angle of water on coal is the key statement for a multitude of theoretical analyses concerning the behavior of coal in processing environments. Most of these processing environments involve coal with a mean particle diameter considerably smaller than 100 p and often as small as 10 pm. For example, the surface characteristics of coal are the key factor in processing by froth flotation, agglomeration, coalescence, dust wetting, etc. Most of the investigations of the contact angle of water on coal have been conducted on massive blocks of coal and few authors have probed the mechanism in sufficient detail to allow a reasonable extrapolation of these data to the behaviour of fine coal. This investigation considers the four key variables which affect the contact angle of water on coals of different rank and places these variables in a mathematical relationship from which the contact angle can be predicted given the dmmf carbon and mineral matter content and the state of surface oxidation. A comparison of the calculated values with those of some recent experimental values suggests that the approximations are reasonable.

INTRODUCTION

A knowledge of the variation of the contact angle of water on coal as the rank and the contamination of the coal changes is a fundamental issue in the fields of froth flotation [ 11, selective agglomeration [ 21, particle wetting [ 31, and numerous other very practical fields [ 1,2]. Detailed investigations have been carried out accumulating numerous values of the contact angle of water on many different coals. The classic works of Sun [ 41, for example, have been carried forth more recently by such investigators as Gutierrez-Rodriguez and Aplan [ 6,7], Fuerstenau [ 81, Rosenbaum and Fuerstenau [ 91 and others [ 10,111. Some of these investigators [lo] have explored the various relationships of the contact angle with the coal rank, dmmf% carbon (dry, mineral matter free), and oxygen content. Such an approach has taken a more serious approach with the application of the Cassie-Baxter analysis by Rosenbaum and Fuerstenau [ 91 to coal where the organic content was partitioned between paraffinic and aromatic molecules as is illustrated in Eqn (1)) Table 1. A further justification for such a relationship was provided by Johnson and Dettre

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[ 121 in their classic works on the effects of micro-patchwork surface changes on the contact angle of a drop on that surface. The extensive amount of data on the contact angle of water on coal and the various analytical approaches still leave an investigator without much insight into just what the coal surface looks like and what are the key variables in the coal/water surface reaction. Furthermore, one is at a loss to extrapolate from observations on a block of coal to what might take place on micro-particles of coal as might occur in froth flotation or coal-water slurries. The analysis presented follows the Cassie-Baxter approach and is concluded by what appears as a complete equation representing the contact angle of water on coal. The solution provides some understanding of the properties of the coal/water interface as well as opening some interesting questions regarding the properties of coal. ANALYTICAL EXPRESSION

Coal is a three-dimensional cross-linked polymeric mixture of aromatic, paraffinic and hetero-organic molecules. The solid contains a system of pores with a pore volume ranging from less than 1 to over 30 vol.% of the solid, with average pore diameters in the range of 4 nm, both depending on the rank of the coal. Furthermore, the coal also contains mineral matter particles with average diameters ranging from the high millimeter range to submicrometer range [ 131. Clearly, the coal surface will appear as a patchwork assembly of areas ranging from exceedingly hydrophobic, as are the paraffinics, to areas exceedingly hydrophilic due to the pure water where the pore system, full of water, intersects the surface plane. The interfacial tensions of these surfaces under water will vary from in excess of 50 mJ rn-’ to hydrophilic areas where the tension approaches zero and hydrogen bonding persists. Let us assume that the Cassie-Baxter relationship in the form of Eqn (1) , Table 1, is valid, which is reasonable considering that the variation of the surface tension in a two component system is a linear relation with the mole fraction of its components, provided the components are closely related in atomic content and structure [ 141. The organic material of coal, however, also contains a significant fraction of oxygen heteroatoms which increases as coal rank decreases, i.e. decreasing dmmf% carbon, as was described by Blom [151.Such heteromolecules lying in the coal surface will permit water to hydrogen bond to those sites and create an island of bound water on a generally hydrophobic surface. The island may be considered as a unique patch. Equation (2)) Table 1, accounts for such a patch area where (0’) represents the fraction of area due to the oxygen-containing molecular groups and (1-o’) represents the remainder of the mixed hydrocarbon area. Following a similar analysis Eqn (3) accounts for that area fraction due to

23 TABLE 1 Key equations cos(C”‘) =A cos(a) + (1-A) cos(P) The contact angle of water on a pure mixture of paraffinic (p) and aromatic (a) hydrocarbons.

(1)

cos(C”) =o’ cos(0) + (l-o’) cos(C”‘) The contact angle of water on a mixture of pure hydrocarbons and oxygen-containing hydrocarbon molecules.

(2)

cos(C’) =p’ cos(p) + (l-p’)

(3)

cos(C) =fcos(p) + (l-f) cos(C’) The contact angle of water on a porous organic surface such as coal.

(4)

cos(C”) The contact angle of water on an organic molecular surface containing areas where pores intersect the surface.

the regions where the pores intercept the surface while Eqn (4) accounts for that area fraction due to the presence of mineral matter. Each of the sites are treated as individual patches due to the extremes in interfacial tension between the hydrophobic and hydrophilic patches. The cosine of the contact angle of water on coal, cos (C) , is determined by substituting the solution of Eqn (1) into Eqn (2)) that of Eqn (2) into Eqn ( 3) and that of Eqn (3) into Eqn (4). The other variables in the equations of Table 1 necessary for a solution are defined in Table 2 [ Eqns ( 5) - (15) 1. The values of the contact angle of water on aromatic molecules is assumed to be in the range of 88” and that for paraffin molecules in the range of 110” which is in general agreement with Adamson [ 141. As a first approximation the contact angle of water on the surface areas due to organic oxygen molecules, pores and mineral matter is assumed zero. In the relation of the three variables, area due to aromatic molecules, oxygen groups and pores, to the dmmf% carbon we are faced with a practical problem of converting the usually observed weight fractions into surface area fractions. This is particularly difficult when one has no idea of the respective molecular weights or the degree of surface excess due to fracture planes. Therefore as a first approximation let us assume that the weight (or volume in p’ ) fractions reflect the surface fractions except in the case of the oxygen polar groups which we have set at l/3 of the weight fraction following the discussion below. The fraction of aromatic molecules in coal relative to the dmmf% carbon is given as Eqn (11) , Table 2, according to Whitehust [ 161. The fraction of surface oxygen relative to the dmmf% carbon is given by the bracketed portion of

24. TABLE 2 Assumptions cos(a)

for the solution of the contact angle of water on coal

= CO888” =0.035 Contact angle of water on aromatic

(5) hydrocarbons

cos(P)

= cos 110” = - 0.342 Contact angle of water on paraffinic hydrocarbons

(6)

cos(0)

= 1 Contact angle of water on oxygen polar sites

(7)

cos(p)

= 1 Contact angle of water on pore areas (water filled)

(8)

cos(f’)

= 1

(9)

Contact angle of water on mineral matter C%

= dmmf% carbon in coal: variable

00)

A

= fraction of surface area due to aromatic molecules = O.O2C% + 1.04

(11)

= l/3 of the weight fraction of molecular oxygen (organic ) plus adsorbed oxygen = ( -2.6x 1O-3 C% -0.224) + h

(12)

h

= fraction of surface oxidized by air

(13)

p’

= fraction of surface that is pore area = 2.642~10-~ C%*-0.4689C%+20.818 = the equilibrium inherent moisture content in

(14)

0'

volume percent

f

= fraction of surface due to mineral matter:

(15)

variable

Eqn (12) as derived from Blom [ 151. The (h) term in Eqn (12) is a direct add-on fraction unrelated to the carbon content and accounts for that area of surface which has been oxidized by direct exposure to air (oxygen). The contact angle studies by Fuerstenau [ 81 and Gutierrez-Rodriguez et al. [ 71 amply demonstrate that oxygen reacts instantaneously with some coals, see discussion below. A review of the literature on the oxidation of some atomically clean metals [ 171 will develop an appreciation for the rapidity of surface oxidation on active sites. The pore areas as developed from the pore volume is a complex issue as was

25 CONTACT ANGLE OF WATER ON COAL

50-c 15

w

w Carbon

w

(dmmf%)

Fig. 1. The calculated results for the contact angle of water on coal with no surface oxidation (h=O) and mineralmatter varing as (0) O.l%,f=O.OOl; (X) 5%,f=0.05; (V) lO%,f=O.l. The lower curve (#) shows the results of the calculation for the conditions of 0.1% mineral matter and 20% surface oxidation ( h = 0.2).

recently discussed by Thomas and Damberger [ 13 1. Probably the most reasonable value for pore volume is obtained from the value of the equilibrium inherent moisture of the coal sample as defined in ASTM D-1412 [ 18 1. Such values are related to the dmmf% carbon as is illustrated in the works of King and Wilkins [ 191. Equation (13) was derived from the average curve representing the data presented by King and Wilkins. The extreme precision given in Eqn (14)) in the light of some of the approximations, appears as unnecessary. However, the fourth significant figure allows for a porosity of about 1.4 vol.% at a curve minimum of @3.7%C which represents the observed data. The complexity of the pore issue lies in the fact that if the surface of coal has a contact angle exceeding 90” then according to the Kelvin equation [ 141 pore condensation will not take place. Thus the water content may not reflect the true pore volume. Furthermore, the surface chemistry of the pore surfaces may not be the same as that of the physical surface of the coal. This problem extends into the changes that take place in the pore system when all of the water is removed from the pores [ 131. Such changes are observed during the adsorption of nitrogen, carbon dioxide and water itself [ 131. RESULTS

Let us first examine the solution of the Equations as presented in Table 1 with the assumptions as given in Table 2 under the conditions that no air oxidation (h= 0) has taken place and the mineral matter content is varied from 0.1% to 10% (f=O.OOl; 0.05 and 0.1). The top three curves in Fig. 1 illustrate the accepted, but unexplained observation that there is a maximum

26

at about 88%C [ 5-71 with decreasing contact angles as %C either increases or decreases from that maxima. Furthermore as the mineral matter content increases the curves are displaced to lower contact angles. Most investigators [ 4-71, however, observe considerably lower values of the contact angle but one must remember that they prepared their samples and conducted their experiments in air with little regard for oxidation. The observations of the physical separation of mineral matter from coal as a function of raw coal particle size down to particle diameters of 2 pm or less appears to support the position of the predicted curves. For example, consider the case of a Pittsburgh seam coal where there is aobut 5 wt% mineral matter with particle diameters smaller than 10 pm as reported by Keller [ 201. A homogeneous mixture of 45 wt% coal particles of a size 70x 10 pm in pure water without a dispersant does not support a large fixed gas content in that mixture. That is there is a very small air bubble attachment to the coal particles which suggests a contact angle below 90’. If, however, this same system is wet milled under water in a sealed mill (to prevent air oxidation) to a particle size below 3 pm, the observed stable air content in the slurry is in the range of 50 vol.% indicating that large areas of the system have a coal/water contact angle in the range above 90’. The study by Keller [ 201 indicated that Pittsburgh seam coals contain about 4.5 wt% mineral matter in the size range between 10 and 1 pm. Thus, during milling the larger particles became discrete mineral matter particles and were eliminated from the surface sites of the coal. The surface of the coal after milling contained less mineral matter and as such produced a higher contact angle with water. The product coal after the removal of the free mineral matter had an ash content of 0.6 wt%. A consideration of the mineral matter content in coal and its effect on the surface properties clearly must focus on that content with particle diameters less than 20 ,um, since much larger sizes that do exist in coal would invalidate a macro contact angle measurement altogether. Practically speaking we do not know whether or not coal fracture during milling affects surface concentration of mineral matter sites. Suppose that coal fracture were enhanced along coal/mineral matter interfaces due to a plane of weakness. In such a case small particles of coal would have a higher concentration of mineral matter in their surfaces than if trans-grain boundary fracture prevailed. The extreme deashing of the Pittsburgh seam coals appears to suggest that fracture is enhanced along the coal/mineral matter boundaries. The fourth, or lowest, curve in Fig. 1 represents the effect of direct surface oxidation of the coal particles with a mineral matter content of 0.1 wt% to the extent of 20% (h=0.2). The effects of the natural oxygen content has been included in Eqn (11)) Table 2, as such varies regularly with dmmf% C. The rate of monolayer accumulation on a coal surface under normal conditions is about 10U6Torr s-l as may be calculated from the kinetic theory of gases [ 211, provided the accommodation coefficient is assumed one. That is, a monolayer

27

is formed at a partial pressure of oxygen of 10e6 Torr (mm Hg) in 1 s. An accommodation coefficient of one, however, is quite unlikely as that suggests that for every molecular impact of oxygen with the surface that molecule remains in the adsorbed, or reacted state, on the surface. The point to be examined is that for all but the most rigorous experiments there is more than sufficient gaseous oxygen available to oxidize the coal surfaces. Cursory observations in the handling of fine coal indicates that air milled coal is severely oxidized while coal milled under water in an air tight ball mill will retain much of its natural hydrophobicity. The product slurry with an average particle diameter in the range of 20 pm or less from wet milling will continue to oxidize when stored in plastic containers depending on the particular coal. Some coals will change dramatically in 24 h while others appear unchanged over several months of storage. COMPARISON WITH EXPERIMENTAL

DATA FROM THE LITERATURE

Over the past few years three authors [ 6-8,221 have published detailed measurements of the contact angle of water on various coals and taken together there appears to be little one might generalize from the results. Taken individually, on the other hand, their arguments for the conclusions do appear vindicated. Probably the most difficult data to access are those of Murata [22] shown in Table 3 and plotted in Fig. 2 where the calculated points are under the conditions given for dmmf% C and wt% mineral matter ( %MM) assuming no surface oxidation by air, i.e. h = 0. The agreement between the calculated and observed values are acceptable for carbon contents greater than 85%C where two points, the Akabira and Takashima seam coal, are low possibly due to surface oxidation. The observed data for %C less than 85% all lie significantly above the calculated values is difficult to understand unless one examines the procedure used to obtain the data. Murata used 90 pm pulverized coal and pressed that powder into 13 x 2 mm discs under a pressure of 1 mg cme2. The contact angle was measured on the surface of the disc. Under the conditions one would certainly expect the coal porosity to be seriously degraded. In order to examine the effects of porosity let us return to the equations given in Table 1 and replace the fraction of porous area equation (Eqn (13)) Table 2) with a constant ofp’ =O.Ol. The solution for this case with the values off= 0.05 and h = 0 is shown in Fig. 3. As one might expect the relationship is a linear decrease with contact angle as the dmmf% C increases which reflects the changes in both Eqns (1) and (2) as carbon content increases. That is, both the paraffinic/aromatic molecular ratio and the molecular oxygen content decrease with increasing carbon which are the only variables left in the contact angle equation. One concludes from Figs 1 and 2 that porosity is the controlling parameter for the contact angle values in Murata’s experiments. And his val-

28 TABLE 3 The observed contact angle of water on coal as published by Murata [ 221. The calculated values of the contact angle were obtained by using the values for the % carbon and mineral matter content of each in Eqn (4) Seam (country )

Taiheiyo Taiheiyo62 Ashibetsu-8 Ashibetsu-70 Akabira-9 Horonai Miike-66 Takashima YaIlournb Beluga’ Bangko”

Carbon (dmmf% 1 83.1 83.2 89.6 88.6 87.8 85.2 88.5 88.3 79.3 71.6 74.8 76.4

Contact angle

Mineral matter (%o)

Obs.

Calc.

9.8 12.5 6.7 12.9 5.7 10.6 17.0 4.4 2.5 0.8 8.1 2.1

87 90 a7 82 72 85 86 73 113 89 93 99

81 81 88 85 89 84 82 90 76 42 58 67

“Indonesia. bAustraIia. ‘Alaska.

ues ought to be in the range of 90” depending on the amount of porosity lost due to the compacting pressure used in preparing those samples. One may further conclude from a comparison of Murata’s observed data and the calculated values that the proposed equation appears to fit some of the data well while other values require an explanation to resolve significant differences.

dmmf%C

Fig. 2. A plot of Murata’s observed Table 3.

contact

angle data [ 221 and the calculated

values given in

29

CONTACTANGLE OF WATER ON COAL

Fig. 3. A plot of the calculated values for the contact porosity of all of the coals is less than 0.1%.

angle of water on coal assuming

that the

The data provided by Fuerstenau [ 81 and the respective calculations seems to fare a little better than those just discussed. In Table 4 the observed data [ 8 ] were averages of at least 10 tests and the calculated values required certain TABLE 4 A comparison of the observed values for the contact angle of water on coal obtained by Fuerstenau [ 81 and values calculated using Eqn (4) Coal-seam

Carbon (dmmf%)

Mineral matter (5)

Contact angle Aif

Somerset-B&C (CO ) Observed Calculated(h)d

86.5

13.5

56 56 (0.5)

Geneva-L. Sunnyside Observed Calculated (h)

87.3

9.6

86 85 (O.l)e

Braztah No. 4/5-D (UT) Observed Calculated (h)

85.4

13.4

“Air: Polished and measured in air. bArgon 1: Polished in argon and measured in argon. ‘Argon 2: Polished in argon measured in air. d(h) : Air oxidation variable. “Calculation with mineral matter at < 1%. ‘Cleaved sample in argon: 104 ‘. gAir exposure 2.5/3.5 h.

90 91 (0)’

Argon lb

Argon 2

73 73 (0.2)

62g 62 (0.4)

102 92 (0)’

97’ 91 (o)e

889 89 (0.05)e

919 91 (o)e

30

parameter assumptions to provide a value equivalent to the observed data. For example for the calculation of the contact angle of water on the Somerset coal the observed value for the mineral matter was used, but in order to calculate the observed contact angle of 56’ the equation required the air oxidation term (h), Table 2, to be set at 0.5. Although that appears rather high, the second sample which was prepared in argon and tested in argon required (h) to be only 0.2. The third sample prepared in argon and tested in air required h=0.4. The air oxidation values appear to be consistent with the test sequence. A similar situation is true for the Geneva coal calculations. However, in order to achieve the very high contact angles it was necessary to neglect the presence of the mineral matter altogether. That was also true for the Braztah coal. The very high values of the contact angle of water on those samples suggests that maybe even the assignments of the contact angle of water on either the paraffinic or aromatic surfaces may be too low or those compounds are capable of establishing a surface excess through the fracture process. Furthermore the Geneva and Braztah coals do not appear to be oxidized rapidly when exposed to air. Very possibly (and as the author has no knowledge of the prior history of the coal samples under test), the (h) value that we have assigned is not just a reflection of air oxidation due to exposure during testing but an accumulated oxidation due to exposure of the samples that have been a long time out of their natural beds under conditions that do not prevent oxidation. The results would be similar in either case. The results of Gutierrez-Rodriguez and Aplan [ 61 are shown in Table 5 and Fig. 4 along with the calculated values using the data shown and h=0.3. The general trend of the calculated values appears to follow the observed data. A comment on the state of oxidation seems appropriate in the light of the discussions provided by Gutierrez-Rodriguez and Aplan [ 6,7]. Standard analytical procedures for the measurement of the oxygen content in coals will probably provide little information on the extent of surface oxidation that effects the contact angle measurements as the oxygen concentration involved in a partial monolayer of bulk surface contamination is far below the error limits of any of the oxygen analytical procedures. More often than not coal analyses are broad averages of a large sample and many coals are stored for long periods under questionable conditions before they are used for a test. Proper storage probably can only be achieved in a vacuum-tight glass or metal container under a purified inert gas at atmospheric pressure. Schwartz et al. [ 301 reported recently data for the contact angle of water on coal as well as some inportant measurements of the chemical characteristics of those coal surfaces using ESCA (electron spectroscopy for chemical analysis). The coals were identified as Poland, USSR (Siberian), and Federal Republic of Germany (Blumenthall) . The important data for those coals are given in Table 6. Clearly the calculated contact angle using the equations from Table 1 agree quite favorably with the experimental data. More importantly,

31 TABLE 5 The observed contact angle of water on coal as published by Aplan et al. [ 61. The caIcuIated values for the contact angle were obtained by using the % carbon and the mineral matter content of each in Eqn (4) Coal-seam

Carbon (maf%) 94.3 89.1 89.1 88.3 84.3 82.4 83.2 77.5 79.6 77.4 79.4 75.5 77.2 73.1 72.6 70.0 76.4 71.6 95.0 84.5

1. Anthracite-reading 2. LV Bituminous-L. Kittanning 3. MV Bituminous-Pocah. No. 3 4. MV Bituminous-San Patricia 5. HVA Bituminous-Pittsburgh 6. HVA Bituminous-Elkhorn No. 3 7. HVA Bituminous-Illinois No. 5 8. HVB Bituminous-Illinois No. 6 9. HVB Bituminous-Indiana No. 6 10. HVC Bituminous-“D” seam (Cola) 11. HVC Bituminous-Somerset “F” 12. HVC Bituminous-L. Cherokee 13. Sub-Bituminous A-Upper Block 14. Sub-Bituminous B-Monarch (WY) 15. Sub-Bituminous B-Big Dirty 16. Sub-bituminous C-Wildcat (TX) 17. Sub-Bituminous C-Hanna No. 5 18. Lignite-Darco Lignite (TX) 19. Anthracite-Primrose (PA) 20. Cannel Coal-Pelton Collieries (Au)

APLAI’I DATA

m,

R

R

a

a

Contact angle

,D

Obs.

Calc.

63 72 72 73 69 57 55 52 46 56 50 48 41 47 47 50 46 40 48

67.7 71.5 70.4 68.2 68.9 69.1 69.9 56.4 59.3 56.9 60.0 47.2 56.5 43.2 40.6 20.0 54.2 32.0 64.1 71.2

(UI

I 8

D

maf XCMBON

Fig. 4. A plot of Aplan’s observed contact angle data [ 61 and the calculated values given in Table 5.

TABLE 6 A comparison of the observed values for the contact angle of water on coal published by Schwartz et al. [ 301 and the values calculated using Eqn (4) Coals Poland

USSR

Germany

dmmf% Carbon Oxygen (% ) Observed contact angle (deg. ) Time=0 Time = 5 min Calculated contact angle

86.1 6.8

77.4 16.4

89.5 5.0

95 90 89.5

62 0 68.6

90 87 87.0

Ultimate analysis (C/O) ESCA surface (C/O) Surface/bulk (C/O)

12.7 6.2 0.49

4.6 1.4 0.3

20.8 4.0 0.05

4.3 3.5 0.81

12.4 14.8 1.19

9.2 7.5 0.82

Mineral matter - observed Bulk (W) Surface as (Al + Si ) ESCA Surface/bulk ratio

however, is the evidence from the ESCA regarding the surface oxygen content and the mineral matter. The observed values for the surface oxygen/bulk content ratio has wide variation, but the average value is near to our figure of choice 0.3. Furthermore, the determination of the surface/bulk ratio for the mineral matter content based on (Al + Si) content in the surface also indicates that our choice of a 1:l ratio was reasonable. DISCUSSION

If indeed Eqn (4) in Table 1 and the necessary variables are correct, probably the most questionable issue is the assumption that the weight (vol.% in the case of p) fraction or some proportion thereof reflects the area fraction. A number of investigations similar to those of Schwartz et al. [ 301 cited in Table 6 could establish the facts of the matter. There was some justification for accepting one third of the weight fraction of oxygen as representative of the surface area based on the observation that as the fraction increases from 0.333 to one the contact angle of water versus carbon curve maximum drifts from about 88%C toward 9O%C. Observed data invariably sets the maximum value very near 88%C. Furthermore the molecular fraction of oxygen is substantially less than its weight fraction in coal. Another concern which enters into the establishment of the surface area fraction is that due to the presence of oxygen

33

in the organic molecules lying in the surface plane of the coal and their relationship to the hydrogen bonding of water molecules which will ultimately define the hydrophilicity of the surface. That is, does one heteroatom establish one hydrogen bond link or is an area generated? An interesting insight into this problem is provided by the investigations of Salazar and Sepulveda [ 231 where silica surfaces were methylated to varying degrees of hydrophobicity and the effect measured as an ability of the different surfaces to nucleate undercooled water. The smallest undercooling was observed on a surface which was about 85% hydrophobic suggesting a rather unique network of attached water molecules resembling an ice structure. Clearly bridging of the water molecules attached to the surface is an important surface behavior. Such bridging may indeed be responsible for the very low receding contact angles observed generally on coal. Salazar’s sample with 100% hydrophobicity showed no tendency to effect the undercooling of water; thus a maximum undercooling of - 40’ was observed in the presence of the potential nucleant. That important observation seems to be consistent with the recent observations of Israelachvili et al. [ 24,251 and Pashley [ 261 who have identified a new field force acting between two fully hydrophobic surfaces and the ability of two of these surfaces in close proximity to cavitate water into a vapor void between the surfaces. The pressure to stabilize the cavitated void certainly exceeds that necessary to stabilize a gas bubble between the surfaces, if gas, or air, were available in the system. The observations are consistent with the Kelvin equation [ 141. The contribution of the pore volume intercept with the surface and its effect is established. The existence of some pores in a unit volume of coal is established through mercury porosimetry [ 271. On the other hand the porous system in coal cannot be investigated with such molecules as ammonia, methanol, ethanol or a number of other rather large organic molecules as such are imbibed into solution in the polymer matrix [ 281 as well as into the pores. Whether or not water lies only in the mechanical pore system or in both the pores and in solid solution with the polymers of the coal is not known. Therefore, when we refer to the porosity of the coal and suggest water absorption as a method for its determination, there is a valid question as to just what is an appropriate model. The calculation of the contact angle suggests that there is a direct relation between the volume percent of the pores (as measured with water) and the surface area, but a quick calculation suggests that the relationship should be 3:l. Reducing the porosity quadratic by l/3 distorts the shape of the contact angle of water versus dmmf% C curve beyond probability. In fact a 1:l ratio seems to agree reasonably well with some of the reported data. The pore model is unclear but the pore system as defined appears to have a strong influence on the contact angle of water on coal. The term mineral matter represents a host of various clays the results of the coalification process are also undefined. Some observations during the separation of coal from mineral matter in the particle size range down to 1 pm

34

suggest that generally the mineral matter is hydrophilic as the majority of those free mineral matter particles remain dispersed in water during oil agglomeration of the coal particles [ 291. Whether or not those particles become hydrophilic during the milling process in water is not known. Therefore the assumption that the contact angle of water on the mineral matter is zero cannot be substantiated. CONCLUSIONS

A set of equations has been brought together which appear to involve all of the important variables affecting the contact angle of water on coal. The relationships were explored and the results appear to correlate reasonably well with the observed data even though the information available from those investigators did not provide all of the variables necessary for a unique solution of the calculated values. The extent of air oxidation of the coal sample and porosity are not typical data established in contact angle experiments but their importance to the contact angle system has been established, Thus an investigation of the proposed equations under conditions where unique solutions are available should contribute to our understanding of the surface of coal. For example, the contact angle equation was tested successfully in a subsequent experiment involving the calculation of the free energy of spreading of an oil over water-wet coal particles of a mean diameter less than 10 pm. These data will be reported in the following paper. ACKNOWLEDGEMENT

The author expresses his sincere appreciation to Professor R.J. Good for his discussions and contributions during the review of this paper and the associated research.

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