Polyanskii, N. G., Russ. Chem. Rev., 31, 496-512 (1962). Polyanskii, N. G., ibid., 39, 244-58 (1970). Polyanskii, 3.G., Tulupov, P. E., ibid.,40, 1030-46 (1971). Iiossini. F. D., Pitaer. K. S.,rlrnett, R. L., Braun, R. &I., Pimentel, G. C., “Selected Values of Physical and Thermodynamif; Properties of Hydrocarbons and Related Compounds, API Project 44, Carnegie Press, Pittsburgh, Pa., 1953. Satterfield, C. N., “Mass Transfer in Heterogeneous Catalysis,” MIT Press, Cambridge, Mass., 1970.
Venuto, P. B., Hamilton, L. A., Landis, P. S., Wise, J. J., J . Catal., 5,81-98 (1966). RECEIVED for review Aumst 15. 1972 ACCEPTED Novehber 6; 1972 We gratefully acknowledge support of this work provided by the University of Delaware Research Foundation and by the donors of the Petroleum Research Fund administered by the American Chemical Society.
Cellular Convection in Polymer Coatings--An Assessment Charles M. Hansen* and Percy
E.
Pierce
Research and Development Center, PPG Industries, Inc., Springdale, Pa. 15144
Cellular convection (Bdnard cells) in polymer coatings often gives rise to troublesome phenomena such as pigment flocculation, pigment segregation, and loss of gloss. The driving force for this i s the surface tension gradient caused by evaporating solvent. The theoretical background for cellular convection is reviewed, and practical remedies for suppressing these undesirable effects are listed.
P o l y m e r coating defect>soften arise from circulatory motion within the liquid film after it has been applied. This is usually called vortexing or Hknard cell formation in honor of Henri B6nard who was the first to study the phenomenon systematically ( B h a r d , 1901). Bartell and Van Loo (1925a) were the first to describe the circular motion in paint films. They noted that the phenomenon had been observed and recorded in other systems by others as far back as 1678. Lord Rayleigh (1916) presented a mathLematicalanalysis of the phenomenon in 1916 based on a n unstable density gradient. Although Rayleigh’s theory had some satisfactory features, the cells observed by Bbnard were subsequently shown to be driven by surface tension, not gravity (Block, 1956). h theory of cellular convection based on surface tension forces was developed by Pearson (1958). Surprisingly, it was not until 1960 that a mathematical analysis explained that the most probable coilfiguration for such cells is hexagonal (Palm, 1960). Theory
Theoretical work on B6nard cell formation has primarily been concerned with mathematical explanations of the various observed phenomena. Pearson’s article (1958) initiated a series of efforts to explain the role of surface tension in the circular convection. Important in these efforts are numbers which must be exceeded if the cells are t o form. The most important of these are the Rayleigh number, h, and the Xarangoni number, B:
where g = gravitational constant, cm/sec2 a = thermal expansion coefficient, cm3/OC,
p
temperature gradient over film, “C/cm film thickness, cm v = kinematic viscosity, cm*/sec K = thermal diffusivity, cm2/sec u = surface tension, dynesicm p = viscosity, g,/cm-see d
= =
If the critical Rayleigh number is exceeded, the cells are driven by density gradients, whereas exceeding t’he critical 3Iarangoni number indicates the cells are formed by surface tension effects. The simultaneous and reinforcing action of both driving forces can also be found (Nield, 1964). Scriven and Sternling (1964) showed that for steady cellular convection driven by surface tension, there is u p f l o ~beneath the depressions and downflow beneath elevations of the free surface. Thse converse is true in buoyancy-driven flow. . h a n d and Balninski (1969) showed that the centers of cells found ill Saran films cast from a mixture of 65% methylethylketone and 357c toluene were indeed depressed. &\nand (1969) and h a n d and Karem (1969) then proceeded to analyze their experiments in terms of the numbers meiit’ionedabove. Smith (1966) extended the theories of surface tensiondriven convect~ion,slightly modifying the conclusions of Scriveri and Sternling by including surface waves. Roschmieder (1967) particularly studied “roll” cells which eventually broke down to form the hexagonal pattern under given circumstances. The roll cells are generally associated with motion driven by gravity and the hexagonal pattern with t’hat driven by surface tension (Grodzka and Bannister, 1972). Ind. Eng. Chem. Prod. Res. Develop., Vol. 1 2 , No. 1, 1973
67
convection was carried out on a recent space flight. It was found that surface tension could drive the convection in the low-gravity environment, a certain critical value of temperat Lire gradient was necessary to initiate flow, and the cells .de---> I ^ ^A^..& " ....*..^.'"L'.lL^L~Y".,,"..c,,-."y* ,P.",d"lrn ""A p1t;,t;,,w U" a L " p Y 2% pU1J6"L.a. ,U.""YRa Bannister, 1972). See Figures 1-3. Whitehead (1971) reviewed the literature related to cellular convection and heat transfer driven by density gradients, noting the irony that such studies as he discusses were stimulated by BBnard's work, even though the phenomenon observed by BBnard was driven by surface tension. Bell (1952) and I3ell and Fawcett (1952) presented rather convincing evidence that Rbnard cells in paint films were driven by density gradients, but, of course, we now know this is not in fact the true mechanism. Wapler felt the cells were caused by diffusion within the film (Wapler, 1953), whereas Jehsenillarw.edel and Marwedel reported on the surface tension effects causing convection currents in paint films drawing on experience in the glass industry (Jehsen-Marwedel, 1960; Jebsen-Marwedel and Marwedel, 1960,1961,1965; Marwedel, 1960, 1966; Marwedel and Jebsen-Marwedel, 1965, 1970a,h). The local surface tension gradients in paint films occur b e cause of solvent evaporation. When the air above the film is saturated with the evaporating liquid, circulatory motion :es (Bell, 1952). The evaporating solvent affects the ace tension in two ways which reinforce each other to ;e the motion (Patton, 1964). The cooling on evaporation jes the surface tension to increase along the path of motion LIL uhe cell a t the air surface. Since the driving force is for liquids of lower surface tension to spread over those of higher surface tension, the motion tends to continue once i t gets started. The other factor is that the surface tensiou of most solvents is lower than that of most polymeric hinders used in coatings. This also causes an increase in surface tension as solvent evaporates. The liquid emerges to the air surface a t the center of the cell, flows outward to the cell boundary, turns toward the substrate at the cell edge, and emerges to the air surface again after traveling back to the center along the subst.ra.te.The more rapid the evaporation of the solvent, the greater is the velocity of the motion. The cells are larger for thicker films than for thinner ones (Jebsen-Marwedel and Marwedel, 1960). This is in agreement with the theory of Rayleigh. Should the thickness be very small, the cellular convectioii may not even start before the volatile has essentially left the film. The viscosity is then too high to allow the required mobility. Pearson's theory also 1:iredicts there wil1 be no vortexing in films below a given thickii ess.
....",
Figure 1. Schematic diagram of BGnard cells showing cellular convection in top and side views
Figure 2. Final result of cellular convection in high-solids polyester coatinu: reflected illumination a t low angle of incideni r -
1he i!'iarangom nuinuer can ue consluerea EO inaicate what courses of action might he taken to reduce its magnitude and thereby reduce the tendency toward U6iiard cell formation. Reducing the magnitude of the change in surface tension with temperature or increasing the thermal coilductivity do riot seem to he reasonable variables over which the coatings chemist can exercise control. Reducing @, the temperature gradient, implies use of less volatile solvents, since the cooling effect of rapid evaporation will then be reduced. Reducing t,lre film thickness and increasing the viscosity of the system will also lead to greater stability. These courses of action have been suggested in the coatings literature by va,rious authors as remedies for I?4nard cell formation. It might also he mentioned that consideration of the Ilayleigh iiumber will suggest the same courses of action to remedy the prohle m. BCnard Cell Formation
in 1iquids
and Paint Films n f t m nl.a The cells found in paintt fiimc _____.I _.__.. I.- 1,C.unmnni nP n t least approach this ideal shape. Since the cells can be found in paint films dried liorizoiitally with the wet film on either side (Van Loo, 1956; Lock, 1960), gravity does not seem to be of major significance, in agreement with the surface tensiondriving force. I t is generally agreed that in liquid layers thicker than about 4 mm, gravity is the primary driving force (Grodzka and Bannister, 1972). For thinner films surface tension coiitrols. This mould include paiot films. Because of the uncertainties in these relationships, research on cellular 68 Ind.
Eng. Chem. Prod. Rer. Develop., VoI. 12. No. 1,
__
1973
a,Lu
Flooding and Floating The separation of pigments leading to color differences (flooding and floating) has been attributed to vortex action (Bartell and Van Loo, 1925a,h; Shur, 1951; Bell, 1952; LeBras et al., 1955; Ferguson, 1959; Lock, 1960; Patton, 1964; Crowl, 1967; Jettmar, 1969, 1970). The circulating motion entrains one pigment more than another, leading to segregation after the film has been applied. The degree of entrainment can he estimated if one knows the pigment (or flocculate) particle size for the pigments involved. T o prevent differential separation of the pigments, one must control the particle sizes such that their velocities are extremely close (Bell, 1952; Haselmeyer, 1968; Haselmeyer and Wahn, 1966; Kresse, 1970) or else promote some degree of coflocculation so there will he good pigment intermixing regardless of the vortexing motion.
Jettmar (1965) has measured the velocities with which different pigments circulate in this type motion by use of a film taken with a microscope. He reported that coarser pigments would be whirled around the cell five to ten times, whereas finer pigments would complete the circuit over a hundred times. The particles much less than 1 p in diameter traveled a t about 0.04 cm/sec while the coarser pigments (3 p) traveled a t 0.01 cm/sec. Since the smallest pigments traveled a distance equivalent to about 400 of their diameters each second, there was ample opportunity to seek out those components of the binder which would preferentially adsorb on their surface. Jettmar showed that such preferential adsorption occurred by electron microscopy. The literature on flooding and floating has been reviewed by Logue (1961a,b). The literature covered hy this review will not he treated in detail here, even though many of the discoveries prior to that date have influenced current progress and research effort. The more recent literature has emphasized the entrainment of the smaller pigment particles in the vortexing action by use of a modified form of Stokes Law to predict relative entrainment velocities (Bell, 1952; Haselmeyer, 1968; Haselmeyer and Wahn, 1968; Kresse, 1970). This form of the equation for the relative entrainment velocities is:
V = K(d,
- d,)RS/q
where V is the velocity; dn and d, are the densities of the pigment and binder solution, respectively; R is the particle or flocculate radius; and ’i is the viscosity. Since density differences are not the primary factors influencing the velocity, one is led to a control of pigment flocculation to approximately equal particle size to prevent separation of the pigments from each other. Since titanium dioside is generally particle size-controlled for optimum optical properties, the smaller colored pigment will have to be flocculated some to increase its particle size to that of the white pigment, or, more commonly, coflocculated with the white pigment when colored and white pigments are used together (Jettmar, 1969; Kaluza, 1972). Practical Remedies to Suppress %nard Cells
Other courses of action to prevent the cellular motion from being a problem include adding silicone oil to modify the surface tension and to promote a more uniform and slower solvent evaporation (Shnr, 1951; Bell, 1952; Krauss, 1962; Haselmeyer, 1968; Haselmeyer and Wahn, 1968; Kresse, 1970); increasing the viscosity of the medium to resist the driving force tending to cause the motion (Dewey, 1946; Ferguson, 1959; Jettmar, 1969); using less volatile solvents, particularly in the stage where the film is still rather mobile (Jettniar, 19GB); and ,using solvents having higher surface tensions to more closely match that of the polymeric hinder (Haselmeyer, 1968; Haselmeyer and Wahn, 1968; Marwedel and Jebsen-Marwedel, 1970a,b). Promoting “secondary flow,” the flowing out of the cells after the cellular convection has ceased, by including a solvent of low volatility has also been recommended (Bartell and Van Loo, 1925a,b; Van Loo, 1956). Ferguson (1959) pointed out th.e effect of relative humidity on the formation of BBnard cella since higher relative humidities lead to more rapid solvent evaporation and a greater driving force for the cellular convection. Since the cells were reported in pure liquids (Wapler, 1953; Linde et al., 1964), it is questionable how much some of these remedies will actually contribute to solving a given problem. The cells have been noted under
Figure 3. Scanning electron micrograph of BQnard cells in acrylic coating pigmented with aluminum powder; film thickness, 35 p ; 45’ viewing angle; 200X magnification
silicone oil (Haselmeyer, 1968; Haselmeyer and Wahn, 1968). Fergusou (1959) discussed several remedies for eliminating flotation problems and concluded by stating that about 10% of the cases he encountered apparently had no solution. Relafed Phenomena
The vortexing phenomenon makes itself most evident by causing such problems as flooding and floating of pigments with accompanying color changes, hut other problems are also present. Gloss may be reduced because of surface irregularities. Cratering is also a closely related phenomenou where material is transported “uphill” by surface tension forces. Hahn (1971) has discussed this a t some length as has Fink-Jeusen (1962). With vortexiug, pigment tends to collect a t the center of the cells and a t times a t the edges of the cells where the local velocity is low. This segregation can proceed to the extent that the coating surface is pure binder (Jettmar, 1966, 1969, 1970). Such a condition may lead to premature failure on exterior exposure. BBnard cells are not always bad since they can be controlled to make “hammer finishes,” special coatings with the ability to hide rough surfaces better and with an appealing esthetic effect (Lamm, 1961). Literature Cited
Anmd, J. N., J . Colloid Interface Sei., 31, 203 (1969). Anand, J. N., Bdwinski, R. Z., ihid., 196 (1969). Anand, J. N., Karem, H. J., ihid. 208 (1969). Bartel, F. E., Van Loo, M., I d .hnng. Chem., 17, 925 (1925a). Bartel, F. E., VanLoo, M., ibid., 1051 (1925b). Bell, S. H., J. Oil Colour Chem. Ass., 35,373 (1952). Bell, S. H., Fawcett, E. W. M., Paint Mfr., 22,99 (1952). Bknard, H., Ann. Chim. Phys., 23, 62 (1901). Block, M. J., Nature, 178, 650 (1956). Growl, V. T., J.Oil Colour Chm. Ass., 50, 1023 (1967). Dewey, P. H., Off. Dig., 18,336 (1946). Ferguson, I., J. OilCOlouT Chem. Ass., 42,529 (1959). Fink-Jensen. P.. F d w oeh Luck. 8. 5-14. 3 9 4 9 (1962); identical t o Farhe
+ &ek,
68,155 (1962).
Grodsku, P. G., Bannister, T. C., Science, 176,506 (1972). Hahn, F’. J., J . Paint Z’echnol. 43,58 (1971). Haselmeyer, F., Farhe Lack, 74, 662 (1968). Haselmeyer, F., Wahn, W. H., Paint Mfv., 38, 16 (1968). Jebsen-Marwedel, I%., Deut. Faden Z., 14,435 (1960). Jebsen-Marwedel, H., Marwedel, G., Furhe Lack, 66, 314
+
+
Ind. Eng. Chem. Prod. Res. Develop., Vel. 12, No. 1. 1973
69
Koschmieder, E. L., J.Fluid Mech., 3 0 , 9 (1967). Krauss. W.. 6th FATIPEC Conar.. 332 (1962). Kresse,’ P., ‘Deut. Farben Z., 24,”52l (1970); see also Paint Technol., 35, 5 (1971).
Lamm, T’. P., Of.Dig., 33,1408 (1961). LeBras, L. It., Bobalek, E. G., Von Fisher, W., Powell, A. S., ibid., 27, 607 (195.5).
Linde, H., Pfaff, S.,Zirkel, C., Z . Phys. Chem., 225, 72 (1964). Lock, A. B., J . Oil Colour Chem. Ass., 43,859 (1960). Logue, L. A., Paint Jfjr., 31, 5 (1961a). Logue, L. A,, ibid., 55 (1961b). Marwedel, G., Farbe Lack, 66,379 (1960). Rlarwedel, G., ibid., 74, 18 (1968). hlarwedel. G.. Jebsen-Marwedel., H.., Deut. Farben 2.. 24. 103
+
(1970a):
I
I
\ - - - - I
I
+
.
’
Marwedel, G., Jebsen-Marwedel, H. ibid., 157 (1970b). Marwedel, G., Jebsen-Marwedel, Farbe + Lack, 71, 91 (1965).
Nield, D. A., J . Fluid Xech., 19,341 (1964). Palm. E.. ibid.. 8. -18.1 - - (196Oi. Pattdn, T. C., “Paint Flow and Pigment Dispel:sion !” p 443, Riley, New York. York, N.Y.. N.Y., 1964. Pearson, Pearson,’J. K. A., J.’ J . FZuid‘Jlech., Fluid Jlech., 4, 489 (1958). Ravleieh. Lord. Phil. Phzl. X a a . . 32 Ber. 6). 329 (1916). Schven, L. E.. Schven. E., Sternlinn. Sternling, %: V.. V., ‘.J. J . Flkyd Flu;d Jieih,, I f e i h , , 19, 324 (1964). Shur, E. G., Of.Dzg., 23, 867 (1951). Smith, K. X.,J . FluzdJIech., 24,401 (1966). Van Loo, AI., Of. Dig., 28, 1126 (1956). Wapler, D., Farbe Lack, 59,352 (1953). Whitehead, Jr., J. A., Amer. Sci., 59, 444 (1971). 1).
k.,
RECEIVED for review September 18, 1972 ACCEPTED November 21, 1972
Potassium Recovery from Bittern Solutions Fatma AI-Awadil and Abdulaziz K. Al-Mahdi*2 Chemistry Department, Kuwait University, Kuwait
Prior to potassium recovery, calcium was removed from seawater by increasing the concentration of brines, and magnesium by forming the magnesium ammonium phosphate complex. The Salutsky method was used. It depends upon the formation of a complex double salt of potassium sulfate and calcium sulfate which can be precipitated and separated from the bittern, after which the solid i s treated with fresh water and decomposed to the simple sulfates. This results in a K2S04 solution and a solid gypsum phase. The latter can be recycled, whereas potassium sulfate can be recovered from the former. Different conditions were tested, including types of gypsum, temperature, and the effect of NaCl on the recovery of potassium. Sulfuric acidtreated local gypsum used with multiple-batch treatments gave the highest recovery. Yields are tabulated and approximate economics discussed.
S e a w a t e r is the main source of supplying potable water to the 733,196 population of the State of Kurvait. Deep ground brackish water a t Xinagish and Sulaibiyah is the only other plentiful source of supply where the total dissolved solids do not exceed 3900 ppm. R a t e r demand is rising steadily by 200 million galjyr. Estimates show that the mater demand will rise to cover 250 million gal/yr when the population of the State reaches over a million. In a comprehensive survey of Kuwait’s water supply, Temperley (1965a) indicates the importance of the study of dissolved solids as by-products of the seawater distillation plant or the brackish water with higher total dissolved solids rrhich reaches to 10,000 ppm in some areas. Present address, Water Resources Development Centre, Shuwaikh, Kuwait. * Permanent address, Foundation of Scientific Research, Ministry of Higher Education & Scientific Research, Baghdad, Iraq. 70 Ind.
Eng. Chem. Prod. Res. Develop., Vol. 12, No. 1 , 1973
The salinity of seawater and hence the chemical constitution differ from one area to another, the average total dissolved solids content being 36,000 ppm. The total dissolved solids content of the Arab Gulf ranges from 39,000 ppm in the open sea 30 miles from the coast to 42,000 ppni a t the Arabian coastline. Kuwait Bay seawater’s seasonal salinity varies bettveen 44,000 ppm in the cool season to 48,000 ppm at the end of the hot season (Temperley (1965b). The large number of known elements in seawater indicates that probably all of the earth’s naturally occurring elements exist in the sea. Knonm abundances of the different elements in seawater have been reported (Chem. Eng. LYews, 1967; Tallmadge e t al., 1964). K i t h the volume of the oceans being 1.37 billion km3, we can imagine what huge reservoirs and rich sources of various elements the oceans are. Nagnesium, bromine, sodium in various forms, and potassium have been recovered from seawater by various workers (Butt e t al., 1964; Salutsky et al., 1965; Thorp and Gilpiii,
