of about 22 weeks with a continuous input of 0.075 ppm of NO2. Conclusions The results of this work indicate that indoor control of NO2 can be achieved ,by relatively simple and convenient means via the use of a zinc chloride coated copper-fiber filter in the air circulation system. Relatively long-lived and efficient removal can be achieved without adding excessive additional pressure-drop load to existing blowers or fans. The development of a design model is outlined for application purposes. It is envisioned that these filters will be of use in a number of industrial applications where NO2 concentrations in the ambient air exceed safe limits. Typical application sites might include foundry buildings, glass industry shops, etc.
Literature Cited Mitchell, R. I . , Cote, R. W.. Lanese, R. R . , Keller, M. D., paper presented at the A.G.A./IGT Research and Technology Conference, Dallas, Texas. Mar 1974. Shy, C. M., Creason, J. P., Pearlman, M. E., McClain, K. E., Benson. F. G.. Young, M. M . , J. Air Pollut. Contr. Ass., 20 ( E ) , 539 (1970a). Shy. C. M.. Creason, J. P., Pearlman, M. E., McClain, K. E., Benson, F. B., Young, M. M., J. AirPoilut. Contr. Ass., 20, ( 9 ) , 582 (1970b). Shy, C. M.. Hasselblad, V., Burton, R . M., Nelson, C. J., Cohen, A. A,, Arch. Environ. Health, 27, 124 (1973). Tuesday, C. W.. Symposium held at General Motors Research Laboratories, New York, N.Y., 1971.
Received f o r review May 8,1974 Accepted September 3,1974 This work was supported by the American Gas Association (A.G.A.). The author extends his appreciation for the many helpful discussions afforded by A.G.A. representative during the course of the research.
Viscosity of Severely Oxidized Engine Oil James A. Spearot Fuels and Lubricants Department. Research Laboratories. General Motors Corporation. Warren, Michigan
Severely oxidized engine oils are shown to consist of an oxidized Newtonian oil phase and a dispersed insoluble particulate phase. T h e rheological behavior of such dispersions was investigated for insolubles concentrations from 0 to 23 wt %, shear rates from 2 to 14,000 sec-’, a n d temperatures from 20 to 80°C. Michaels and Bolger’s constitutive equation for clay suspensions which assumes the existence of “flocs”-primary particles and entrapped water-also described the behavior under shear of t h e d e graded oil samp1e.s. By analogy, t h e presence of particle aggregates consisting of insoluble oxidation products and an adsorbed oxidized oil fraction is postulated. T h e existence of aggregates is supported by plots of t h e reduced viscosities of t h e oil suspensions vs. aggregate volume fraction. These plots are shown to agree with the data obtained by Eilers for suspensions of spheres with a wide diameter distribution. Further evidence supporting t h e existence of such structures in thickened oils was obtained from adsorption chromatography experiments which showed that the oxidized oil fraction in t h e oil phase is sufficient to produce t h e aggregate concentrations estimated from the viscosity measurements.
Introduction Understanding the rheological behavior of suspensions of organic or organometallic solids in mineral oils is essential in such diverse fields as the production of asphalt, the formulation of lubricating grease, and the degradation of engine oil. Each of these materials-asphalt, grease, and severely oxidized engine oil-consists of a suspension of interacting solid particles in a Newtonian oil phase. Knowledge of which physical parameters influence the viscosity of such suspensions as asphalt and grease is important not only in manufacturing these materials but also in predicting the load carrying capacity of the finished product. The effect which organic solids have on the viscosity of oxidized engine oil must be understood if the detrimental consequences of using such oil in an engine are to be assessed quantitatively. Unfortunately, although the literature concerning the effects of inert particles on the viscosity of a Newtonian fluid is vast, data and theoretical analyses on the more practical situation involving interacting particles are still quite sparse. The information presented in this work supports a mechanism which explains how the viscosity of a Newtonian oil phase is increased by the presence of interacting solid particles. Specifically, a fraction of highly polar solids is, first, extracted from a sample of oxidized engine oil and then characterized using several analytical techniques. By resuspending portions of this solid fraction
into the oxidized oil, the parameters which influence the viscosity of such “thickened oils” are investigated and explained in terms of a physical model. Related Investigations. The effects which inert solids have on the viscosity of a Newtonian fluid have been reviewed in several places (Thomas, 1965; Rutgers, 1962a,b), and it is evident that a large amount of time has been spent studying these systems since Einstein (1911) developed the relationship
In eq 1, p r is the reduced viscosity of the suspension, or the viscosity of the suspension divided by the viscosity of the suspending fluid, and $s is the volume fraction of rigid noninteracting spheres present. Equation 1 is strictly valid for particle concentrations approaching zero. Many other equations, however, have been suggested to account for the increases in suspension viscosity which occur when greater quantities of solids are present. One such model, developed by Brinkman (1952), is written as p r = (1 - 4 y - 5 (2 ) Equation 2 was formulated assuming a wide particle diameter distribution, and although it gives an infinite reduced viscosity at a volume fraction of 1.0, an unrealistically high solids content, it accurately predicts the viscosities of suspensions of up to 40 vol70 solids. Ind. Eng. Chem., Prod. Res. Develop., Vol. 13, No. 4,1974
259
The work done on suspensions of interacting particles is not as encompassing as that for inert systems. There are several references, however, which indicate the nature of such suspensions, and offer explanations for their characteristically high viscosities. First, the data and analyses of Michaels and Bolger (1962a,b, 1964) are particularly significant. The apparent viscosities of suspensions of kaolin in water were shown to consist of three terms-a term accounting for hydrodynamic dissipation such as described by eq 1 and 2, a term accounting for the breakage of structural bonds between particles, and a term accounting for the resistance of the continuous structural network to strain. In addition, Mshaels and Bolger proposed that the basic structural unit in such suspensions is not the primary clay particle, hut a collection of clay particles and combined water termed a “floc.” The “floc” volume conIo 0 e“ ‘M centrations were measured in sedimentation experiments ENGINE Tis, HOURI and were correlated with the viscosities of the clay susFigure 1. Effect of oil temperature on viscosity change. pensions. Asphalt, another example of a suspension of interacting particles, has been investigated by Reerink (1973). Asphalt consists of a highly polar, organic solids fraction, termed asphaltenes, suspended in an oil phase. Reerink demonstrated, using the data of Mack (1932), that the reduced viscosities of asphalts do not obey eq 1 as a function of asphaltene content. The discrepancies were attrihuted at high temperatures to the concept that asphaltene particles exist in suspension as flat ellipsoids, a particle shape which will produce a higher suspension viscosity than will perfectly spherical p articles. As Reerink indicat+ IC 10 MICRONS ed, however, this hypothesis cannot he supported a t lower temperatures due to the polal IMLUIC. VI LIIC. d s p a ~ ~ a ~ r a Ea lgure L. uxiamon proouers aispersea m an OLIphase and the necessary interactions which must exist between particles. and separating Out the Oil phase with a >xhlet extraction A third example of a suspension io which the particles apparatus. The extraction was conducted for a total of 30 interact with one another is found in used engine oil analhr using 300 m1 Of n-heptane. Most Of ”le solid material yses. Kahel (1970) has demonstrated that, under extreme remaining in the after extraction could engine operating conditions, the viscosity of a lubricating he removed hy replacing the re’boiler containing oil can-.increase exponentially with time as shown in Fig. . . +ha ha-tona onrl n:l t...T.rr nhora ..ri+h onnthar rehoiler containl.lr ,l-.L.+by...vlu.l ure 1. ‘These data were obtained in an engine dynamomeing 300 ml of distilled benzene. Only a very small residue ter experiment carried out under ASTM Sequence IIIC was left in the thimble after 8 hr of extraction with henTest conditions (1973). Controlling the oil sump temperazene. In the more than ten such extractions conducted, ture at successively lower values delays the onset of the this residue was never greater than 0.2 wt 7% of the origicatastrophic viscosity increase, hut not indefinitely. nal sample, which indicates that essentially all of the Several authors have considered the phenomenon of “oil thickened oil could he recovered from the Soxhlet apparathickening” (Bardy and Asseff, 1970; Kuhn, 1973; Cecil, tus. The n-heptane and benzene solvents were removed by 1973), hut the conclusions reached in these studies are not evaporation in a vacuum oven at reduced pressure and the in total agreement. In general, the importance of oil “insseparated phases were weighed. Table I lists the results of oluhles” has been recognized, hut neither the reactions 12 independent separations of the same thickened oil and which result in the formation of these solids nor the shows that the mean n-heptane solids phase concentration mechanisms by which these solids increase the viscosity of in the sample was 19.2 wt %. an oil sample are well understood. Using ASTM Test Procedure D-664, total acid numbers of 11.0 and 64.0 were measured for the oil and solid phasCharacterization of Thickened Oil es, respectively. Experiments conducted on a Waters Associates Model 200 gel permeation chromatograph (gpc) To determine the chemical and physical nature of a thickened oil sample, the final drain oil from a Sequence demonstrated that, although the oil phase had an average IIIC engine test was subjected to several different lahoramolecular weight of 500, slightly higher than a sample of tory analyses. Examination of the grease-like oil with a unused oil, the solid phase had a much larger average moLeitz Ortholux optical microscope showed that the sample lecular weight of 38,000. In addition, Figure 3 shows that the apparent molecular weight spectrum of the solid consisted of two separate phases-a continuous oil phase phase is quite broad with components ranging in molecuand a dispersed “solids” phase. Figure 2 is a photomicrograph taken at 25°C with a total magnification of 616X. lar weight from 200 to 106. These data were obtained The diameters of the largest particles observed are apusing tetrahydrofuran as a solvent for both phases and proximately 5 to 8 p , although there appears to be a large using known organic compounds and polystyrene standards for calibrating the chromatographic column. number of particles with smaller diameters. The solids phase observed in the microscopic investigaThe extent of oxidation in the oil phase was determined tion was removed, from the thickened oil for further analyhy washing a sample of the oil through an adsorption ses. This was accomplished by placing 10 g of the thickchromatography column packed with separate layers of ened oil in a Whatman double thickness filtering thimble 150 g of unactivated 30/60 mesh Fuller’s Earth and 150 g
1
VY
IC”
IW
~
~
-
260
Ind. Eng. Chem., Prod.
Res. Develop., Vol. 13, No. 4.
1974
yL.u
y.lyl..ll
I
0
O
O X I D I Z E D OIL PHASE DISPERSED S O L I D S PHASE
1 1 I
D
VOLECULA? WEIGHT
Figure 3. Apparent molecular weight distribution of oil and solid phases from thickened engine oil.
10"
lo1
102
lo4
103
S H E A R RATE 5EC.l
Table I. n-Heptane Extraction Results
Figure 4. Effect of shear rate on the viscosity of thickened oil.
Oil phase (wt
Sample
96 of
thickened oil)
1 2 3 4 5 6 7 8 9 10 11 12 Arithmetic mean Standard deviations
80.3 80.1 82.6 83.2 80.4 80.3 75.2 83.7 78.9 84.4 76.9 7 7.3 80.3 12.87
Solids phase (wt 96 of thickened oil) 21.3 19.6 15.5 21.7 19.7 16.1 21.0 22.6 19.8 15.4 17.4 19.7 19.2 k2.48
of activated (24 hr a t 500°F) 28/200 mesh silica gel. The first solvent used to wash the column was n-heptane. The fraction of oil which passed through the two adsorbents will be termed the "white oil" fraction. The fraction of the oil phase which adsorbed on the column packing was removed with 400 ml of a second solvent (an acetone-benzene, 50350 solution), and it will be termed the soluble oxidation products fraction. The results of separating six samples of the oil phase are shown in Table 11. The white oil fraction comprised 44.5 wt YO of the thickened oil sample. Infrared spectrophotometric studies have indicated that the white oil fraction is devoid of any oxidation products and is quite similar in composition to the base stock from which the original oil was blended. The soluble oxidation products fraction comprised 33.9 wt YO of the thickened oil sample, and oxidation products in the form of both carbonyl and hydroxyl compounds are evident from its infrared spectrum.
Effect of Solids Concentration on Oil Viscosity To determine the effects of solids concentration on the viscosity of a thickened oil sample, portions of the solid phase were resuspended in samples of the oil phase. The first step in this procedure was to partially dissolve a specific amount of the solid phase in benzene. That fraction of the solid phase which was insoluble in benzene was evidently finely dispersed enough to remain suspended in the solvent, since only small amounts of the material could be detected settling out of the resulting mixture over a period of l hr. As soon as the solid phase was uniformly distributed in the benzene, the benzene-solids slurry was
Table 11. Chromatographic Separation of the Oil Phase White oil Soluble oxidation fraction products fraction (wt % of (wt of thickened oil) thickened oil)
w
Sample
4 5 6 7 11 12 Arithmetic mean Standard deviations
44.5 44.0 44.8 44.1 44.7 45.1 44. 5 k0.42
38.7 33.5 35.5 31.2 32.2 32.2 33.9 12.79
added to a measured quantity of the oil phase. The benzene was then evaporated in a vacuum oven, and the solids phase was left resuspended in the oil. The samples prepared in this fashion were investigated with a Haake Rotovisco viscometer, Model RV-3. The measuring head used in this work consisted of a cone and plate combination. The cone angle, p, was 0.3" and the cone radius, R, was 1.4 cm. For a given rotational speed, 9 , the shear rate imposed on the fluid is given by r = -s2 (31
?
The shear stress, T , can be determined, as indicated in eq 4, by measuring the torque, T, exerted on the cone due to the drag of the fluid. 3 T - --
(41 2 .iiR3 The apparent viscosity of the fluid is defined as the ratio of the shear stress to the shear rate
Apparent viscosity data were obtained a t 21.1, 25.6, 37.1, 59.2, and 81.7"C on six fluids with different solids concentrations. As an example, the data collected at 37.1% are shown in Figure 4. Five of the samples were prepared from separated phases as described above, and one sample (19.2 wt %) consisted of the thickened oil obtained directly from the final drain of a sequence IIIC engine test. The oxidized oil phase by itself is Newtonian at all temperatures studied, and at 37.loC, for example, its viscosity is approximately twice that of the original oil blend. It is I n d . Eng. Chem., Prod. Res. Develop., Vol. 13, No. 4, 1974
261
=I r
IW S E C - ~
1 37.1'C I
1m.o
/ Sequence IIlc Engine Test Final Drain Sample
0
0
2
4 SHEAR RATE,
6
8
10
r , lo3 s e c - l
Figure 6. Shear behavior of thickened oil samples.
evident from this plot that as the solids concentration increases, not only does the viscosity of the samples increase, but also the non-Newtonian character of the samples becomes more pronounced. It was found that the non-Newtonian character decreases with increasing temperature, but even at 81.7"C, the samples with insolubles concentrations greater than 10 wt % display apparent viscosities which depend on deformation rate. By cross-plotting a portion of the data in Figure 4, a graph of apparent viscosity us. weight percent solids such as shown in Figure 5 can be drawn. These data were all obtained a t a temperature of 37.1"C and a shear rate of 100 sec-1. It is evident from Figure 5 that the presence of only 23 wt % solids will increase the viscosity of an oil sample by-two orders of magnitude. Thus, one can conclude that the very high viscosities characteristic of thickened oil samples are due primarily to the insolubles suspended in the oil phase. Furthermore, since the viscosity of the thickened oil sample obtained from the IIIC engine test falls on a curve drawn through the data obtained with the laboratory prepared thickened oil samples, it is evident that the separation and resuspension techniques used on these samples did not change their basic physical nature. Comparisons of Rheological Models a n d Thickened Oil Data The data collected show a significant relationship between the viscosity of a thickened oil and the concentration of n-heptane insolubles suspended in the degraded lubricant. To establish whether or not this relationship can be predicted using a physical model, several different equations for relating viscosity and solids content were examined. Since Einstein's equation, eq 1, is an exact solution for dilute suspensions of inert spheres, and since both Einstein's equation and Brinkman's equation, eq 2, are relatively simple mathematical expressions, these were investigated first even though it was recognized that both expressions were developed for noninteracting suspensions and inherently should not be valid for the fluids under consideration. In addition, Figure 4 shows that the apparent viscosities of thickened oils are functions of shear rate, a variable which does not appear in either the equations of Einstein or Brinkman. In applying either eq 1 or 2 to the data collected from the thickened oils, the viscosities measured a t high shear rates were employed. Figure 4 indicates that, regardless of 262
Ind. Eng.
Chern., Prod. Res. Develop., Vol. 13,No. 4 , 1974
0
1
2 SHEAR RATE,
3
4
5
r ,io3 s e c - '
Figure 7. Shear behavior of thickened oil samples. the solids concentration present in a given oil sample, the viscosity of the sample tends toward a value which is independent of shear rate a t high levels of shearing deformation. This can be illustrated better by plotting the data in another fashion. Figures 6 and 7 are plots of shear stress versus shear rate for the thickened oil suspensions a t 37.1"C. At low shear rates the plots are, in general, nonlinear, and for the more concentrated suspensions yield stresses are observed. At high shear rates, however, the shear stress becomes linear in shear rate, indicating a constant or Newtonian viscosity. Since both Einstein's and Brinkman's equations were developed assuming a Newtonian viscosity, the viscosities measured from the linear portions of such shear stress-shear rate plots as Figures 6 and 7 were used to check the utility of these equations. For the two highest insolubles concentrations in Figure 7, 19.2 and 22.8 wt 70,it was not possible to increase the deformation rate sufficiently to reach the linear region of the plot. Due to the large viscosities of these two samples, viscous heating occurred at relatively low values of shear rate. The temperature rise due to viscous dissipation was monitored by a thermocouple embedded in the plate of the viscometer, If the temperature of the sample increased by more than 1"C, viscous heating was assumed and the data obtained were ignored. This occurred a t high shear rates for the two most concentrated suspensions, and thus, values of the high shear rate viscosity could not be determined. For the remaining samples, the reduced viscosities of
6 TEMPERATURE 25.6
5 0
59.2 81.7
I
4
I
BRINKMAN MODEL
/
”544,
/
,
0
0
1.1
0.2
0.3
0.4
1
0.5
I 0.6
*s
Figure 8. Reduced viscosities and model predictions as a function of the solids volume fraction. the suspensions were calculated by dividing the high shear rate viscosities at a given temperature by the viscosity of the oil phase. The densities of the oil and solids phases were determined a t the temperatures of interest, and the volume fraction of solids in each sample was calculated. Figure 8 is a plot of reduced viscosity us. volume fraction of solids present in each of the suspensions. The equations of Einstein and Brinkman are also plotted in this figure. It is evident that a discrepancy exists between the data obtained from the oil samples and the viscosity predictions of Einstein and Brinkman. Einstein’s equation, having been derived for dilute suspensions, cannot be expected to give reasonable predictions for concentrations greater than a few volume per cent. Data of Eilers (1941), however, have shown that Brinkman’s equation gives useful predictions for concentrations of up to 40 vol ’70of the dispersed phase. As pointed out earlier, Brinkman’s equation was developed for suspensions of inert noninteracting particles. Thus, the most logical explanation for the lack of agreement between the data and Brinkman’s equation is that the polar nature of the solids in the thickened oil must be taken into account when describing the reduced viscosities of such suspensions. Michaels’ a n d Bolger’s Model for Clay Suspensions. The viscosity predictions of Einstein’s and Brinkman’s equations can be improved, and the discrepancies between data and theory can be further explained by using an analysis due to Michaels and Bolger. The original analysis was proposed to describe the viscosities of suspensions of kaolin in water and is based on two fundamental assumptions. First it is assumed that in suspensions of interacting particles, structures can exist. These structures are formed when collections of particles are bonded together by weak physical interactions such as those associated with dispersion, hydrogen bonding, or electrostatic forces. When the fluid is at rest these aggregates or structures are continuous throughout the material. As the deformation rate is increased, however, it is proposed that the structures are uniformly broken down until, at high shear rates, a limiting aggregate size is reached. Michaels and Bolger propose that this limiting structure is composed of a collection of primary solid particles. Specifically, even a t high shear rates the forces binding a group or “floc” of primary particles together will be sufficient to prevent the floc from being destroyed by shearing forces. This high-shear structure will also include a quantity of adsorbed or entrapped liquid. The presence of this liquid fraction associated with the floc will increase the apparent volume fraction of solids in the suspension to some value
which is greater than the volume fraction of the solid phase alone. The second fundamental assumption is that for suspensions of interacting particles the shear stress, T, corresponding to some applied shear rate can be written as a linear combination of three other stress terms -I -_ TN + T C R + 1, (6 The term T N is attributed to the stresses produced by the deformation of the continuous structures in the fluid. Michaels and Bolger derive an expression for T N in terms of shear rate, floc diameter, volume fraction of flocs, and the forces acting between the collections of solid particles. The derivation, however, is in part empirical, and for the purposes of describing the thickened oil samples it will be necessary to use only the asymptotic values of T ~ S a t high and low shear rates. Specifically
asr and as
-- --0,
T~
’Y
m? T N
0
(7)
At low shear rates the aggregates are continuous throughout the sample and the suspension behaves like a solid. Thus, T N must approach the yield stress, T Y , of the suspension. At high shear rates the aggregates reach a limiting size and a t that point are assumed to be rigid or nondeformable. Thus, 7 N must approach zero. The second stress term in eq 6, T ~ R can , be attributed to the destruction of the weak physical bonds acting between aggregates in the suspension. In general, T C R is a nonlinear function of shear rate. However, if the forces acting between aggregates are assumed to be London dispersion forces of the type described by Hamaker (1937), a t high shear rates after the limiting floc size is reached, T C K is given by the equation
In eq 8, d is the average diameter of the particle aggregates and a. represents the minimum distance that can exist between two aggregates. The floc volume fraction is @ f and A,, is an inter-aggregate force constant defined by the equation due to Hamaker H = -A0 - d
24 a? H i s the inter-aggregate bonding force. The final term in eq 6, T V , represents that portion of the stress used to overcome purely viscous drag forces, or that fraction of the stress which would be present in eq 6 even if the particles in the suspension did not attract one another. Many relationships have been suggested for T ~ but , if either Einstein’s or Brinkman’s equation is used to define the hydrodynamic viscosity of the suspension, then T V can be derived from eq 1as or from eq 2 as = P,,r(l -
4r)-2’5
(11) The complete Michaels and Bolger equation for relating the shear stress of a suspension of attracting particles to an applied shear rate is mathematically cumbersome and, as indicated previously, is, to a limited extent, empirical. If the equation is examined a t high shear rates, however, it reduces to a form which is, within the limits of the assumptions used to derive it, exact. In addition, the high shear rate form of eq 6 is useful in describing the behavior of the fluids under discussion in terms of a limited number of material properties. Specifically, a t high shear rates, eq 6 reduces to 7,
Ind. Eng. Chem., Prod. Res. Develop., Vol. 13,No. 4 , 1974
263
+
m"). Analogously, if 6 represents the mass of that portion of the oil phase which is associated with the aggregates, then a , the mass fraction of solids in the aggregates, is defined as m,/(m, 6). Assuming the volumes of all the individual phases in the thickened oil are additive, then the volume fraction of aggregates, @ A , can be given by
+
m,
4 A
, 0
0.1
0.2
0.3
04
05
06
4 Figure 9. Reduced viscosity predictions assuming aggregate formation.
por(i -
4+)-2-5
1 -cy PA Ps
1
cy @A
The reduced viscosities can be calculated as before, but, instead of eq 2, are now described by cp*)-2*5
(15)
where $ f , the floc volume fraciion, has replaced the volume fraction of solids, 4,. The concept that the reduced viscosities of a suspension of interacting solid particles should be considered a function of some aggregate phase rather than the volume fraction of solid particles present can be used to explain the discrepancies between the thickened oil data presented earlier and Brinkman's equation. By analogy to the model of Michaels and Bolger, it can be assumed that a particle structure exists in the thickened oil samples. These "micelles'' or aggregates consist of a collection of primary insoluble particles and a fraction of the oil phase either adsorbed or associated with the solids. The resulting structures, it is proposed, would be very similar in nature to the sludge aggregates photographed by Bowden and Dimitroff (1962). These agglomerations of particles create an aggregate volume fraction, @ A , which is greater than the volume fraction of solids present in the suspensions. Aggregate Volume Fraction Determination. In their work, Michaels and Bolger measured values of @ f in a sedimentation experiment and demonstrated that the reduced viscosities of the clay suspensions as a function of & agreed with other data in the literature. Because of the opacity of the thickened oil samples it would be very difficult to conduct a sedimentation experiment, and thus, another method is needed to determine the aggregate volume fraction, $ A . An expression for @A can be derived from a material balance. If m, represents the mass of the solids phase and m, represents the mass of the oil phase, then X,the mass fraction of solids in the thickened oil, is given by m,/(m, 264
+- (1 - 0 ) Po
Ind. Eng. Chem., Prod. Res. Develop., Vol. 13, No. 4 , 1974
- (1 - P,/P,)
(17)
= 1
2-
(1 - P,/P,)
When a is equal to unity, the insoluble particles act independently of the oil phase and @ A reduces to $, the volume fraction of solids in suspension
@,
-
(16)
In eq 16, U A and U B are the partial volumes of the aggregate and the bulk oil phases, respectively. The unassociated or bulk oil phase is that quantity of oil which is not an integral part of the aggregate structures in the dispersions. If the density of the aggregate phase, p A , is given by
(13)
Equation 13 represents a linear relationship between shear stress and shear rate of the sort proposed by Bingham and Green (1919), and graphically it can be portrayed as shown by the dotted lines in Figures 6 and 7. The viscosity of a suspension can be obtained from the slope of the dotted lines, and mathematically is given by
Pr = (1
6
where p s and po are the densities of the solid and total oil phases respectively, then the aggregate volume fraction can be derived as
Substituting in eq 8 and 11provides
: 4 +
+
= VA = &2)PA V u A t v B m s + 6 m - 6 -ID PA Po
=
(18)
Po/ P, Po/Ps)
1
X- - (1 -
Brinkman's equation can now be employed along with eq 18 and 17 to give
= (1 -
[G ( 2 -
l)] 4,}
-2.5
(19)
The value of p r given by eq 19 is plotted in Figure 9 as a function of the volume fraction of insolubles with a as a parameter. As a approaches unity the insoluble particles tend to act independently of each other and of the oil phase, and Brinkman's original equation, eq 2, becomes valid. As a approaches zero a greater quantity of the oil phase is associated with the particle structures, and the apparent volume fraction of aggregates increases even though the volume fraction of insolubles remains constant. In applying eq 19 to the thickened oil samples, the value of a must be fit to a portion of the viscosity data, since, although the density ratio, p s / p o , can be measured independently, an estimate for the mass fraction of insolubles in the aggregates is not available. Since the data of Eilers (1941) indicate that Brinkman's equation is valid a t low volume fractions of the dispersed phase, and since in the limit of zero volume fraction Brinkman's equation reduces to that of Einstein, an exact solution, the reduced viscosity data for the least concentrated sample (4.84 wt % solids) were used to determine the mass fraction of insolubles in the structures. Knowing the mass fraction of insolubles in a sample and the corresponding reduced viscosity a t a given temperature, eq 19 can be used to calculate a value for a . Using this technique values of a were determined for each of the five temperatures investigated. These values
6
IW
5
80
TEMPERATURE I I
. 3
-
0
4 *r
-
60
”%,
-
*
/
Iy
1
21.1 C
25.6 37.1 59.2 81.7
-
7 112
CR 3
40
2
20
1
0
0
01
12
02
03
04
05
Ob
+A
I
0
II
03
04
05
06
+A
Figure 10. Reduced viscosities and model predictions as a function of aggregate volume fraction. were found to be only a slight function of temperature and, for the thickened oil system considered in this work, CY can be assumed to have a constant value of 0.36. With this value for cy, the aggregate volume fraction, @ A , can be calculated for higher concentrations of solids from eq 17. If the reduced viscosities of the thickened oil samples are now plotted versus 4>1, the comparison with Brinkman’s model shown in Figure 10 is obtained. The agreement between the experimental data and the model predictions is greatly improved over that in Figure 8. The experimental data tend to fall above the predictions of the model, but it is expected that Brinkman’s equation will give low estimates for the reduced viscosity of concentrated suspensions. As noted previously, Brinkman’s equation predicts an infinite reduced viscosity a t a volume fraction of 1.0. In fact, the viscosity of a suspension of rigid spheres should become infinite at a volume fraction corresponding to a close packed arrangement of the spheres. Thus a t high volume fractions, Brinkman’s equation should give low estimates of reduced viscosity. Eilers’ data for asphalt emulsions are also plotted in Figure 10. The suspensions studied by Eilers were composed of sets of spheres with wide diameter distributions. Since the gpc and microscopic investigations have indicated that the thickened oil samples are also composed of particles with a wide distribution of “diameters,” the agreement between the present set of data and that of Eilers adds credibility to the concept of aggregate formation. Relationship between Dispersion Viscosity and Soluble Oxidation Products. Using the definition of a and its value of 0.36 obtained from the reduced viscosity data, it can be calculated that with every gram of insolubles present in the thickened oil sample studied, 1.78 g of the oil phase must be associated to form the aggregates. Thus, for the thickened oil as it is taken from the IIIC engine test, which has an insolubles concentration of 19.2 wt %, it can be calculated that 34.2 wt % of oil is adsorbed in the aggregates. In an effort to determine if a specific fraction of the oil phase is associated with the micellar structures, the results of the adsorption chromatography experiments described previously were reexamined. The thickened oil was shown to consist of 44.5 w t % of unoxidized oil. An attempt was made to suspend a portion of the n-heptane insolubles phase in the white oil fraction. It was determined that, using the same experimental techniques described earlier, it was impossible to create a stable dispersion of the insolubles phase in the white oil. Only after
Figure 11. Apparent yield stresses as a function of aggregate volume fraction. portions of the oxidized oil fraction were added to the white oil fraction could significant quantities of the insolubles be suspended. In fact, 30 to 35 wt % of the oxidized oil fraction had to be added to the solution before it was possible to suspend all 19.2 wt % solids found in the oil removed from the IIIC engine. This would indicate that, if the concept of micelle or aggregate formation is correct, the oil fraction in the aggregates consists of essentially all of the soluble oxidation products present in the oil phase. Apparent Yield Stresses in Thickened Oils. The concept of aggregate formation has been used to explain the relationship between the high shear rate viscosities of thickened oil and the concentration of insolubles present in these suspensions. Additional information regarding the character of thickened oil can be obtained by examining the stress term in eq 13, T C K , corresponding to the energy required to break the physical bonds between the aggregates. Values of 7cR can be obtained for each suspension from the intercepts a t zero shear rate of the dotted lines in plots such as Figures 6 and 7. According to eq 10, the stress, T C K , should be proportional to the square of the aggregate volume fraction. By plotting the square root of T ~ us. @)% as shown in Figure 11, the analytical relationship, eq 10 is verified. The slope of each line in this graph, K , can be related to the force fields acting between the aggregates. (20)
Using both the photomicrograph, Figure 2, and the gpc results, Figure 3, the average diameter of the micellar structures is estimated to be 0.1 p . If it is assumed that these structures are covered with an adsorbed oil layer, then a,,, the minimum distance that can exist between two particles, will be approximately 60 A or twice the length of an average oil molecule. Using these crude estimates for d and a,, the force constant, A,, for the bond between two aggregates can be calculated. The values of A , obtained from eq 20 vary with temperature from 6.17 X 10-11 erg at 21.1”C to 9.43 X 1 0 - 1 3 erg a t 81.7”C and are plotted in Figure 12. It is apparent that A0 is a strong function of temperature-a fact which would indicate that the attractions between aggregates are the result of something other chan dispersion force interactions. Dispersion forces are due directly to the effects which a fluctuating electric dipole has on the induced dipoles of neighboring molecules. The forces which arise due to such interactions depend on the electrical properties of and the distance between the molecules involved but do not depend on temperature (Fowkes, 1965). Using the approximation due to Hamaker, eq 8, Michaels and Bolger have estimated A, for the clay-water Ind. Eng. Chem.. Prod. Res. Develop., Vol. 13,No. 4, 1974
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~
products. The calculated value,of the mass fraction of insolubles in the aggregates would indicate that the entire fraction of soluble oxidation products is required to form the aggregates. 4. The force constants estimated for the interactions between aggregates are larger than those attributable to London dispersion forces alone. In addition, the fact that the force constants are shown to be a significant function of temperature would also indicate that other force fields are important in predicting the interactions which occur between particles.
0
M
40
60
80
'C
Figure 12. Variation of force constants with temperature. system to be from 1O-IO to 10-11 erg. All of their data, however, were obtained a t 25°C and it was not determined whether the value of A, was a function of temperature. Fowkes (1971) has shown that values of the Hamaker constant can be calculated from the contribution made by dispersion forces to the surface or interfacial tension of a material. For the system, graphite in mineral oil, a value of 2 X 10-13 erg is suggested for A , . If this value is correct, then for the thickened oil sample, a similar system, it must be concluded that the greater values of A, calculated are the result of additional force fields acting between the particles in suspension. This possibility is reasonable in light of the high acid number of the insolubles phase. The acidity of the insoluble particles could allow either hydrogen bond or electrostatic interactions to be significant in an estimation of the force field present. Conclusions A sample of thickened oil obtained from a Sequence IIIC engine test is shown to consist of an oxidized solids phase (19.2 wt %) dispersed in an oxidized Newtonian oil. The largest particles in the sample are 5-8 p in diameter. The dispersed solids can be separated out of suspension with n-heptane, and subsequent analyses show them to be highly acidic. Using an adsorption chromatography column, the Newtonian oil phase is separated into an unoxidized oil fraction (44.5 wt 70)and an oxidized oil fraction (33.9 wt %) . The rheological properties of thickened oils are qualitatively predicted by the equations of Michaels and Bolger which assume the presence of structures in the fluid. At high shear rates, these structures are broken down until a limiting size is reached. These limiting structures or aggregates, as they are referred to in this work, are composed of both insolubles and a fraction of the soluble oxidation products present in the oil phase. Using this model to describe the thickened oil samples, the following conclusions can be made. 1. If Brinkman's correlation is used to express the reduced viscosities of the suspensions in terms of the volume fraction of aggregates, it is calculated that the mass fraction of insolubles in the aggregates is 0.36. 2. The mass fraction of insolubles in the aggregates is not a function of temperature. 3. Since the insolubles cannot be resuspended in a sample of unoxidized oil, the oil fraction which is part of the aggregates probably is composed of soluble oxidation 266
Ind. Eng. Chem., Prod. Res. Develop., Vol. 13,No. 4, 1974
Acknowledgment I would like to thank Mr. Richard H. Kabel for providing the thickened oil sample analyzed in this work and also for allowing me to use the data shown in Figure 1. I appreciate the effort provided by Mr. Edward L. White in obtaining the gpc curves shown and by Mr. Bernard E. Nagel and Mr. Robert E. Woodward in measuring the acid numbers reported. Mr. George A. Peters ably assisted in the adsorption chromatography separations. Nomenclature a, = minimum distance existing between particle aggregates A, = Hamaker constant in eq 9 d = limiting aggregate diameter H = London-Hamaker dispersion force between aggregates m, = mass of oil phase in a sample of thickened oil m, = mass of solids phase in a sample of thickened oil R = radius of cone in the cone and plate viscometer T = torque exerted on the cone of the cone and plate viscometer due to the drag of a fluid ua = volume of the aggregate phase in a sample of thickened oil ub = volume of the oil not associated with the aggregate phase in a sample of thickened oil V = total volume of a sample of thickened oil X = mass fraction of the n-heptane insolubles in the thickened oil
Greek Letters = mass fraction of the n-heptane insolubles in the aggregate phase /3 = coneangle r = shearrate 6 = mass of the oil phase associated with the aggregates in a sample of thickened oil papp = apparent viscosity of a suspension p o = viscosity of the oil phase pLr = reduced viscosity of a suspension, defined by eq 1 p, = true viscosity of a suspension P A = aggregate phase density p , = oil phase density p , = solids phase density T = shear stress T C K = stress associated with the breakage of bonds between aggregates in the fluid T N = stress describing the reversible deformation of the continuous structures in the suspension T~ = stress associated with the viscous drag of a fluid suspension T~ = apparent yield stress of a suspension = aggregate volume fraction in the suspension 4f = floc volume fraction in the clay suspensions of Michaels and Bolger 4, = insolubles volume fraction in the suspension R = rotational speed of the cone and plate viscometer CY
Literature Cited ASTM Sequence Test IIIC. Amer. Soc Test. Mater. Special Technical Publication 3 15F, 53 (1973). Bardy. D. C..Asseff, P. A , , S A € Trans., 79 ( 3 ) . 1908 (1970).
Bingham. E. C., Green, H., Amer. SOC. Test. Mater. Proc.. 19 ( I I ) , 640
(1919). Bowden, J. N., Dimitroff, E . , Amer. Chem. SOC., Div. Petrol. Chem., Prepr., 7 (4).8-45(1962). Brinkman. H. C., J. Chem. Phys.. 20, 571 (1952). Cecil, R., J. lnst. Petrof., 59 (569), 201 (1973). Eilers, H.. KolloidZ.. 97, 313 (1941). Einstein, A., Ann. Phys. (Leipzig), 34, 591 (1911). Fowkes, F. M.. "The Chemistry and Physics of Interfaces. 1," S. Ross, Ed., pp 1-12.American Chemical Society, Washington, D. C., 1965. Fowkes. F. M., "The Chemistry and Physics of Interfaces. 2,"S. Ross, Ed., pp 153-168, American Chemical Society, Washington, D. C.,
Kabel, R. H., SA€ Trans. 79 ( 3 ) , 1688 (1970). Kuhn, R. R., Amer. Chem. SOC.,Div. Petrol. Chem., Prepr., 694 (1973), Mack, C., J. Phys. Chem., 36, 2901 (1932). Michaels. A. S.,Bolger, J. C., lnd. Eng. Chem., Fundam., 1, 24 (1962a) Michaels, A. S., Bolger. J. C., lnd. Eng. Chem.. Fundam., 1, 153
(1962b). Michaels, A. S.,Bolger, J. C., lnd. Eng. Chem.. Fundam.. 3, 14 (1964). Reerink. H., lnd. €ng. Chem., Prod. Res. Develop., 12, 82 (1973). Rutgers, Ir. R., Rheol. Acta, 2 (4),305 (1962a). Rutgers. l r . R., Rheol. Acta, 2 (3), 202 (1962b). Thomas, D. G . , J. Colloid Sci., 20,267 (1965).
Receiued for reuieu: M a y 10, 1974 Accepted August 30, 1974
1971. Hamaker, A. C.. Physica. 4, 1058 (1937).
Preparation and Characterization of 12-Molybdophosphoric and 12-Molybdosilicic Acids and Their Metal Salts George A. Tsigdinos Research Laboratory. Climax Molybdenum Company of Michigan, A n AMAX Subsidiary, Ann Arbor, Michigan 48105
A method for preparing sodium 12-molybdosilicate a n d t h e free 12-molybdosilicic acid is described a s
well as an improved method for preparing 12-molybdophosphoric acid. Methods for preparing salts of t h e two heteropoly acids with t h e cations manganese, cobalt, nickel, copper, lanthanum, and silver are also described. T h e acids and salts t h u s prepared were examined for their thermal behavior, solubility, and hydrolytic stability in aqueous a n d mixed solvents.
Considerable research has been devoted to the use of heteropoly compounds in catalysis (Tsigdinos, 1969). In particular, 12-molybdophosphoric and 12-molybdosilicic acids and several of their metal salts are shown to partake in such diverse catalytic processes as hydrodesulfurization (McKinley, 1957), epoxidation of olefins (Sheng and Zajacek, 1968), alkylation (Shenderova, et al., 1967; Sebulsky and Henke, 1971), preparation of saturated carbonyl compounds (British Patent, 1965), and in the direct oxidation of benzene to phenol (British Patent, 1969). Heteropoly compounds have also been found to act as flame retardants for wood (Truax, 1933, 1935; Amaro and Lipska, 1973). Of particular importance to the catalytic behavior of the compounds in question is the preparation, solubility, and solvolytic behavior in both aqueous and organic media, and the thermal stability and oxidation-reduction behavior. Although the preparation of some of these compounds has been reported in the older literature, the products obtained were often not fully characterized, nor was the pure compound obtained in all cases. A critical evaluation of preparative procedures of heteropoly compounds has appeared elsewhere (Tsigdinos, 1974). Therefore, the present work constitutes a detailed investigation of new and improved methods for preparing, in pure form, 12-molybdophosphoric and 12-molybdosilicic acids and their salts with the cations M n z f , Co2+, Nizf, C$+, La3+, and Naf . In addition, these compounds were characterized by means of chemical analysis, thermal stability studies, solubility, and solvolytic behavior in aqueous and organic media. The oxidation-reduction behavior of the 12-heteropoly acids has been reported elsewhere (Tsigdinos and Hallada, 1973). It is anticipated that this knowledge will be useful in the application of these compounds to catalytic processes.
Experimental Section Materials. The molybdenum trioxide used was Climax Pure grade. The heteropoly acids employed were materials prepared according to procedures developed in this work. All other reagents used were Baker Analyzed grade. Preparation of Compounds. (a) 12-Molybdophosphoric Acid. One mole (144 g) of Moo3 was placed in a 2-1. flask equipped with stirring and reflux condenser, and 1400 ml of water was added. To this was then added 9.57 g 85% H 3 P 0 4 (1h~mole), and the solution was brought to boiling (30 min) and boiled for 3 hr with vigorous stirring. The green color that developed during this period was removed by the addition of a few drops of bromine water. At the end of the heating period, the yellow solution was cooled and the white insolubles remaining were filtered through Whatman No. 42 paper. The mother liquor was then concentrated to a volume of 100 ml by evaporative boiling for 3-4 hr. Upon cooling, the concentrate developed yellow crystals which were filtered and air dried (approximately 130 g yield). This crude product was purified by dissolving in 100 ml of water, filtering the small amount of fine insolubles, if present, and allowing the clear yellow solution to crystallize in the air. The large yellow crystals that formed were filtered and air dried. The yield was 106 g. The crystalline acid effloresces slowly a t room temperature; thus the amount of water of crystallization varies somewhat from sample to sample. The analysis of the product, H3[PMo12040].14H20 is given in Table I. It was ascertained in separate experiments that a volume of nearly 6 1. of water was necessary to bring all molybdenum trioxide employed into solution by the phosphoric acid during the boiling step of the preparation. (b) 12-Molybdosilicic Acid. For this preparation, 42.63 g of NazSi03-9H20 (0.150 mol), 36.3 g (0.150 mol) of NazMo04.2H20, and 237.6 g (1.65 mol) of Moo3 were placed in a 2-1. flask equipped with stirrer and condenser. TO I n d . Eng. Chem., Prod. Res. Develop.. Vol. 13, No. 4, 1974
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