Estimation of properties of ternary mixtures of solids using the mixing rule

Powder Technology 134 (2003) 16 – 23 www.elsevier.com/locate/powtec

Estimation of properties of ternary mixtures of solids using the mixing rule M.A. Silva *, M.N.N. Miranda Thermo Fluid Dynamics Department, FEQ, Chemical Engineering School, State University of Campinas (Unicamp), PO Box 6066, 13083-970 Campinas SP, Brazil Received 11 December 2002; accepted 31 March 2003

Abstract In this work, a model ternary system of zeolite NaY, kaolin (both from AldrichR) and alumina (from VetecR), was studied. True and bulk densities, powder and particle porosities, specific surface area, and sorption isotherms were determined for single solids and mixtures. Physical properties and sorption isotherms of mixtures were calculated from the mixing rule using mass and volume fractions of each solid in the mixture. Calculated and experimental values presented very good agreement for true density, specific surface area, and sorption isotherms. For bulk density and porosity, the mixing rule does not work well, since the mixtures do not follow the mass proportion due to the particle – particle interactions. Zeolite NaY presents isotherm type I, while kaolin and alumina present isotherm type II, all mixtures present the curves between those of the single solids. The results show that it is possible to use the mixing rule to evaluate some physical properties as well as the sorption isotherms of binary and ternary mixtures of solids. D 2003 Elsevier B.V. All rights reserved. Keywords: Alumina; Kaolin; Physical properties; Sorption isotherm; Zeolite NaY

1. Introduction New materials for new products and applications are extremely necessary in electronics, biomedical, food, and other industrial sectors. As a consequence, new trends can be observed in powder processing [1]. The use of mixtures of different solids can be found in many fields of industrial practice. Knowledge of the physical properties of the mixture of solids from the properties of the single solids can offer some advantages and improvements for industrial processes. Some studies have been developed in order to get a better understanding of the water transport in mixture of solids [2– 5]. In the study of water transport in porous media, it is very important to separate the effects due to the particle structure from those due to the composition of the mixture [4]. The physical characterization of the single solids and their mixtures is therefore fundamental. In the production of fluid catalytic cracking catalyst (FCC catalyst), an important step is the spray drying of the catalyst mixture suspension. van der Sanden et al. [3] * Corresponding author. Tel.: +55-19-3788-3923; fax: +55-19-37883922. E-mail address: [email protected] (M.A. Silva). 0032-5910/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0032-5910(03)00131-1

used a mixture of zeolite Y, clay, alumina, and silica as the catalyst formulation. Their results were not good enough to predict the properties of the FCC catalyst, and they concluded that further investigation of the structural properties was needed. Silva and Souza [6] achieved very good results using the mixing rule for binary mixtures of zeolite NaY and kaolin. Zeolite NaY is a crystalline hydrated aluminosilicate of sodium. The dehydrated skeleton has a regular structure of cages, which is interconnected by four windows in each cage. The window aperture is formed by the ˚ [7]. 12-member oxygen rings with a free diameter of 7.4 A Kaolin is also a crystalline hydrated aluminosilicate; it does not have alkali earth elements or regular structure of cages [8]. The good results obtained for binary mixtures stimulated the research continuation using the mixing rule to get the properties of ternary mixtures. Thus, a third single solid was added to the study: alumina, which was chosen in order to have another solid component of FCC catalyst. This work aims to determine some physical properties of kaolin, zeolite NaY, and alumina, as well as of mixtures of these three solids. The objective of the work is also to present equations that relate the properties of the mixtures with the properties of the pure solids through the mass and volume

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Table 1 Experimental planning

Table 3 Experimental true densities for single solids and their mixtures

Sample

Mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Solids (dried mass fraction) Kaolin

Zeolite NaY

Alumina

K

Z

A

1 0 0 0.2 0.4 0.6 0.8 0 0 0 0 0.8 0.6 0.4 0.2 0.4 0.4 0.2 0.33

0 1 0 0 0 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.4 0.33

0 0 1 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 0 0 0 0 0.4 0.2 0.4 0.33

1 0 0 0.2 0.4 0.6 0.8 0 0 0 0 0.8 0.6 0.4 0.2 0.4 0.4 0.2 0.33

0 1 0 0 0 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.4 0.33

0 0 1 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 0 0 0 0 0.4 0.2 0.4 0.33

fractions of the samples, that is, the mixing rule. The detailed study can be found in Ref. [9].

True density (g/cm3)

Standard deviation

2.629 2.102 3.951 3.584 3.296 3.106 2.817 3.406 3.109 2.767 2.465 2.504 2.434 2.335 2.187 2.881 2.558 2.737 2.732

0.008 0.004 0.003 0.005 0.003 0.002 0.008 0.002 0.010 0.004 0.015 0.003 0.003 0.004 0.008 0.016 0.018 0.010 0.017

LEO 440i) was used, with secondary electron beam and magnification of 10,000 times. 2.3. Particle size distribution

2. Methodology 2.1. Sample preparation The solids used in this work were alumina (VetecR), kaolin, and zeolite NaY (both from AldrichR). Firstly, homogeneous samples of each solid were obtained using the Rotary Sample Divider Laborett 27 (FritschR). All samples were dried in an oven for 24 h at 110 jC. Then, the mixtures were made according to the proportions shown in Table 1. The samples were analysed for the following experimental determinations: particle size distribution, true density, bulk density, porosity, sorption isotherms, and surface area. 2.2. Scanning electron microscopy images Scanning electron microscopy (SEM) was used for evaluation of the particle size and shape, and based on this result, it was possible to choose the correct lens to be used in the determination of particle size distribution. A high vacuum scanning electron microscope (LeicaR

Table 2 Particle diameters for the single solids Solid

d(v,0.1) (Am)

dmean (Am)

d(v,0.9) (Am)

Kaolin Zeolite NaY Alumina

0.43 1.28 18.06

5.78 5.94 95.07

8.78 9.80 167.20

The particle size distribution was determined using the Mastersizer S (MalvernR), which operates on the principle of Mie light diffraction with a laser-type transmitter of 2 mW helium –neon. This determination was done only for the single solids using water as liquid dispersant and 300RF lens (size range: 0.05 –880 Am) for kaolin and zeolite NaY and 300 mm lens (size range: 0.5 – 880 Am) for alumina. Table 4 Experimental bulk densities for single solids and their mixtures Mass fraction K

Z

A

Bulk density (g/cm3)

Standard deviation

1 0 0 0.2 0.4 0.6 0.8 0 0 0 0 0.8 0.6 0.4 0.2 0.4 0.4 0.2 0.33

0 1 0 0 0 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.4 0.33

0 0 1 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 0 0 0 0 0.4 0.2 0.4 0.33

0.283 0.306 0.822 0.702 0.510 0.390 0.299 0.763 0.558 0.416 0.345 0.282 0.297 0.260 0.298 0.417 0.341 0.422 0.391

0.022 0.017 0.011 0.017 0.015 0.009 0.012 0.010 0.011 0.005 0.013 0.008 0.007 0.006 0.011 0.013 0.007 0.013 0.015

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Table 5 Specific surface area for single solids and their mixtures Mass fraction K

Z

A

1 0 0 0.2 0.4 0.6 0.8 0 0 0 0 0.8 0.6 0.4 0.2 0.4 0.4 0.2 0.33

0 1 0 0 0 0 0 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.4 0.33

0 0 1 0.8 0.6 0.4 0.2 0.8 0.6 0.4 0.2 0 0 0 0 0.4 0.2 0.4 0.33

Surface area (m2/g) 13.86 511.13 0.46 3.10 6.67 8.25 11.68 100.13 191.91 279.32 394.12 109.25 187.35 301.01 393.56 99.15 198.72 181.62 170.64

2.4. Physical properties The Helium pycnometer (Accupyc 1330, MicromeriticsR) had been used to determine the true density, using the correction for high surface area powders [10]. The bulk density was determined for the samples in powder using Eq. (1). qbulk ¼

mass of powder volume of powder under freely poured conditions ð1Þ

The experimental data of nitrogen adsorption isotherms were obtained by using the surface area analyser Gemini III 2375 (MicromeriticsR); from these data, the equipment provided the total pore volume (Vpore in cm3/g), the surface area using the BET method, and the micropore volume (cm3/g) by the t-method. All these methods are well described in Lowell and Shields [11]. Particle porosity and powder porosity were determined using Eqs. (2) and (3), respectively, based on Keey [12]. volume of open pores total volume of particle Vpore ¼ 1=qtrue þ Vpore

Fig. 1. SEM images of alumina (A), zeolite NaY (B), and kaolin (C).

The proposed equations to relate the properties of single solids and their mixtures are based on the mixing rule. Eq. (4) is based on the mass fractions of the samples

particle porosity w ¼

volume of voids total volume of powder
 1 Vpowder  þ Vpore mpowder qtrue ¼ Vpowder

ð2Þ

powder porosity e ¼

ð3Þ

Fig. 2. Particle size distribution for the single solids: alumina, zeolite NaY, and kaolin.

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Fig. 3. True density of kaolin, zeolite NaY, and alumina and their binary mixtures as a function of mass fraction.

Fig. 4. Experimental and calculated true densities for binary and ternary mixtures of kaolin, zeolite NaY, and alumina using Eq. (4) (mass fraction) and Eq. (5) (volume fraction).

Fig. 5. Experimental and calculated bulk densities for binary and ternary mixtures of kaolin, zeolite NaY, and alumina using Eq. (4) (mass fraction) and Eq. (5) (volume fraction).

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Fig. 6. Powder and particle porosities of kaolin, zeolite NaY, and alumina and their binary mixtures as a function of mass fraction.

and Eq. (5) on the volume fractions, where / is any property but equilibrium moisture content, for which is used Eq. (7). /mixture ¼

n X

xj /j

ð4Þ

yj /j

ð5Þ

j¼1

/mixture ¼

n X j¼1

In Eq. (5), volume fraction can be expressed as a function of mass fraction and true density as in Eq. (6). xi qtrue;i ð6Þ yi ¼ X n xj j¼1

qtrue;j

Xmixture ðaw Þ ¼

n X

xj Xj ðaw Þ

ð7Þ

j¼1

The error between experimental and calculated values was obtained using Eq. (8). Error ¼

/calc  /exp  100 /exp

ð8Þ

3. Results and discussion Fig. 1 shows that zeolite NaY and kaolin present similar size while alumina is much bigger. The former can be considered as granular particles and the latter as flaky particles as defined in Ref. [12]. A comparison for particle size can be done observing Table 2, verifying that alumina is approximately 16 times bigger than the other two. Fig. 2 shows the complete particle size distributions for the single solids. The experimental data of true density are presented in Table 3. As seen in Fig. 3, the experimental results show a linear relationship between the true density of the binary mixtures and those of the single solids, and the calculated true density using Eq. (4) presented a very good agreement with the experimental data, with a maximum error of 5%. Using Eq. (5) (results not showed here) the maximum error was 6.6%. It is important to remark that the maximum error is much smaller for binary mixtures containing zeolite NaY and kaolin, less than 1% for Eq. (4) and 2.1% for Eq. (5), which can be explained since these particles have similar shape, size, and not so different true densities. The results for all mixtures can be observed in Fig. 4. For ternary mixtures, the maximum error of 1% was obtained using Eq.

Fig. 7. Nitrogen adsorption isotherms of alumina (A), zeolite NaY (B), and kaolin (C).

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Fig. 8. Experimental and calculated nitrogen adsorption isotherms for binary mixtures of kaolin and zeolite NaY.

Fig. 10. Experimental and calculated nitrogen adsorption isotherms for binary mixtures of kaolin and alumina.

(5) against a maximum error of 7.7% using Eq. (4). That is, when particles of very different shapes, sizes, and true densities are mixed, the mixing rule using volume fraction presents excellent results because the volume difference among the particles is taken into account. In the case of bulk density (Fig. 5), Eq. (5) presented better agreement with the experimental data than Eq. (4) because the mixtures do not follow the mass proportion due to the different particle size distribution. As bulk density was obtained under freely poured conditions, the weight, size, and shape of the particles influence the way they pack. Coarser flaky material packing such as alumina presents bigger interparticle voids than fine granular powders such as kaolin and zeolite NaY. These small particles can fill the interparticle voids of alumina, and as a consequence of that and also because alumina particles are heavier than the other two, binary mixtures containing alumina present a bulk density as big as twice the bulk density of binary mixtures of kaolin and zeolite NaY (see Table 4). Moreover, the values obtained for bulk density must be considered only as

an indicative guide because the influence of the wall container is different for the particles of each solid studied due to the large size difference between them. Keey [12] citing Scott (1960) affirmed that ‘‘the influence of a wall persists for a distance of 50– 100 times the size of the granules.’’ The powder porosities of pure kaolin, zeolite NaY, and alumina are quite similar, 0.888, 0.771, and 0.792, respectively. Despite the similarities between kaolin and zeolite NaY related to true density and particle size distribution, it seems that they have different particle – particle interactions. Probably, aggregates or agglomerates are formed between kaolin particles providing bigger voids, and the segregation is more intensive in zeolite NaY powder, mainly because kaolin has 20% of particles with diameter less than 1 Am against 6.5% for zeolite NaY. For alumina, Yu et al. [13] found that fine powder presented higher porosity than coarse powder and the porosity of binary mixtures of both decreased with the increase of the volume fraction of the large component. Similar results were found in this work for

Fig. 9. Experimental and calculated nitrogen adsorption isotherms for binary mixtures of alumina and zeolite NaY.

Fig. 11. Experimental and calculated nitrogen adsorbed volume for binary and ternary mixtures of kaolin, zeolite NaY, and alumina using Eq. (4) (mass fraction).

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rule to estimate the properties of mixtures leads to very good results. It is possible to use an analogy with the behaviour of gases; that is, for ideal gases (the molecule – molecule interactions can be considered negligible), it is possible to determine the properties of the mixtures using the mixing rule. Very good results using the mixing rule (confidence of 90% at least) were obtained for the following properties of mixtures of kaolin, zeolite NaY, and alumina (binary and ternary ones): true density, sorption isotherms, and specific surface area. On the other hand, the mixing rule is not adequate to obtain properties where the particle – particle interactions cannot be negligible, such as bulk density and porosity.

Fig. 12. Experimental and calculated specific surface area for binary and ternary mixtures of kaolin, zeolite NaY, and alumina using Eq. (4) (mass fraction).

binary mixtures of alumina and kaolin as shown in Fig. 6. On the other hand, the particle porosities of these solids are completely different, 0.038, 0.365, and 0.002, for kaolin, zeolite NaY, and alumina, respectively. As shown in Fig. 6, the particle porosity of the mixture is completely controlled by the solid with the higher particle porosity. The effect of the presence in the mixture of zeolite NaY particles with their micropores is clearly evidenced in Fig. 6. Nitrogen adsorption isotherms of the single solids can be seen in Fig. 7. Zeolite NaY presents isotherm type I, characteristic of microporous particles, while kaolin and alumina present isotherms of type II. The same kinds of isotherms were obtained by Miranda [9] for water desorption. Of course, zeolite NaY presented the highest hygroscopicity, and kaolin was 10 times more hygroscopic than alumina. It can be observed in Figs. 8– 10 that the binary mixtures presented isotherms between those from the single solids according to the mass proportion in the mixture. Consequently, the proposed equation (Eq. (7)) showed a good agreement with the experimental data, not only for binary mixtures but also for the ternary ones as shown in Fig. 11. Nitrogen adsorption isotherms were also used to calculate specific surface area from the BET equation (see Table 5). A linear relationship was found between the specific surface area of the single solids and their mixtures. The calculated values using Eq. (4) presented a very good agreement with the experimental data as shown in Fig. 12.

4. Conclusions For mixture properties where the particle – particle interactions do not exist or are negligible, the use of the mixing

List of symbols aw water activity d particle diameter (Am) Vpore pore volume (cm3 g 1) Vpowder total volume of powder (cm3) x mass fraction X moisture content, dry basis y volume fraction Greek letters e powder porosity / generic property qbulk bulk density (g cm 3) qtrue true density (g cm 3) w particle porosity

Acknowledgements The authors wish to acknowledge Rhodia Brasil for the Master’s Degree scholarship for M.N.N. Miranda.

References [1] P.G.J. van der Wel, Trends in powder technology, Powder Handling and Processing 10 (1998) 139 – 142. [2] B. Kroes, The influence of material properties on drying kinetics, PhD thesis, Eindhoven University of Technology, Eindhoven, 1999. [3] S.C.T. van der Sanden, W.J. Coumans, P.J.A.M. Kerkhof, Desorption isotherms and diffusion coefficients of catalytic materials, in: C.B. Akritidis, D. Marinos-Kouris, G.D. Saravakos (Eds.), Drying’98, vol. A, Ziti Editions, Thessaloniki, 1998, pp. 762 – 769. [4] M.A. Silva, P.J.A.M. Kerkhof, W.J. Coumans, Estimation of effective diffusivity in drying of heterogeneous porous media, Industrial and Engineering Chemistry Research 39 (05) (2000) 1443 – 1452. [5] F.V. Souza, Structural properties of binary mixtures of solids, MSc Dissertation, State University of Campinas, 2001, in Portuguese. [6] M.A. Silva, F.V. Souza, Drying behaviour of binary mixtures of solids. Accepted to be published in Drying Technology (Marcel Dekker, New York) in March 2003. [7] R.T. Yang, Gas Separation by Adsorption Processes, Imperial College Press, London, 1997, First published by Butterworths, 1987.

M.A. Silva, M.N.N. Miranda / Powder Technology 134 (2003) 16–23 [8] Huber, Kaolin Clays and Their Industrial Users, Huber, New York, 1955. [9] M.N.N. Miranda, Structural properties of ternary mixtures of solids, MSc Dissertation, State University of Campinas, 2002, in Portuguese. [10] P.A. Webb, C. Orr, Analytical Methods in Fine Particle Technology, Micromeritics Instrument, Norcross, 1997.

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[11] S. Lowell, J.E. Shields, Powder Surface Area and Porosity, 3rd ed., Chapman & Hall, New York, 1991. [12] R.B. Keey, Drying of Loose and Particulate Materials, Hemisphere Publishing, New York, 1992. [13] A.B. Yu, J. Bridgwater, A. Burbidge, On the modelling of the packing of fine particles, Powder Technology 92 (1997) 185 – 194.