Model Based on Electrostatic Repulsion and Hydrogen Bond Forces

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A Model Based on Electrostatic Repulsion and Hydrogen Bond Forces to Estimate the Size of Nanoparticle Agglomerates in Fluidization Maryam Tahmasebpoor, Reza Ghasemi Seif Abadi, Yaghub Rahimvandi Noupoor, and Parastoo Badamchizadeh Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.6b02792 • Publication Date (Web): 28 Nov 2016 Downloaded from http://pubs.acs.org on November 30, 2016

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Industrial & Engineering Chemistry Research

A Model Based on Electrostatic Repulsion and Hydrogen Bond Forces to Estimate the Size of Nanoparticle Agglomerates in Fluidization

M. Tahmasebpoor*, R. Ghasemi Seif Abadi, Y. Rahimvandi Noupoor, P. Badamchizadeh Department of Chemical & Petroleum Engineering; University of Tabriz, Tabriz, Iran, PO Box 51666-16471

Abstract A comprehensive model was derived based on the balance between drag, collision and gravity as separation and van der Waals and hydrogen bond as adhesion forces to estimate the equilibrium size of agglomerates formed during the fluidization of nanoparticles. Due to the approximately less than 9% of the total amount of forces, drag and collision forces were not considered in the final model. Also, the influence of using vapor of different alcohols on the fluidization behavior of hydrophilic silica and alumina nanoparticles was studied by experiments. To justify the improving effect of using alcohols, the electrostatic repulsion force was added to the model for the first time. Methanol and 2-propanol were the most effective alcohols on fluidization improvement and consequently the smallest size

*

Corresponding author, Maryam Tahmasebpoor; Tel: +98 41-33392936; fax: +98 41-33340191; E-mail: [email protected]

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of agglomerates was estimated using physical properties of these two alcohols. The Richardson-Zaki analysis indicated that the fluidization degree of cohesive hydrophilic nanoparticles can be greatly improved by adding polar alcohols to the system. The agglomerate sizes predicted based on R-Z showed a good agreement with the calculated ones by model in the presence of alcohols.

Keywords: Fluidization, Force Balance Model, Alcohol Vapor, Hydrogen Bond, Electrostatic Repulsion


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1. Introduction The formation of agglomerates is a common phenomenon in ultrafine particles because of the relatively large interparticle interactions; such as the van der Walls, electrostatic and capillary forces, between their primary particles. Thus, gas fluidization of nanoparticles essentially refers to the fluidization of nanoparticle agglomerates1-4. The agglomerate properties (e.g. stability, size and size distribution) determine the resulting fluidization behaviour of nanoparticles5-6. Therefore, a good understanding of the intrinsic properties of the nanoparticles and their agglomerates is needed for a fundamental understanding of their fluidization behaviour. Yao et al.1 proposed a multistage formation mechanism for the SiO2 nanoparticle agglomerates during fluidization. According to these authors, in the first stage, the primary silica particles adhere to each other in chains, which in turn join together to form a tridimensional netlike structure. In the second stage, the tridimensional netlike structures coalesce into larger simple agglomerates with the size ranging from about 1 to 100 µm. Finally, the simple agglomerates congregate together to produce complex agglomerates with the size ranging from about 200 to 400 µm. Based on multistage formation mechanism, different researchers have suggested different models to quantify the interparticle interactions in a fluidized bed of fine particles and hence to calculate the equilibrium size of agglomerates during their 3 ACS Paragon Plus Environment


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fluidization. These models are mainly based on energy balance7-8 or force balance914

. Zhou and Li9-10 estimated the sizes of agglomerates based on the assumption that

the sum of buoyant weight and the cohesive force of the agglomerates is balanced by the sum of drag force and the collision force between the agglomerates. The model proposed by Iwadate and Horio11 assumed that the bed expansion force caused by bubbles was equal to the cohesive rupture force between two contiguous agglomerates. Tamadondar et al.14 estimated the sizes of agglomerates based on the balance between drag, collision, and gravity forces as separation forces, and the van der Waals force as an adhesion force. It should be noted that all these mentioned semi-empirical models require input of several experimental observations, which are unknown a priori14-15. On the other hand, influence of electrostatic interactions has been neglected in all previous models, while generation of electrostatic charge is a significant problem when fluidizing dry powders of nanoparticles. Great levels of electrostatic charge may be generated through triboelectrification, i. e. charge separation associated with the rubbing together of dissimilar/similar material surfaces16. It was shown that addition of alcohol molecules to the fluidization gas advantageously reduces the build-up of electrostatic charges between nanoparticles and improves their fluidization behaviour16-17. Therefore, it is obvious that paying no attention to decreasing or increasing influence of electrostatic force in the developed models to predict the 4 ACS Paragon Plus Environment

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sizes of nanoparticle agglomerates may lead to error between the experimental and the models results. Tahmasebpoor et al.17 showed that hydroxyl groups present on the surface of dry and hydrophilic nanoparticles significantly increase the interparticle forces due to hydrogen bridge formation. In the other words, the attraction between dry and hydrophilic nanoparticles is stronger than the attraction between dry and hydrophobic nanoparticles because of the formation of hydrogen bridges between the hydroxyl groups on the surface of the hydrophilic particles. As a result, hydrophilic nanoparticles form larger agglomerates than hydrophobic ones. They mentioned that the change in surface characteristics of nanoparticles (using isopropanol) can strongly affect the interaction between the particles and consequently influence their fluidization behaviour. De Martin and van Ommen18 were the first to include an additional attractive force due to the formation of hydrogen bridges between the surfaces of dry and hydrophilic nanoparticles in the model based on force balance. However, the main weakness of their proposed model is that hydrogen bonding force has been assumed as the same for all dry and hydrophilic nanoparticles18. The main objective of this paper is to provide an improved force balance model to estimate agglomerate size of nanoparticles during fluidization by considering the hydrogen bond between agglomerates of hydrophilic nanoparticles. In addition, the 5 ACS Paragon Plus Environment


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effect of using the vapor of different alcohols in dissipating electrostatic charges between surfaces of agglomerates is discussed for the first time by model and also experimental data. The proposed model only needs the particle characteristics like size and density, and also physical properties of alcohols. It means there is no need to input any experimental parameters to predict the agglomerates size in this model.

2. Theory In spite of the small size and relatively large interparticle forces, nanoparticles can be fluidized due to the formation of extremely porous and light agglomerates. These agglomerates are in a dynamic balance of continuous adhesion and separation forces during fluidization and the equilibrium size of the agglomerates is determined by a balance between these two kinds of forces. Typical forces considered in fluidized beds are gravity, drag and collision as separating forces and van der Waals as adhesion force11. The application of any assistance method reduces the equilibrium agglomerate size and needs to be included in model by an additional force18. The idea behind the force balance between adhesion and separation forces is very simple. In fact, the internal van der Waals force keeps particles together in the agglomerate while external forces (drag, gravity and collision) cause the agglomerate to break up from outside. If external forces are 6 ACS Paragon Plus Environment

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greater than the internal, they can break the agglomerate into smaller pieces and if internal forces are greater than the external, the agglomerate can still absorb more particles and grow in size. Therefore, the equilibrium agglomerate size is the one for which external and internal forces are in dynamic equilibrium8, 14. The force balance we used here is as: van der Waals force (FvdW) + Hydrogen bond force (FOH) – Electrostatic repulsion force (Fer) = Drag force (FD) + Collision force (FC) + Gravitational force (Fg). FvdW + FOH - Fer = FD + FC + Fg

(1)

The following assumptions are made to simplify the proposed model: a) agglomerates are assumed to be identical spheres with an equivalent diameter d**; b) the wall effect is not considered; c) liquid bridging forces are neglected. Below, detailed descriptions of mentioned forces are presented.

2.1 van der Walls force FvdW The existence of an attractive force between neutral molecules; for the first time, was proposed by van der Waals. In the case of neutral molecules, temporary fluctuating of dipoles of atoms induces a transitory polarity to the molecules and this polarity leads molecules to interact with each other, even if they are nonpolar. These interactions result in an adhesion force between macroscopic particles which is called the van der Waals force. Two general approaches are used to calculate van 7 ACS Paragon Plus Environment


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der Waals forces. The first one which is known as Hamaker’s microscopic approach is based on a molecular model, and the second one known as Lifshitz’s macroscopic approach is based on a molar model. In the microscopic approach, the van der Waals interparticle force between two neighboring particles is obtained by integrating the intermolecular forces between all pairs of molecules around the point where the particles are in contact. According to Hamaker’s theory, the van der Waals interaction between two micron-sized agglomerates is given by8,18: =

(2)

Where is the minimum inter-particle distance of closest approach between two molecules19 (~0.4nm), is the Hamaker coefficient which is directly related to the molecular properties and dasp is asperity of the micron-sized particles corresponding to micron-sized agglomerates18 (~ 0.1–0.2 µm). The Hamaker coefficient for the interaction of two identical materials 1 over an intervening medium 2 can be calculated by relation below20:

=

" !

+

$%& *+ + , '(√ *+ !+ ,-⁄

(3)

where ɛ, n, KB, h, νe and T are permittivity, refractive index, the Boltzmann constant, Planck’s constant, main absorption frequency and temperature respectively.


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2.2 Collision force FC It is thought that agglomerates in a fluidized bed of nanoparticles shed their outer edges by the frequent collisions among agglomerates because of the continuous gas flow through the bed. This fluidization phenomenon which leads to size reduction of agglomerates has been considered as separating collision force in many models presented in the literature. On the basis of the theory of elasticity, Zhou and Li9-10 proposed an equation to calculate the collision force between two vertically aligned agglomerates coming into collision with a relative velocity V correlated as follows21: / = 01.5345,+ 78 9:8

(4)

Where 345,+ is the dimensionless average particle pressure for non-sticky systems, ɛb is bed voidage and 78 is the bubble diameter in the fluidized bed. A variety of correlations has been presented in the literature to calculate Db and we used the one presented by Valverde and Castellanos22 as below: ;
?.@

B A

C

∗

D E

?.(

FG ?.@

(5)

Where µ is the viscosity of fluid (1.77 × 10 K 3L. M for N2 at room conditions) and Bo is Bond number22-23 (~1). Multistage agglomerates which were mentioned in introduction identify the parameters OP , d* and d** in Eq. (5). Primary nanoparticles form multistage agglomerates during fluidization by three steps1. First, primary 9 ACS Paragon Plus Environment


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nanoparticles of size OP and density ρp agglomerate into 3-D netlike structures (sub-agglomerates of size d). Second, the sub-agglomerates coalesce into simple agglomerates of size d*, and finally these simple agglomerates join into complex agglomerates of size d**and density ρ**. Eq. (5) is used to calculate bubble diameter of both agglomerate bubbling fluidization (ABF) and agglomerate particulate fluidization (APF) regimes. Finally, the collision force of two identical spherical agglomerates can be expressed by9-10: ST U (A∗∗ )-

Q = 0.166(O ∗∗ )

V

"

'⁄ K

(6)

Where K is a function of Poisson’s ratio and Young’s modulus of particles10.

2.3 Drag force FD In a uniform bed of particles having bed voidage of :8 , the drag force on a single particle is :8 .> times that on a single isolated particle and can be generally given by24: ; = W;

A Y S

X

:8 .>

(7)

Where dp, ρf, U and CD are particle diameter, fluid density (1 kg m−3 for N2 at room conditions), superficial gas velocity and drag coefficient respectively. The type of fluid flow where inertial forces are small compared with viscous forces is named 10 ACS Paragon Plus Environment

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Stokes flow or creeping flow. This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small; all results in the low Reynolds number, i.e. Z[ ≪ 1. For creeping flow regime the drag coefficient can be expressed by using Stokes’ law, W; = 24⁄Z[P which the particle Reynolds number, Rep24 is defined as Z[P = AX Y

C

. However, typical values of the Reynolds number around the agglomerate in

a fluidized bed of nanoparticles are small which corresponds to laminar conditions2,15. Therefore, substituting Stokes’ law into Eq. (7) and correcting it for agglomerates in a fluidized bed, we obtain drag force as25: ; = 3_O ∗∗ `a:8 .>

(8)

2.4 Gravitational force Fg The difference between the gravitational force and the buoyancy force can be considered as the effective gravitational force on agglomerate and can be presented as8: S

B = *b∗∗ − bd ,(O ∗∗ ) 9 (

(9)



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2.5 Hydrogen bond force FOH The surface of hydrophilic particles contains hydroxyl groups which make these particles able to form hydrogen bridge linkages with other hydrophilic particles and induce enhanced interaction between the particles. Hydrophobic particles are produced in a process called hydrophobization in which hydroxyl groups of the hydrophilic particles are replaced by organic groups. This process gives the hydrophobic particles noticeably better dispersibility than the hydrophilic ones by substituting strong attractive forces resulting from the stable hydrogen bridges17. It has been shown that the hydrogen bonds affect the dynamic behavior of the nanoparticle agglomerates during fluidization. Therefore, the formation of direct hydrogen bonds between hydrophilic nanoparticles must not be ignored in force balance models to predict their agglomerates size during fluidization17. Based on a description for the contact area between micron-sized agglomerates composed of nanoparticles which are assumed to be perfectly packed, de Martin and van Ommen18 proposed the total force between two agglomerates due to hydrogen bonding as: FOH = 2 X π(hmax- l) COHfOH O ∗

(10)

Where hmax is the range of the hydrogen bond interaction, l is the minimum interparticle distance19 (~ 0.4 nm), COH is the concentration of active hydroxyl groups on the surface of a particle, X is the fraction of the surface of a particle 12 ACS Paragon Plus Environment

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exposes to the bonding and fOH is the average strength of a hydrogen bond. They summarized Eq. (10) as FOH = e f d* in which e f =2Xπ(hmax- l)COHfOH and assumed that e f is the same for all dry and hydrophilic particles and it was left as a fitting parameter in the model18. However, it is obvious that polarity affects hydrogen bonding because hydrogen bridges occur due to a bond being polar26. In fact, one side of the bond becomes slightly more negative because it pulls more electrons towards itself and the other side of the bond becomes more positive. Then, the partially negative bond of one molecule is attracted to the partially positive bond of another molecule. This intermolecular force is mainly affected by polarity of particles; therefore, the same hydrogen bonding force for all hydrophilic nanoparticles doesn’t seem an acceptable assumption. Based on Clausius-Mossotti equation27 there is a relation between the polarizability e of the atoms or molecules and dielectric constant : of these substances. Clausius-Mossotti relation is defined as follows: ' !

=

S

eg

(11)

where NA is Avogadro's number. As a result, we considered the dielectric constant as a parameter affecting the polarity of particles and consequently the intermolecular hydrogen bonds force between them. Substituting : into FOH equation, we obtain: h = :e′O ∗

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De Martin and van Ommen18 used agglomerate sizes reported both in conventional and centrifugal fluidized beds with/without using of surfactant and heat pretreatment in the presence of various gases including dry air, nitrogen and neon to obtain e′. In this study, we used the results that obtained the size of hydrophilic nanoparticle agglomerates only in the presence of N2 gas and standard condition (Table 1). We obtained e′~7 × 10

K

by minimizing the sum of squares between

the data reported in Table 1 and the model.

2.6 Electrostatic repulsion force Fer Due to the large amount of surface energy of nanoparticles, they tend to adhere to each other and form micron size agglomerates28. In contrast with this fact, in nanotechnology, we need stable colloidal solvents and separated nanoparticles from the solvent. The main approach for surface stabilization of nanoparticles and accordingly prevention them from the agglomeration phenomena has been proposed as the generation of electrostatic repulsion28. In the most cases, this repulsion occurs due to chemisorption of ions like proton (H+) and hydroxyl (OH-) or other charged agents on the surface of nanoparticles. Therefore the composed nanoparticles become as the same electrical charge as each other and they repulse each other. This electrical repulsion prevents the particles from getting close to each other; therefore it prevents them from agglomeration. In case of two particles 14 ACS Paragon Plus Environment

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with spheres diameter of dp dispersed in a liquid, the total electrical repulsion force is given by28-29: jk = 2_:? :k OP l?

j (mno)

(13)

'!j (mno)

Where ε0 is the permittivity of free space (=1), εr is the relative dielectric constant of the liquid, Ψ0 is the surface potential of liquid and l is the surface separation distance (~0.4 nm)20,29. The parameter k-1 is known as Debye length and it is defined as28: p

'

=0

q r Vs t

(14)

>Sj uv

Where KB is the Boltzmann constant, T is the absolute temperature, e is the electronic charge, and ci is the concentration of the electrolyte species i in solution. It has to be noted that the magnitude of the Debye length depends solely on the properties of the electrolyte and not on the surface charge or potential29. The electrostatic repulsion may be examined with less intensity in the gas phase. The mechanism by which electrostatic charge is reduced in gas phase by using some polar vapors is not fully understood16. However, such beneficial result may be explained by the fact that these substances exhibit polarity that is effective in reducing electrostatic charge16. In the case of presence of alcohol vapor in surrounding media of particles, the positive section of these polar molecules (hydrocarbon chains) bind to the negative surface of hydrophilic particles, leaving 15 ACS Paragon Plus Environment


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the hydrocarbon chains to interact with other non-polar chains. Through this binding action, the generation of electrostatic charge due to friction of polar molecules may be reduced. In other words, the layer of positive hydrocarbon chains; formed around the hydrophilic silica particles, generates a force of repulsion between the particles and reduces the tendency of the particles adhering to each other16,18 (see Fig. 1). We used Eq. (13) in our proposed model to show the electrostatic repulsion force between the particles in the presence of alcohol vapors in which εr was substituted as the relative dielectric constant of alcohol vapors. Also, due to the overall good agreement between the measured zeta potentials ζ and the surface potentials Ψ0 for polar media29, we used zeta potential amounts in our model. In this work, all alcohols were used as received and no electrolyte was intentionally added. Therefore, the concentration of the electrolyte in solution was assumed zero which makes the parameter k as zero. All parameters has been presented for used different alcohols at Table 2.

2.7 Proposed model Inserting Eqs. (2), (6), (8), (9), (12) and (13) into Eq. (1), leads to the final expression for the average size of the suspended agglomerates and is rewritten as follows:


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+ :e′O ∗ − 2_:? :k OP Ψ? ×

ST U (A∗∗ )-

V

'⁄ K

"

j (mno)

'!j (mno)

− 3_O ∗∗ `a:8 .> − 0.166(O∗∗ ) ×

S

− *b∗∗ − bd ,(O∗∗ ) 9 = 0 (15) (

This is an algebraic equation which is nonlinear with respect to the agglomerate size and is solved by the Newton-Raphson method to obtain d**.

3. Experiments The experiments were carried out in a gas–solid fluidized bed made of normal glass with 26 mm inner diameter and 800 mm height. High-purity nitrogen (99.98 %) at room temperature was entered into the column through a sintered porous distributor. To study the effect of hydrogen bridges and also electrical repulsion on fluidization behaviour, 5 different types of alcohols including methanol, 1propanol, 2-propanol, 1-butanol and 2-butanol were added to nitrogen before it entered the bed using a bottle filled with alcohol. The gas flow leaving the system was cleaned with a water bubbler and then filtered using a HEPA filter to prevent the elutriation of nanoparticles to the atmosphere. The experimental setup is shown schematically in Fig. 2. Hydrophilic silica and alumina nanopowders (both supplied by Evonik industry) were used in the experiments. Hydrophilic nanopowders are characterized by a surface containing hydroxyl groups, where the concentration of these groups can



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vary from one type of material to another17. Properties of used nanoparticles are listed in Table 3. Before experiments, the particles were sieved using a 425 µm sieve placed on a shaker to remove large agglomerates that encourage channelling during fluidization. The bed expansion (H/H0) at different superficial gas velocities and also the minimum fluidization velocity Umf were determined to interpret the cohesiveness and fluidization behaviour of the particles. H is the height of the bed at a certain superficial gas velocity and H0 is the height of the bed at zero gas velocity. Umf was measured by the pressure drop across the bed for different gas velocities using a micro-manometer (model FM 393). One of the pressure taps was located in the freeboard and the other 2 cm above the distributor. Umf was reported as the gas velocity at which an increment in the gas flow does not result in an increment in the pressure drop anymore18. After each change in gas velocity, 3 minutes waiting time was taken for the bed to stabilize before the bed expansion and the pressure drop was measured. Because of the very light and fragile nature of the agglomerates, any size measurement method involving direct contact with the agglomerates (ex-situ SEM) has been found to give severely erroneous results30. Therefore, measuring the agglomerates size by SEM does not represent the actual size of the agglomerates formed under fluidization conditions and gives much lower value 18 ACS Paragon Plus Environment

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compared to that obtained from the physical sampling methods. In-situ measurement methods based on imaging of laser illuminated agglomerates improve reliability and accuracy as it obviates the risk of agglomerates distortion when they are processed for the microphotograph examination2-3,30. In addition, the agglomerate sizes measured by different researchers by using the laser based method were found to be quite close to each other30. In this study, to validate the proposed model, we used data directly obtained from laser-based planar imaging from the literature and also data indirectly obtained from Richardson-Zaki equation.

4. Results and Discussions Parameters used in this work and required in the proposed model are summarized in Table 4.

4.1 Experimental analysis The dependence of the bed expansion H/H0 on the superficial gas velocity is studied as an indicator of the characteristics of the agglomerates in the bed to interpret the cohesiveness of the particles18. The results for the bed expansion of hydrophilic silica and alumina nanoparticles at different superficial gas velocities are shown in Figs. 3 and 4, respectively. These results have been obtained in the 19 ACS Paragon Plus Environment


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absence and presence of alcohols. As can be seen, in the absence of alcohol, the bed expands up to about 2.2 and 1.67 times the initial bed height at gas velocity of 0.05 m/s for SiO2 and Al2O3 respectively. The lower expansion of Al2O3 nanoparticles might be attributed to its higher bulk density and/or stronger hydrogen bridges between particles of Al2O3 compared to SiO2. Therefore it may be proposed that Al2O3 nanoparticles must have larger and/or denser agglomerates18. Additionally, a non-uniform fluidization with large bubbles rising up very quickly through the bed (agglomerate bubbling fluidization (ABF) behavior) was observed for both particles in the absence of alcohol. This limited bed height expansion and also undesirable bubbling phenomena need to be improved to enhance the fluidization performance. By adding different alcohols to the fluidizing gas, the bed expansion ratio increased in all cases especially in the case of SiO2 agglomerates. It can be shown that there is an obvious difference between influences of different alcohols on the fluidization behavior. For SiO2 agglomerates, the bed expansion ratio in the presence of methanol, 1-propanol, 2propanol, 1-butanol and 2-butanol alcohols reached up to about 3.3, 2.9, 3.2, 2.5 and 2.4, respectively in the gas velocity of 0.05 m/s and reached up to about 2.03, 1.97, 2.09, 1.77 and 1.84, respectively for Al2O3 agglomerates. It is believed that using of a fluidizing gas that includes vapor of a polar solvent; like used alcohols here, will be effective in dissipating electrostatic charge within 20 ACS Paragon Plus Environment

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the fluidization chamber16. This phenomenon happens by binding the polar section of alcohols to the surface of nanoparticles. Through this bonding, alcohol molecules expose their organic groups result in decreasing the interaction between nanoparticles and consequently friction of polar molecules16. This might be the main reason of reducing the generation of electrostatic charges in the presence of alcohols. As shown in Figs. 3 and 4, methanol, 1-propanol and 2-propanol are the most effective alcohols in enhancing the fluidization quality both for SiO2 and Al2O3 nanoparticles. It might be attributed to the better bonding of these alcohols to the surface of examined nanoparticles. Type of fluidization of nanoparticles in absence and presence of different alcohol vapors and also their minimum fluidization velocity are summarized in Table 5. Umf results confirm all mentioned observations so that both nanoparticles in the presence of methanol, 1-propanol and 2-propanol have the smallest Umf. This may be due to the formation of smaller agglomerates in the presence of these alcohols and must be caused by a decrease of the inter-particle forces, which will be studied more by the model in the following.

4.2 The importance of forces in the proposed model If the formation of direct hydrogen bonds is not considered in the model of calculating the agglomerates size during fluidization, the cohesive force between



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dry hydrophilic nanoparticles and consequently the resulting agglomerate size will be strongly underestimated17. Results showed that there is a considerable difference between the estimated agglomerates size of hydrophilic SiO2 nanoparticles in two cases of modeling; with and without considering FOH. For example, the size of agglomerates obtained directly from laser-based planar imaging for A300 nanoparticles has been reported approximately as 361 micron (see Table 1). And, the size of agglomerates was estimated by our proposed model as ~ 350 micron when hydrogen bond was considered as an effective adhesion force in the modeling compared to ~210 micron when it was not considered. Therefore, formation of hydrogen bridges during fluidization of hydrophilic nanoparticles must not be neglected in force balance models of predicting their agglomerates size. It should be mentioned that no any hydrogen bonds forms between hydrophobic nanoparticles (e f = 0). Two experimental inputs are needed in order to calculate the amount of drag and collision forces; superficial gas velocity U and bed voidage :8 , which shows dependency of the model to experimental observations. To determine the influence of FD and FC on agglomerates size calculated by model, the amount of these forces to the total sum of forces were calculated at an average superficial gas velocity of 0.05 m/s (see Table 6). As it can be seen, the effect of drag and collision forces on the size of agglomerates is quite small compared to the other forces (approximately 22 ACS Paragon Plus Environment

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9% of the total amount of forces). Accordingly, the effect of drag and collision forces were neglected in our proposed model and the final model was derived based on the balance between van der Waals, hydrogen bonding, gravity and electrostatic repulsion forces.

4.3 Estimating the size of agglomerates By neglecting the role of drag and collision forces in estimating the agglomerates size, the following relation can be obtained:

+ :e′O ∗ − 2_:? :k OP Ψ? ×

j (mno)

'!j (mno)

− *b∗∗ − bd ,(O ∗∗ ) 9 = 0

(16)

This equation does not need any experimental data such as bed expansion or superficial gas velocity to estimate the size of agglomerates and can be easily used as a simple model to calculate the agglomerates size of hydrophilic nanoparticles during fluidization. Table 7 shows the results of agglomerates size calculated by Eq. (16) for SiO2 and Al2O3 nanoparticles in the absence and presence of five different alcohols. The estimated results obtained by model are in good agreement with the experimental observations, so that, among all used alcohols, methanol and 2-propanol have most significant effect on fluidization improvement (see Figs. 3 and 4) and also the smallest size of agglomerates is estimated by using physical properties of methanol and 2-propanol in the proposed model (see Table 7). 23 ACS Paragon Plus Environment


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To justify how the alcohols affect the size of agglomerates, two parameters of the model are investigated. These physical parameters which play principal role on controlling the agglomerates size and consequently fluidization behavior of particles are surface potential and dielectric coefficient. As shown in Table 2, the highest surface potential values of the alcohols correspond to 2-propanol, methanol, 1-propanol, 1-butanol and 2-butanol, respectively. On the other hand, the highest dielectric constant values between the alcohols correspond to methanol, 1-propanol, 2-propanol, 1-butanol and 2-butanol, respectively. The surface potential of a solvent is a criterion for the stability of colloidal solutions. The less the surface potential of a solvent, the more the tendency of dispersed particles inside to adhere to each other and agglomerate. In the other words, nanoparticles have lower tendency to agglomerate and stick together in solvents with higher surface potential31. Therefore, the colloidal solution of nanoparticles will be more stable in the case of using solvents with higher surface potential. Besides, the dielectric constant of a solvent is a measure of its polarity. The higher the dielectric constant of a solvent, the more polar it is20. For example, the dielectric constant of methanol vapor ɛ ~ 28.42, is higher than that of 2-butanol vapor ɛ ~ 11.48; e. g. methanol is more polar than 2-butanol. As a result, it can be concluded that the more suitable alcohol in enhancing the fluidization behavior of nanoparticles is the one has the higher surface potential and also dielectric constant values. 24 ACS Paragon Plus Environment

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Considering the values of surface potential and dielectric constant of five used alcohols in Table 2, the maximum values of these mentioned parameters correspond to methanol, 1-propanol and 2-propanol. So, it is expected that using these three alcohols results in formation of smaller agglomerates compared to 1butanol and 2-butanol. This is in good agreement with the experimental observations too. It should be mentioned that there are no any laser based experimental reports in the literature for the size of agglomerates in the presence of alcohols. For this reason, to validate the proposed model we only used the experimental data reported in the literature for SiO2 and Al2O3 fluidization in dry nitrogen. Fig. 5a shows that the average weighted relative error of our model is 8%, which is a reasonable estimation for the size of the fluidized agglomerates of SiO2 nanopowders. de Martin and van Ommen18 earlier proposed a simple model based on van der Waals, hydrogen bond and gravity forces between micron-sized simple agglomerates. Fig. 5b presents the results of their proposed model compared to the experimental data. As it can be seen, the average relative error of de Martin and van Ommen model is 18%. This confirms that considering the effect of dielectric constant of nanoparticles in the form of : in hydrogen bonding force relation increases the accuracy of the model. The average weighted relative error of Valverde and Castellanos32 model is 29%, considerably larger than the average relative error of 25 ACS Paragon Plus Environment


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our proposed model. This high error is mainly because of neglecting hydrogen bond in force balance. Finally, the Richardson–Zaki equation was used to estimate the size of fluidized agglomerates in the presence of different alcohols. This equation relates the superficial gas velocity U with the bed voidage and the terminal velocity Ut for an agglomerate as: ` = `x :8+

(17)

Which can be rewritten as the following linear equation: log U = log U} + n log ε8

(18)

Where n is the R–Z exponent and it is determined by the particle properties and bed properties; :8 is the bed voidage and can be given by mass balance of the particle in the fluidized bed as: ε8 = 1 −

q

(1 − :8? )

(19)

The initial bed voidage (εb0) of single SiO2 nanoparticles is within the range from 0.2 to 0.25 and then εb0 = 0.22 was chosen for the calculations performed2,33. The value of εb0 for Al2O3 particle bed can be assumed to 0.2, which bed exhibits higher bulk and particle densities than that of SiO2 particles33-34. By drawing a plot of lg U vs. lg :8 of nanoparticles (see Fig. 6), the R–Z index n and the terminal velocity Ut can be obtained. All the linear fitting trendlines of the experimental data shown in


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this figure has the correlation coefficients of above 0.9, so the fluidized systems obey the Richardson–Zaki equation very well. From the values of Ut and assuming Stokes law, the average size of the agglomerates can be calculated from2: O ∗∗ = 0

'>CY

(20)

*A∗∗ AX ,B

Where ρ** is the density of the agglomerates, considered similar to the bulk density of the powders, ρf is the fluid density, μ is the fluid viscosity and g is the gravity acceleration. The R–Z index n, Ut and also resultant agglomerate sizes for silica (A130) and alumina (AluC) nanoparticles in the presence of different alcohols are listed in Tables 8 and 9, respectively. It is believed that the R–Z index n of nanoparticles can be an indicator for the characteristic of fluidization2,35. The fluidization quality of APF nanoparticles (such as SiO2-methanol) is better than those of ABF (such as Al2O3-1butanol). Consequently, the index n of APF nanoparticles is relatively higher compared with ABF nanoparticles. Nam et al.35 have shown that a Richardson–Zaki exponent of n = 5 is valid for APF nanoparticle agglomerates. Therefore, it can be concluded that those materialalcohol systems which have index n ≥ 5 show APF behavior and those with n < 5 present ABF behavior. Type of fluidization of both powders in presence of different alcohols are presented in Table 5 based on index n quantity. Also, the



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average sizes of the agglomerates predicted based on experiments (Ut) compare reasonably well with the model calculated values in Table 7.

5. Conclusion A model based on the balance of forces acting on the agglomerates of cohesive nanoparticles during fluidization was developed. The equilibrium agglomerate sizes of silica and alumina particles formed in the fluidized bed were calculated with the proposed model. Compared with the values predicted by existing models, the average sizes of agglomerates calculated by this model were in reasonable agreement with experimental data in dry nitrogen (average weighted error of 8%). A series of experiments were conducted to elucidate the effect of adding different alcohols vapor on the fluidization behavior of nanoparticle agglomerates. Among all used alcohols, methanol, 2-propanol and 1-propanol were the most effective ones on fluidization improvement especially for silica nanoparticles. By adding the electrostatic repulsion force in the model; the smallest size of agglomerates was also estimated using physical properties of methanol, 2-propanol and 1-propanol respectively. This result confirms that two physical parameters of surface potential and dielectric coefficient of alcohols play principal role on controlling the agglomerates size and consequently fluidization behavior of particles. Finally, the average sizes of the agglomerates predicted based on Richardson-Zaki equation 28 ACS Paragon Plus Environment

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compare reasonably well with the model calculated values in the presence of alcohols.



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6. List of symbols AH

Hamaker constant [J]

Bo

bond number

ci

concentration of the electrolyte species i in solution

CD

drag coefficient

COH

concentration of active hydroxyl groups on the particle surface

d**

complex agglomerate diameter [m]

d*

simple agglomerate diameter [m]

O5P

asperity of the micron-sized particles corresponding to micron-sized agglomerates [m]

dp

primary particle diameter [m]

Db

bubble diameter [m]

e

electronic charge [C]

fOH

average strength of a hydrogen bond

FC

collision force [N]

FD

drag force [N]

Fer

electrostatic repulsion force [N]

Fg

gravitational force minus bouyancy forces [N]

FOH

hydrogen bond force [N]

FvdW

van der Waals force [N]

g

gravity acceleration [m/s2]

h

Planck’s constant [J.s]

hmax

range of the hydrogen bond interaction

H

bed height [m]

H0

initial bed height [m]


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K

function of Poisson’s ratio and Young’s modulus [Pa-1]

p -1

Debye-Huckel double layer thickness [m]

KB

Boltzmann constant [J/K]

l

distance between interacting bodies [m]

n

refractive index of material

NA

Avogadro's number

345,+

dimensionless average particle pressure

Rep

the particle Reynolds number

T

absolute temperature [K]

U

superficial fluid velocity [m/s]

Ut

terminal velocity [m/s]

V

relative velocity of agglomerate [m/s]

X

fraction of the surface of a particle exposes to the hydrogen bonding

Greek letters :

:?

dielectric constant of material permittivity of free space

:8

bed voidage

εb0

initial bed voidage

:k

electrical permittivity of a medium relative to that of vacuum

e

polarizability

e′

fitting parameters for all dry and hydrophilic particles

µ

fluid viscosity [Pa.s]

j

UV main absorption frequency [Hz]



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b∗∗ bd

agglomerate density [kg/m3] fluid density [kg/m3]

bP

primary particle density [kg/m3]

ζ

zeta potentials [V]

Ψ?

surface potential [V]


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References (1) Yao, W.; Guangsheng, G.; Fei, W.; Jun, W. Fluidization and agglomerate structure of SiO 2 nanoparticles. Powder Technol. 2002, 124 (1), 152-159. (2) Zhu, C.; Yu, Q.; Dave, R. N.; Pfeffer, R. Gas fluidization characteristics of nanoparticle agglomerates. AIChE J. 2005, 51 (2), 426-439. (3) Hakim, L. F.; Portman, J. L.; Casper, M. D.; Weimer, A. W. Aggregation behavior of nanoparticles in fluidized beds. Powder Technol. 2005, 160 (3), 149160. (4) Yu, Q.; Dave, R. N.; Zhu, C.; Quevedo, J. A.; Pfeffer, R. Enhanced fluidization of nanoparticles in an oscillating magnetic field. AIChE J. 2005, 51 (7), 19711979. (5) Wang, Z.; Kwauk, M.; Li, H. Fluidization of fine particles. Chem. Eng. Sci. 1998, 53 (3), 377-395. (6) Matsuda, S.; Hatano, H.; Tsutsumi, A. Ultrafine particle fluidization and its application to photocatalytic NO x treatment. Chem. Eng. J. 2001, 82 (1), 183-188. (7) Morooka, S.; Kusakabe, K.; Kobata, A.; Kato, Y. Fluidization state of ultrafine powders. J. Chem. Eng. Jpn. 1988, 21 (1), 41-46. (8) Matsuda, S.; Hatano, H.; Muramoto, T.; Tsutsumi, A. Modeling for size reduction of agglomerates in nanoparticle fluidization. AIChE J. 2004, 50 (11), 2763-2771. (9) Zhou, T.; Li, H. Estimation of agglomerate size for cohesive particles during fluidization. Powder Technol. 1999, 101 (1), 57-62. (10) Zhou, T.; Li, H. Force balance modelling for agglomerating fluidization of cohesive particles. Powder Technol. 2000, 111 (1), 60-65. (11) Iwadate, Y.; Horio, M. Prediction of agglomerate sizes in bubbling fluidized beds of group C powders. Powder Technol. 1998, 100 (2), 223-236.



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(12) Mawatari, Y.; Ikegami, T.; Tatemoto, Y.; Noda, K. Prediction of Agglomerate Size for Fine Particles in a Vibro-fluidized Bed. J. Chem. Eng. Jpn. 2003, 36 (3), 277-283. (13) Chaouki, J.; Chavarie, C.; Klvana, D.; Pajonk, G. Effect of interparticle forces on the hydrodynamic behaviour of fluidized aerogels. Powder Technol. 1985, 43 (2), 117-125. (14) Tamadondar, M. R.; Zarghami, R.; Boutou, K.; Tahmasebpoor, M.; Mostoufi, N. Size of nanoparticle agglomerates in fluidization. Can. J. Chem. Eng. 2016, 94 (3), 476-484. (15) van Ommen, J. R.; Pfeffer, R. In Fluidization of Nanopowders: Experiments, Modeling and Applications. The 13th International Conference on Fluidization New Paradigm in Fluidization Engineering, Gyeong-ju, Korea, May 16-21, 2010. (16) Pfeffer, R.; Quevedo, J. Systems And Methods For Reducing Electrostatic Charge In A Fluidized Bed, U.S. Patent 7905433, 2011. (17) Tahmasebpoor, M.; de Martín, L.; Talebi, M.; Mostoufi, N.; van Ommen, J. R. The role of the hydrogen bond in dense nanoparticle–gas suspensions. Phys. Chem. Chem. Phys. 2013, 15 (16), 5788-5793. (18) de Martin, L.; van Ommen, J. R. A model to estimate the size of nanoparticle agglomerates in gas− solid fluidized beds. J. Nanopart. Res. 2013, 15 (11), 1-9. (19) Krupp, H. Particle adhesion, theory and experiment; Adv. Colloid Interface Sci. 1 (1967), 111-239: 1967. (20) Butt, H.-J.; Kappl, M. Surface and interfacial forces; Wiley: Weinheim, 2009. (21) Horio, M.; Iwadate, Y. In The prediction of sizes of agglomerates formed in fluidized beds; Proceeding 5th World Congress of Chemical Engineering, 2nd Int. Particle Technology Forum, 1996. (22) Valverde, J. M.; Castellanos, A. Bubbling suppression in fluidized beds of fine and ultrafine powders. Part. Sci. Technol. 2008, 26 (3), 197-213. (23) Geldart, D. Types of gas fluidization. Powder Technol. 1973, 7 (5), 285-292. 34 ACS Paragon Plus Environment

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(24) Shabanian, J.; Jafari, R.; Chaouki, J. Fluidization of ultrafine powders. Int. Rev. Chem. Eng. 2012, 4 (1), 16-50. (25) Khan, A.; Richardson, J. Pressure gradient and friction factor for sedimentation and fluidisation of uniform spheres in liquids. Chem. Eng. Sci. 1990, 45 (1), 255-265. (26) Jeffrey, G. A.; Saenger, W. Hydrogen bonding in biological structures; Springer Science & Business Media, 2012. (27) Hannay, J. The Clausius-Mossotti equation: an alternative derivation. Eur. J. Phys. 1983, 4 (3), 141. (28) Israelachvili, J. N. Intermolecular and surface forces; Academic press: Orlando, FL, 1985. (29) Barbagini, F. A Fundamental Study of Particle-Substrate Interactions in Liquids of Low Polarity. Ph.D. dissertation, Catholic University of Leuven, Belgium, 2009. (30) Rahman, F. Fluidization Characteristics of Nanoparticle Agglomerates. Ph.D. dissertation, Monash University, Victoria, 2009. (31) Shaw, D. J. Introduction to colloid and surface chemistry, Fourth Edition; Butterworth-Heinemann: Oxford, 1992. (32) Valverde, J. M.; Castellanos, A. Fluidization of nanoparticles: a simple equation for estimating the size of agglomerates. Chem. Eng. J. 2008, 140 (1), 296304. (33) Yang, J.; Zhou, T.; Song, L. Agglomerating vibro-fluidization behavior of nano-particles. Adv. Powder Technol. 2009, 20 (2), 158-163. (34) Liang, X.; Duan, H.; Zhou, T.; Kong, J. Fluidization behavior of binary mixtures of nanoparticles in vibro-fluidized bed. Adv. Powder Technol. 2014, 25 (1), 236-243. (35) Nam, C. H.; Pfeffer, R.; Dave, R. N.; Sundaresan, S. Aerated vibrofluidization of silica nanoparticles. AIChE J. 2004, 50 (8), 1776-1785. 35 ACS Paragon Plus Environment


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(36) Quevedo, J. A.; Pfeffer, R. In situ measurements of gas fluidized nanoagglomerates. Ind. Eng. Chem. Res. 2010, 49 (11), 5263-5269. (37) Haynes, W. M.; ed. CRC Handbook of Chemistry and Physics, 96th Edition (Internet Version); CRC Press/Taylor and Francis: Boca Raton, FL, 2016.


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Table Captions Table 1: Agglomerate sizes reported in literature for hydrophilic (polar) ∗∗ nanoparticles. The first column OjP,' shows data directly obtained from laser∗∗ based planar imaging. The second column OjP, shows data indirectly derived

from the Richardson-Zaki equation Table 2: List of alcohols used in experiments with their physical properties Table 3: Properties of nanoparticles used in experiments Table 4: List of constant parameters used in model Table 5: The fluidization behavior of used nanopowders in the presence of different alcohols. H/H0 obtained at U=5 cm s-1 Table 6: The amount of drag and collision forces to the total sum of forces at average superficial gas velocity of 5 cm s-1 Table 7: Comparison between agglomerate sizes calculated for hydrophilic SiO2 and Al2O3 nanoparticles in the absence and presence of five different alcohols. d**exp shows data obtained from laser-based planar imaging or Richardson-Zaki equation (see Table 1). d**model shows data calculated by the proposed model equation Table 8: The values of n, Ut and d** obtained from Richardson-Zaki equation for silica (A130) in the presence of different alcohols



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table 9: The values of n, Ut and d** obtained from Richardson-Zaki equation for alumina (AluC) in the presence of different alcohols


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Figure Captions Fig. 1: Electrostatic stabilization mechanism of SiO2 nanoparticles in presence of alcohol vapor Fig. 2: The experimental apparatus: (A), Bubbler containing alcohol; (B), Fluidization bed; (C), Gas distributing chamber; (D), Gas filter Fig. 3: Bed expansion curves for SiO2 hydrophilic (A130) nanoparticles fluidized in dry nitrogen and also in the presence of different alcohols Fig. 4: Bed expansion curves for Al2O3 hydrophilic (AluC) nanoparticles fluidized in dry nitrogen and also in the presence of different alcohols Fig. 5: Experimental agglomerate sizes (see Table 1) and sizes predicted by a) Eq. (16) and existing models: b) de Martin and van Ommen [18] and c) Valverde and Castellanos [32] Fig. 6: lg U vs lg εb for SiO2 (A130) and Al2O3 (AluC) nanoparticles in the presence of different alcohols



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Table 1: Agglomerate sizes reported in literature for hydrophilic (polar) nanoparticles. The first ∗∗ column OjP,' shows data directly obtained from laser-based planar imaging. The second column ∗∗ OjP, shows data indirectly derived from the Richardson-Zaki equation

∗∗ ,

∗∗ ,

Source

Name

Material

Gas

(kg/m3)

(nm)

()

()

Hakim et al. [3]

A300

SiO2

N2

2200

7

320

-

Zhu et al. [2]

A300

SiO2

N2

2560

7

585

296

Hakim et al. [3]

A300

SiO2

N2

2200

7

300

Hakim et al. [3]

A300

SiO2

N2

2200

7

240

Average []

361

Hakim et al. [3]

A150

SiO2

N2

2200

14

430

Hakim et al. [3]

A150

SiO2

N2

2200

14

320

Hakim et al. [3]

A150

SiO2

N2

2200

14

290

Average []

-

347

de Martin [18]

A130

SiO2

N2

2200

16

-

342

This work

A130

SiO2

N2

2200

16

-

355

Average []

349

Quevedo [36]

A90

SiO2

N2

2560

20

417

-

de Martin [18]

AluC

Al2O3

N2

3600

13

-

339

This work

AluC

Al2O3

N2

3600

13

-

434

Average []

387


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Table 2: List of alcohols used in experiments with their physical properties

Alcohols

ε

n

Ψ0 = ζ (mV)

[37]

[29]

methanol

28.42

1.33

-44

1-propanal

11.51

1.39

-40

2-propanol

11.48

1.38

-56

1-butanol

8.34

1.4

-26

2-butanol

7.79

1.4

-25

Table 3: Properties of nanoparticles used in experiments

Commerical name

Wettability

Material

Particle

Particle

diameter

density

Bulk AH (J)

density

3

(nm)

(kg/m )

Aerosil 130

hydrophilic

SiO2

16

2200

Aeroxide AluC

hydrophilic

Al2O3

13

3600

6.60 × 10

1.45 × 10

?

55

3.82

1.46

'

60

9.3

1.75

Parameter

Value [Unit]

Reference

Bo

~1 [-]

[22-23]

35 × 10

3 × 10

K

'?

(

[m]

[18]

[3L ' ]

[10]

l

4 [Å]

[19]

345,+

0.077 [-]

[21]

3 × 10'K []

[29]

νe

n

(kg/m )

Table 4: List of constant parameters used in model

d*

ε

3



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Page 42 of 52

Table 5: The fluidization behavior of used nanopowders in the presence of different alcohols. H/H0 obtained at U=5 cm s-1

Material Hydrophilic SiO2 (A130)

Hydrophilic Al2O3 (AluC)

Alcohol

Fluidization type

Umf [cm.s-1]

H/H0

Fluidization type

Umf [cm.s-1]

H/H0

methanol

APF

0.75

3.3

ABF

2.13

2.03

1-propanol

APF

1.41

2.9

ABF

2.93

1.97

2-propanol

APF

1.01

3.2

ABF

1.63

2.09

1-butanol

ABF

2.17

2.5

ABF

3.84

1.77

2-butanol

ABF

2.81

2.4

ABF

3.69

1.84

without

ABF

4.19

2.2

ABF

4.01

1.67

Table 6: The amount of drag and collision forces to the total sum of forces at average superficial gas velocity of 5 cm s-1

Material-Alcohol

SiO2-2 propanol

SiO2-methanol

Al2O3-2 propanol

Al2O3-methanol

FvdW (N)

1.17×10-10

2.45×10-10

1.22×10-9

1.76×10-8

FOH (N)

9.36×10-9

9.36×10-9

2.28×10-8

2.28×10-9

Fer (N)

1.8×10-9

2.77×10-9

1.47×10-9

2.25×10-9

Fg (N)

6.19×10-9

5.5×10-9

1.82×10-8

1.8×10-8

FC (N)

1.31×10-9

1.19×10-9

3.71×10-9

3.64×10-9

FD (N)

1.62×10-10

1.52×10-10

6.57×10-10

6.89×10-10

Ftotal (N)

1.9×10-8

1.92×10-8

4.8×10-8

4.91×10-8

6.9%

9%

8.82%

!

" ×100

7.8%


Page 43 of 52

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 7: Comparison between agglomerate sizes calculated for hydrophilic SiO2 and Al2O3 nanoparticles in the absence and presence of five different alcohols. d**exp shows data obtained from laser-based planar imaging or Richardson-Zaki equation (see Table 1). d**model shows data calculated by the proposed model equation

d**model (µm) (in the presence of alcohol) Material

dp

(hydrophilic)

(nm)

name

d**exp

d**model (µm)

(µm)

(without

methanol

1-propanol

2-propanol

1-butanol

2-butanol

alcohol)

SiO2

Al2O3

7

A300

361

350

312

319

315

322

322

14

A150

347

350

296

315

305

321

321

16

A130

349

350

291

313

302

320

321

20

A90

417

350

281

310

296

320

320

13

AluC

387

454

418

425

421

427

428



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 44 of 52

Table 8: The values of n, Ut and d** obtained from Richardson-Zaki equation for silica (A130) in the presence of different alcohols without Alcohol

alcohol

methanol

1-propanol

2-propanol

1-butanol

n

3.871

5.503

5.334

5.372

Ut (cm/s)

22.935

18.590

20.626

18.879

22.359

22.866

d** (µm)

355

319

337

322

351

355

4.824

2-butanol 4.603

Table 9: The values of n, Ut and d** obtained from Richardson-Zaki equation for alumina (AluC) in the presence of different alcohols

Without Alcohol

alcohol

methanol

1-propanol

2-propanol

1-butanol

2-butanol

n

3.3

4.297

4.084

4.479

3.566

3.763

Ut (cm/s)

34.154

31.456

31.718

30.491

33.643

32.966

d** (µm)

434

416

418

410

430

426


Page 45 of 52

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Fig. 1: Electrostatic stabilization mechanism of SiO2 nanoparticles in presence of alcohol vapor



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Fig. 2: The experimental apparatus: (A), Bubbler containing alcohol; (B), Fluidization bed; (C), Gas distributing chamber; (D), Gas filter


Page 46 of 52

Page 47 of 52

3.4 3.2 3 2.8 2.6

H/H0 [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2.4 2.2 2 1.8

A130 Without Alcohol A130-Methanol A130-1Propanol A130-2Propanol A130-1Butanol A130-2Butanol

1.6 1.4 1.2 1 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

U (cm/s)

Fig. 3: Bed expansion curves for SiO2 hydrophilic (A130) nanoparticles fluidized in dry nitrogen and also in the presence of different alcohols



2.2 2.1 2 1.9 1.8

H/H0 [-]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 48 of 52

1.7 1.6 1.5 1.4

AluC-Without Alcohol AluC-Methanol AluC-1Propanol AluC-2Propanol AluC-1Butanol AluC-2Butanol

1.3 1.2 1.1 1 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

U (cm/s)

Fig. 4: Bed expansion curves for Al2O3 hydrophilic (AluC) nanoparticles fluidized in dry nitrogen and also in the presence of different alcohols


Page 49 of 52

500

a

A300 A150 A90 A130 AluC

d**model (µm)

400

+20 %

300

+20 %

200 100 0 0

b

100

200 300 d**exp (µm)

400

500

500 A300 A150 A90 A130 AluC

400

d**model (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


+20 %

300

-20 %

200 100 0 0

100

200 300 d**exp (µm) 49

ACS Paragon Plus Environment

400

500


500 A300 A150 A90 A130 AluC

c

400

d**model (µm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 50 of 52

+20%

-20 %

300 200 100 0 0

100

200 300 d**exp (µm)

400

500

Fig. 5: Experimental agglomerate sizes (see Table 1) and sizes predicted by a) Eq. (16) and existing models: b) de Martin and van Ommen [18] and c) Valverde and Castellanos [32]


Page 51 of 52

0.8 A130 Without Alcohol A130-Methanol A130-1Propanol

0.6

A130-2Propanol A130-1Butanol

lg U

A130-2Butanol

0.4

0.2

0 -0.35

-0.30

-0.25

-0.20

-0.15

-0.10

-0.30

-0.25

-0.20

lg εb

0.6

0.5

0.4

lg U

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


AluC-Without Alcohol AluC-Methanol AluC-1Propanol AluC-2Propanol AluC-1Butanol AluC-2Butanol

0.3

0.2

0.1

0 -0.45

-0.40

-0.35

lg εb Fig. 6: lg U vs lg εb for SiO2 (A130) and Al2O3 (AluC) nanoparticles in the presence of different alcohols 51 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Table of Contents (TOC) Graphic


Page 52 of 52

Model Based on Electrostatic Repulsion and Hydrogen Bond Forces

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