Athenea Journal

Vol.4, Issue 14, (pp. 22-31)

ISSN-e: 2737-6419

Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

https://doi.org/10.47460/athenea.v4i14.65

Thermoviscosity mechanism approach in forming fayalite-

type ceramic accumulations in particle separators in CFD

reactors

Received (14/09/2023), Accepted (13/11/2023)

Abstract. - This article presents the fundamental bases to generate knowledge in forming fayalite-type

adhesions. Likewise, to determine the conditions that favor the change of viscosity and consequent

conditions of the plasticity of the studied system. The analysis focuses on temperatures between 723K and

1023K and pressures above 5 bar. As a result, the formation of adhesions observed in the production

process that contain the materials involved and commonly associated with the collision between the

particles are estimated, as well as the effect of the different associated energies that arise from this

phenomenon. This mechanism may apply to the study of the adhesions of other ceramic materials under

thermoplastic conditions with behavior in similar conditions to the studied ceramic system, using the

equation modified to that proposed by Mc Lean for thermoelasticity of metals.

Keywords: Thermo-plasticity, relative viscosity, wustite, particle collision, sticking, creep, fayalite.

Enfoque del mecanismo de termoviscosidad en la formación de acumulaciones cerámicas de tipo

fayalita en separadores de partículas en reactores CFD

Resumen: Este artículo presenta las bases fundamentales para generar conocimientos en la formación de

las adherencias de tipo fayalita. Así mismo, para determinar las condiciones que favorecen el cambio de

viscosidad y condiciones consecuentes de la plasticidad del sistema estudiado. El análisis se enfoca en los

rangos de temperaturas entre 723K y 1023 K y presiones superiores a 5 bar. Como resultado, se estiman las

formaciones de las adherencias observadas en proceso productivos que, contienen los materiales

involucrados, y asociadas comúnmente al choque entre las partículas, así como el efecto de las diferentes

energías asociadas que se desprenden de este fenómeno. Este mecanismo puede ser aplicable al estudio

de las adherencias de otros materiales cerámicos en condiciones termoplásticas con comportamiento

similar en condiciones al sistema cerámico estudiado, utilizando la ecuación modificada a la propuesta por

Mc Lean para termoelasticidad de metales.

Palabras clave: Termo plasticidad, viscosidad relativa, wustita, choque de partículas, pegado, fluencia,

fayalita.

Echegaray Alberto

echegaray.alberto@gmail.com

https://orcid.org/0000- 0003-4234-0452

Universidad Nacional Experimental

Politécnica Antonio José de Sucre

Puerto Ordaz- Venezuela

Oscar Dam

oscarcurmetals@gmail.com

https://orcid.org/0002-0594-6757

Universidad Nacional Experimental

Politécnica Antonio José de Sucre

Puerto Ordaz- Venezuela

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

I. INTRODUCTION

These processes tend to operate intermittently during the different iron ore manufacturing processes in

which the Prada [1] fluidized bed technology is used for processing. In these processes, de-fluidization is

generated, which is caused by the adhesion of partially reduced iron in the fluidized bed D. Fuller [2]. This

defluidization is also associated with the formation of accretions on the internal metallic surfaces of

cyclones, caused by the collision between the particles at temperatures below the melting point of iron,

causing intermittent operation. In this work, the concept of interaction between particles is associated with

the apparent viscosity phenomenon. Zhang et al. [3] proposed quantitatively expressing iron-containing

particles to resist creep movement in plasticity. It has also been cited that this concept includes the resulting

combination of external friction interactions. These cohesive forces include the Van der Waals force,

interfacial attraction, and liquid-solid bridges, which are not yet considered to describe particle

agglomerations in fluidized bed processes.

That said, the thermo-viscosity approach to the mechanism of formation of adhesions of silicates in a

particle separator offers the possibility of explaining the model in terms of the condition that favors a

change in viscosity, the consequent condition of plasticity and flow of the resulting materials to form the

observed adhesions that contain the involved materials and that are generated. This is based on the release

of energy from the particle collision and impact on the interior surface of the particle separator, as well as

the resulting temperature that favors the conditions described above. At this point, it is worth an approach

to rheology, as the branch of physics deals with the deformation and flow of solid and liquid materials but

also applies to complex microstructures, such as silicates.

To study the materials above, those whose viscosity changes with the deformation rate in a specific

temperature range are considered and are called non-Newtonian fluids. Therefore, to deal with this

apparent discrepancy, it has been accepted that rheology, in general, might be the answer because it

accounts for the study of liquids with viscosity dependent on the deformation rate. Its theoretical aspects

are the relationship of the flow behavior for the deformation of the material and its internal structure, such

as silicates, and the behavior of this type of material that cannot be described by classical fluid mechanics

or elasticity.

II. THE PROPOSED MECHANISM

The phenomenon studied is located inside a particle separator inside fluidized bed reactors during the

reaction of ferrous oxide to metallic iron, in the range of 500 °C to 800 °C and pressures higher than 5 bar.

The adhesions that the reacting materials contain are involved, mainly FeO and SiO2, and are generated as

a product of the impact of the particles and the associated energies released at temperatures under the

operating conditions described above.

The proposed mechanism aims to consider the condition of the rotating particles within the particle

separator. Therefore, the mechanism is based on mathematical formulations to express the phenomena

considered in terms of apparent viscosity and consequent plasticity observed in samples of the adhesions

of materials with a high presence of ferrous oxide collected from industrial processes. These adhesions were

analyzed using Bauman print-type macro etch techniques to observe distribution lines of non-metallic

materials and particle flow lines. This provided vital information to understand the proposed mechanism

explaining adhesion formation within the particle separator. The formation of adhesions is based on the

condition that favors a change in the apparent viscosity and, consequently, the appearance of the condition

of plasticity and fluidity of the resulting materials to form the observed samples. The proposed mechanism

is schematically described in Fig. 1.

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

Fig 1. (a) Represents the pattern of impact of a particle against a metal wall (b) Indicates how the layers of the crust

are formed by thermo adherence.

In this mechanism, the solid particles heat up during the reaction conversion of ferrous iron to metallic

iron. When they impact the surface of the steel and its roughness, they become viscous as a consequence

of the impact, it releases enough energy Fig. 1a, and it becomes a material viscous (1), which crawls impelled

with the gas flow superimposing the previous imperfections (2) and creating pores (3) and generating the

silicates of Fayalite Fig. 1b. Port analogy is a process similar to that of surface thermoactivity.

A. Energy balance

The energy balance was calculated and presented in a previous document by Echegaray [4] and is

summarized in Table 1.

Table 1. Energy balance within the particle separator.

Symbol

Energy

(KJ/mol)

(Kcal/mol)

Impact on cyclone wall

103

FeO vacancies energy

474

113

Particle’s impact

Inelastic collision

Total

660

163

The calculation of the total energy agrees with the reported energies of Gaskell [5] for the Fayalite

formation reaction, as well as with the softening point of silica in the range of 2000 ° C of approximately

599 KJ reported by Ringdalen [6] With the total energy calculated of 660 KJ/mol, which exceeds the

softening of silica, it is possible to conclude that the formation of Fayalite in the temperature range studied

is thermodynamically possible during an intermediate viscous condition.

B. Effect of temperature on apparent viscosity

According to the previous calculations, the total energy balance is 61 KJ/mol over the 599 KJ/mol for the

softening of the SiO2 particle formation of the Fayalite silicate, notably coinciding with the range of 61 to

65 KJ/mol considered as compensated activation energy for the deformation-creep of the silicate particles

to occur.

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

To obtain the effect of temperature on apparent viscosity, it is necessary to accept the past energy

condition of the solid particles in the gas-solids mixture. These particles that travel in the hot gas stream

not only have a suitable thermal condition but, on the one hand, the iron-containing particles are in a

transient structure from ferrous oxide (FeO) to iron, which in turn means an additional energy gradient

associated with vacancies, which release said energy. On the other hand, among silica particles in a collision

path with wustite, these particles are found in conditions of energy levels similar to thermal coating particles

projected onto a metal surface at high speeds. With these conditions, the occurrence of the fusion reaction

between particles is assured.

C. Adhesions of silicate by action of fluence

Having assumed the formation of a viscous phase formed by FeO-SiO2 as essential components for the

formation of silicates, together with the additional presence of MgO and metallic iron, it is possible to

assume that the viscous phase was formed under a gas velocity of 75m/s entering each cyclone at that time,

the appearance of a deformation force will create a thermo-viscosity situation. The presence of the

deformation force on the viscous silicate led to the consideration of a combination with a creep regime.

Considering the creep regime, a dependent temperature effect, it is necessary to consider the melting

temperature (Tm) of the species involved. In this case, the species in question is metallic iron. This

relationship was driven by the different flow rates for metal powders, covering roughly the metal

temperature ranges from 0 to 1 times Tm. This range has a lower range of 0.3-0.5 of the melting

temperatures of the metal considered, for which it was defined as a creep dependent on the logarithmically

of the temperature, which is governed by an Arrhenius factor, similar to liquid metal streams. The

temperature and tensile creep stress dependence have been studied in α-ferromagnetic iron in the

temperature range 620 °C -700 °C.

The activation energies for creep can be made using the slope change method. In this way, it is shown

that the activation energy compensated by the mathematical simulation model is essentially independent

of the initial stress and of the deformation up to the solidification point. With this method of slope change,

an activation energy compensated by the model of 65 kcal/mol is obtained. On the other hand, when

graphing the logarithm of the variation of the deformation paid by the model versus the inverse of the

absolute temperature, it allows to obtain a straight line that represents an activation energy compensated

by the model of 62 kcal/mol, K Murty et al. [7]. These values are essentially by the self-diffusion value in this

temperature range.

D. Thermoplasticity and fluence relationship

The activation energies, both the creep and the self-diffusion, indicate that the creep process mechanism

is controlled by diffusion and, therefore, by a non-conservative dislocation movement. This means that at

the speeds of deformation and temperatures used, the average vacancy concentration is only a slight

disturbance of the equilibrium vacancy concentration in the tested undeformed samples. The creep data

available on some FCC metals shows that obtaining a reasonable energy estimate for the movement of

vacancies is possible. From a thermo-mechanical approach, in this work, it was possible to establish the

physical meaning of the energy released by a defined particle size within the separated particle. Chica et al.

[8] explain that it starts from Cauchy's first law and multiplies both sides by the viscosity (v). Rearranging

the terms, we finally get that:





󰇡







 󰇢 

󰇛



󰇜

   (1)

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

The product  represents viscous dissipation . The formation of accretions in the form of shells in

the cylindrical zone in the temperature range above 600 °C and pressures above 10 bar is possible in

fluidized bed processes when working with molecular weights in the gas of 10 gr/mol. Therefore, the

appearance of thermoplasticity in the studied temperature range 600 °C (873K) to reach the melting point

of iron requires validation since, from the point of view of the collision between particles, enough energy

may be released to go to the point of thermoplasticity, that is, it starts the process of softening the particles.

E. Effect of temperature on apparent viscosity

Once the apparent viscosity of the studied components has been identified and quantified, as well as

the participation of creep in the proposed mechanism, the next step is to determine the effect of the critical

temperature on the occurrence of thermoplasticity. As mentioned above, in the mechanism studied, there

is an initial conditioning of the partially reduced iron oxide due to its heating by the gas flow. This

precondition has been related to the adherence tendency of the minerals used in fluidized bed reduction

processes. This is a particular tendency of the different minerals and their mixtures used in the process. In

Fig. 2, the transition of the formation of the metallic iron step is shown. This figure shows the effect of the

formation rate of metallic iron, opposite to the reduction of ferrous iron, on the critical adhesion

temperature during the passage from wustite to iron. Depending on the reduction stage, hot particles

naturally develop an active sticking tendency or sticking potential.

Fig 2. Transformation of ferrous iron into metallic iron in the studied area.

The data for the elaboration of Fig. Three were obtained from industrial tests used in a C F. D plant using

mixed Venezuelan and Australian mineral mixtures that are 100 percent Australian. From this figure, it is

possible to estimate the ranges of the temperature values for the occurrence of sticking of iron particles,

partially metalized as a function of the formation of metallic iron of the particles during their transfer into

the particle separators. The temperatures obtained can be assumed as actual, working, or operating

temperatures. This temperature creates an activated state of the particles, prone them to the appearance

of different stages of the sticking phenomena, such as bogging or particle agglomerations in the fluidized

bed, crustal adherences in the upper cylindrical section of the particle separator sand sintering in the

returning particles in the separator leg in the lower portion.

Fig 3. Effect of the metallization rate on the critical adhesion temperature.

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

This activated adhesion potential, thus developed by the partially reduced iron oxide particle, enters the

particle separator on the path of eventual collision with the clean steel surface during initial accretion

formation or further accretion development. This kinetic behavior can be expressed mathematically

according to the following equation,

(T) real operation = 3.987, (dFe°/dt)2 -9.974,9 (dFe°/dt) + 7027,8 (2)

With a correlation R² of 0,7684, representing the reliability of industrial data more significant than 85%,

it is considered very acceptable because it is industrial data.

III. METHODOLOGY

At this point, the appropriate theoretical and thermodynamic basis for the proposed mechanism has

been established, and the empirical relationships between the critical temperature variables of adherence,

viscosity, and creep of the silicates formed during the collision of solid particles as well as with the impact

that exists between the particles and the surfaces of the particle separator two. The following sections

describe the steps to obtain the presented results.

IV. RESULTS

A. Sample preparation

To corroborate the observed system, solid industrial samples were taken from the accretions formed

inside the particle separators, as shown in Fig. 4. These samples were cut, roughened, and etched with a

12% sulfuric acid solution to reveal the flow lines of the formations of the different layers in the opposite

direction of the gas flow entering the mouth of the cyclone separator.

(a) (b) (c)

Fig 4. Sample of gas flow accretion and creep lines (center), samples taken from the thinner incoming tail, Image (a)

shows flow line and layers of deposited material when attacked with 12% sulfuric acid (side of the separator on the

right edge) and the side of the gas to the left of the image (b), which shows the accelerations formed by the collision

between particles, the image (c) shows the shape of the flow lines of the adhesions in the metallic crusts, at the point

where the impact speed decreases. This proposed mechanism complies with thermodynamics and the process

conditions for accumulations.

B. Proposed coefficient for iron oxide dust

Depending on the temperature range, the materials have a thermo creep constant McLean [9] 0-0.3 TM,

0.3-0.5 TM, 0.5-0.9 TM, and 0.9-1.0 TM. Where TM is the melting temperature of the pure element, in this

case, iron; based on this information, the following graph was obtained.

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

Table 2. Comparison of obtained calculation results.

Temperature (°C)

K Termo Creep

Temp. Creep

461

0,3

460

700

0,5

767

1400

0,9

1381

C. Influence of temperature on the thermal adherence constant

The value of the adhesion coefficient in the temperature range between 600°C and 700°C oscillates between

0.478 and 0.514 with a correlation of 0.977 for ceramic materials. These values are based on the range of

coefficients proposed by McLean for metals in a diffusion-controlled creep process to consider a similar

flow in liquid metals. These values are assumed to be related to a combined effect of the working pressure

on the temperatures, which also affects the particle velocity, gas molecular weight, and oxide properties,

such as a plastic-activated stage for any sticking tendency.

Fig. 5. Result of the thermo creep constant when working in a temperature range from 600°C to 700 ° C of 0.4784.

Once the operating temperature is obtained, the thermal creep constant is estimated. This value will be

crucial to know the temperature for the mathematical simulator, as shown in equation 3. In this equation,

KTc is represented as the constant of thermo creep, and Tr is the actual operating temperature in degrees

centigrade. This gives a dimensionless value.

= 0.5491 *ln(Tr) – 3.095 (3)

Using the temperature difference mentioned above, for the occurrence of thermoplasticity in the

considered system, in the temperature range 600 ° C (873K), to reach the melting point of the newly formed

iron required, the value of the system's thermo-creep constant with a value of 0.478. This value represents

a modification of the equation described by McLean applied to ceramic systems. Then, the modified

equation to define the appearance of yield stress in the study system can be represented by Equation 4 and

Figure 6.

Tc = 2.0921*Tr - 1E-12 (4)

0,2

0,4

0,6

0,8

400 500 600 700 800 900 1000 1100 1200 1300 1400

Creep constant (kTc)

Temp. (°C)

Temp. real Vs Termo Creep (k

)

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

Fig 6. Formation of thermal adhesion as a function of accurate operating temperatures.

D. Activation energy in the study system

The formation of adhesions in the form of shells in the cylindrical zone in the range of temperature and

pressure studied is possible in fluidized bed processes when working with molecular weights in the gas of

10 gr/mol. To develop the critical temperature for the thermoplasticity of the partially reduced particle, it is

necessary to assume a specific temperature gradient between the hot gases and the solid particle.

Therefore, this investigation took a difference of 30 degrees Celsius for heat transfer.

   













(5)

Figure 7 shows the thermal creep temperature on the vertical axis as a function of the thermal creep

constant used to visualize the change in temperature as a function of the Arrhenius activation energy.

Fig 7. Activation energy through the Arrhenius relation

Diffusional Control CD; CQ Chemical control; CM Mixed Control

In the case of collided particles, the activation energy values for the temperature range studied help

identify the predominant mechanism: dysfunctional control, mixed control, and chemical control.

The values obtained for the different mechanisms are as follows:

1.-Diffusinal Control

Log K = -0.013 * 1 / T + 0.0045 (6)

3.- Mixed Control

Log K = 0.052 * 1 / T + 0.0038. (7)

2. Chemical Control

Log K = -0.0008 * 1 / T + 0.0028

500

1000

1500

2000

250 450 650 850

Temp. Creep (

°C)

(Tc)

Temp. Real (°C)

(Tr)

Temp. real Vs Temp. Termo creep

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

The influence of temperature can be worked by following the particle collision theory described by

Arrhenius. In these graphs, chemical control is generated where the Bogging formation of accumulations in

the bed can occur. The first hypothesis is rectified: a diffusion control where occurs sintering and finally, a

mixed control is affected by the change in temperature and the constant of the thermal creep, the activation

energy is of the dysfunctional control 5.949 Kcal/mol pending 1.3 X10

; Chemical control 3,661Kcal / mol

pending 0.8X 10

and mixed control 4.805 kcal/mol pending 1.05X10

CONCLUSIONS

1. The application of particle collision theory has helped determine the energies generated for

the formation of adhesions in the particle separators in the range of 600 °C to 700 °C to

determine the formation of fayalite in systems that combine the presence of ferrous oxide, silica

and the presence of magnesium oxide.

2. The values of the adhesion coefficient for ceramic systems, such as the one studied. Within the

temperature range between 600 °C and 700 °C, it oscillates between 0.478 and 0.514 with a

correlation of 0.977. These values modify what Mc Clean proposes for metals by the range of

coefficients presented and already indicated and are applied in a diffusion-controlled creep

process to consider a similar flow in liquid metals for the case of thermospray.

3. This theoretical principle has made it possible to determine a creep temperature constant that

modifies McLean theory for ceramic types of metals when the energy released inside the

particle separator exceeds the transformation value of solid oxides to liquid and is sufficient so

that the oxides studied are susceptible to thermo-viscosity and consequent plasticity.

4. The results summarize the summation of the energies released inside the cyclone separator,

which is 660 KJ/mol higher than the 599 KJ/mol required to melt silicon oxide at 2000 ° C.

5. Applying the Arrhenius equation, it is possible to determine the activation energy for chemical

(CQ), dysfunctional (CD), and mixed (CM) control. As a result, an activation energy of 5.94

kcal/mol CD, 4.81 kcal/mol CM, and 3.66 kcal/mol CQ with a total activation energy of 14.41

kcal/mol for the formation of fayalite, a value very close to the theoretical value.

RECOGNITION

The authors are incredibly grateful to the Graduate Research Directorate at UNEXPO Puerto Ordaz for

the opportunity to carry out this research related to a focus on the thermoviscosity mechanism in the

formation of fayalite-type ceramic accumulations in particle separators in CFD reactors that occur at

temperatures below the eutectic point.

REFERENCES

[1] Á. Prada, (2014). Estudio aglomeración lecho fluidizado. 3-52.

[2] D. Fuller (1965). Fenómenos de Sinterización de finos en proceso de reducción directa. Puerto Ordaz

[3] Y. Zhang., Z. And, Ed Z. Guo., (2015). Apparent viscosity measurement of iron particles. 6th International

Symposium on High-Temperature Metallurgical Processing, 559-564.

[4] A. Echegaray (2021). Balance de energía en la formación de fayalita sub-eutéctica a altas presiones en

separadores de partículas. ORCID 0003-4234-0452.

[5] D. Gaskell (2003). Introduction to the Thermodynamics of Materials. New York: Taylor & Francis 695-696

[6] E. Ringdalen (2016). Softening and melting of SiO2 are essential parameters for reactions with quartz in Si

production 43-44.

[7] L. Murty, M, Gold, & A. Ruoff. (1970). High-Temperature Creep Mechanisms in an Iron Alfa and Other Metals.

41(12), 4917-4937.

[8] L. Chica, O. Bustamante and A. Barrientos (2013) “Disipación de energía mecánica en la descarga de un

hidrociclón: Nueva estrategia de modelo” revista Dyna año 80 Nro. 181 p.p 136-145 Medellín.

[9] D. McLean. (1966). The Physics of high-temperature creep in metals. Science, 1-33.

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Echegarai A. et al. Thermoviscosity mechanism approach in forming fayalite-type ceramic accumulations…

The Authors

Alberto R Echegaray R, Metallurgical Engineer, Graduated from Unexpo Puerto Ordaz of

Venezuela in 2002. Master Science in Metallurgy and Postgraduate in Simulation, Energy

Efficiency, Specialist in Maintenance Management. Studying a PhD in Engineering Science

at Unexpo. Member of the engineering college. I have worked since (1998) in Fior de

Venezuela. In (2000) I moved to the start-up group of Finmet Technology in Orinoco Iron

(Orinoco Briquetera) with the position of operation technician, technical assistant, and later

a Specialist in level IV process. I am currently working in the Energy Management

department attached to the Presidency.

Oscar G Dam G, Metallurgical Engineer graduated from Universidad Central de Venezuela

1972 Master Science in Metallurgy and Diploma (DIC) Graduated from the Imperial College

of Science and Technology 1977, England Doctor in Metallurgy graduated from the

University of London in 1983. Department of metallurgy at the Instituto Experimental de

Guayana since 1978. Postgraduate professor in materials science at Universidad Central de

Venezuela and at the Universidad Experimental de Guayana since 1984, external tutor for

postgraduate studies at the Instituto Venezolano de Investigación Científica.