ISSN-e: 2737-6419
Period: July-September 2025
Revista Athenea
Vol.6, Issue. 21, (pp. 56-66)
research article https://doi.org/10.47460/athenea.v6i21.106
Focus on the Thermoadhesion Mechanism in the Formation of
Fayalite-Type Ceramic Deposi t s i n Particle Separators of
Fluidized-Bed Reactors
Alberto Echegaray*
https://orcid.org/000-0003-4011-3301
echegaray.alberto@gmail.com
Universidad Nacional Experimental Polit
´
ecnica
Antonio Jos
´
e de Sucre
Ordaz, Venezuela
Oscar Dam
https://orcid.org/0002-0594-6757
oscarcurmetals@gmail.com
Universidad Nacional Experimental Polit
´
ecnica
Antonio Jos
´
e de Sucre
Puerto Ordaz, Venezuela
*Corresponding author:
echegaray.alberto@gmail.com
Received (11/08/2025), Accepted (12/09/2025)
Abstract. This study examines the thermoadhesive mechanism responsible for the formation of fayalite-
type ceramic deposits in particle separators within Ćuidized-bed reactors. The analysis focuses on the
inĆuence of temperature, pressure, and collision-induced energy on the changes in viscosity and plasticity
of the material system. Particular attention is given to operational conditions within the temperature
range of 450
◦
C to 750
◦
C and pressures exceeding 5 bar. The Ąndings suggest that deposit formation
occurs when the energy released during particle collisions increases the local temperature of the particles,
thereby reducing their relative viscosity and enhancing their plastic behavior. This transition promotes
adhesion and the subsequent accumulation of material on the internal surfaces of the equipment.
Furthermore, mathematical modeling, incorporating a modiĄed version of McCleanŠs creep theory, is
employed to estimate the critical conditions for deposit formation. These models provide valuable
insights for optimizing process design and operational control in industrial systems involving ceramic
materials.
Keywords: adhesion, particle collision, thermos-adhesion, relative viscosity, wustite.
Enfoque en el mecanismo de ter m oa d h esi ´on en la formaci´on de
dep´ositos cer´amicos de tipo fayalita en separadores de pa rt´ıculas de
reactores de lecho flui d i z ado
Resumen. Este art
´
ıculo analiza el mecanismo termo-adherente que conduce a la formaci
´
on de acumu-
laciones de fayalita en separadores de part
´
ıculas dentro de reactores de lecho Ćuidizado. La investigaci
´
on
se centra en c
´
omo factores como la temp eratura, la presi
´
on y la energ
´
ıa liberada en las c olisiones entre
part
´
ıculas inĆuyen en el cambio de viscosidad y la plasticidad del sistema, particularmente en rangos
de temperatura de 450
◦
C a 750
◦
C y presiones superiores a 5 bar. Se propone que estas adherencias
se forman cuando la energ
´
ıa de impacto calienta las part
´
ıculas, disminuyendo su viscosidad relativa
y favoreciendo su viscosidad pl
´
astica, lo que facilita su adherencia y acumulaci
´
on en las sup erĄcie s
internas del equipo. La utilizaci
´
on de modelos matem
´
aticos, basados en la modiĄcaci
´
on de la teor
´
ıa
de McCle an para la termoĆuencia, permite estimar las condiciones que ge neran estas adherencias, as
´
ı
como su potencial aplicaci
´
on en el dise
˜
no y control de procesos cer
´
amicos similares.
Palabras clave: adherencia, choque de part
´
ıculas, termo adherencia, viscosidad relativa, wustita
EchegarayA., and Dam O. Focus on the Thermoadhesion Mechanism in the Formation of Fayalite-Type
Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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I. INTRODUCTION
During the different iron ore manufacturing processes in which Ćuidized b ed technology is employed for
material processing [
1], these systems tend to operate under an intermittent regime. This intermittent
behavior is primarily caused by the phenomenon of de-Ćuidization, which occurs due to the adhesion
of partially reduced iron particles within the Ćuidized bed [2]. This de-Ćuidization is closely linked
to the formation of accretions on the internal metallic surfaces of cyclones. Such accretions result
from repeated collisions between particles at temperatures below the melting point of iron, thereby
interrupting the continuous Ćow and stability of the process.
In this context, the concept of particle interaction is associated with the phenomenon of apparent
viscosity [
3], which quantitatively expresses the resistance of iron-containing particles to creep movement
under plastic deformation. This concept encompasses multiple factors, including external frictional
interactions, cohesive forces such as Van der Waals forces, interfacial attractions, and liquidŰsolid
bridges, among others. However, these factors have not been fully integrated into current models
describing particle agglomeration phenomena in Ćuidized bed processes.
To better explain the formation of silicate adhesions within mechanical particle separators, this
study proposes a thermoadhesion approach. This approach posits that the energy released from the
collision and impact of particles on the separatorŠs internal surfaces generates localized heating. This,
in turn, induces changes in the viscosity of particulate materials, leading to a transition to a plastic
state that favors adhesion and accumulation on these surfaces.
Rheology, the branch of physics concerned with the deformation and Ćow behavior of matter Ů
ranging from simple liquids and solids to complex microstructured systems such as silicates Ů provides
the theoretical foundation for analyzing this process. Of particular interest are materials whose viscosity
varies as a function of the deformation rate within a speciĄc temperature range. These are known as
non-Newtonian Ćuids.
To address this apparent complexity, rheology is employed as it allows the de scription of Ćow
behaviors where viscosity is dependent on the rate of deformation. This theoretical framework links
the Ćow behavior of a material to its internal structure. For materials like silicates, this relationship
cannot be fully described using classical Ćuid mechanics or elasticity alone, thus requiring more advanced
rheological models to capture their behavior accurately.
II. DEVELOPMENT
The phenomenon under study occurs within a particle separator of a Ćuidized bed reactor during
the reaction between ferrous oxide (FeO) and metallic iron (Fe). This reaction takes place within
a temperature range of 450 °C to 750 °C and at pressures exceeding 5 bar. Under these operating
conditions, the mechanism involves the adhesion of materials, primarily FeO and SiO
2
, induced by the
energy released from particle collisions.
The proposed mechanism considers the behavior of rotating particles within the particle separator.
It is supported by mathematical formulations designed to describe the phenomena in terms of apparent
viscosity and the resulting plasticity. These parameters were evaluated through the analysis of adhesion
samples with a high concentration of ferrous oxide, which were collected from industrial processes
operating under similar conditions.
To characterize these adhesions, Bauman print-type macroetching techniques were employed. This
method allowed for the visualization of the distribution lines of non-metallic inclusions and the Ćow
patterns of the particles. The obtained observations provided essential insights into the dynamics of
adhesion formation and were instrumental in supporting the proposed theoretical model.
The mechanism of adhesion formation is described in terms of the conditions that favor changes in
apparent viscosity, ultimately leading to plasticity and Ćuidity of the material. These transformations
enable the development of the accretions observed in the collected samples. A schematic representation
of the proposed mechanism is presented in Figure
1, which illustrates the sequence of events leading to
the accumulation of material on the internal surfaces of the particle separator.
EchegarayA., and Dam O. Focus on the Thermoadhesion Mechanism in the Formation of Fayalite-Type
Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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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 thermos-adherence.
In this mechanism, the solid particles heat up during the conversion reaction of ferrous iron to
metallic iron. When these particles impact the steel surface and interact with its roughness, they
release sufficient energy (Fig.
1a), causing them to become viscous. This viscous material:
1. Crawls along the surface driven by the gas Ćow,
2. Superimposes over previous surface imperfections,
3. Creates pores and generates fayalite-type silicates (Fig.
1b).
By analogy, this is similar to a surface thermo-adhesion process.
A. Energy Balance
The energy balance, previously calculated and published in [
4], is summarized in Table 1.
Tabla 1. Energy balance within the particle separator
Symbol Meaning Unit (kJ/mol) Unit (kcal/mol)
E
c
Energy per impact 103 30
E
v
Energy per vacancy 474 113
E
p
Energy per particle collision 13 3
E
i
Energy due to inelastic collision 70 17
Total Total energy 660 163
The calculated total energy of 660 kJ/mol agrees with the reported energies for the formation of
fayalite [5], as well as with the softening point of silica, approximately 599 kJ/mol at 2000 °C [6].
This conĄrms that the formation of fayalite within the studied temperature range is thermodynamically
possible under intermediate viscous conditions.
B. Effect of Temperature on Apparent Viscosity
The total energy calculated is 61 kJ/mol greater than the 599 kJ/mol required for the softening
of SiO
2
. This matches the range of 61Ű65 kJ/mol, considered as the compensated activation energy
required for silicate particles to undergo deformation and creep.
The particles in the gas-solid mixture not only possess appropriate thermal conditions but also
contain iron particles undergoing a transient phase change from ferrous oxide (FeO) to metallic iron.
This transformation releases additional energy associated with vacancies.
When silica particles collide with wustite particles, they b ehave similarly to thermally coated particles
projected at high velocity onto a metal surface. Under these conditions, fusion reactions between the
particles are inevitable, ensuring the formation of the viscous phase required for adhesion.
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C. Adhesions of Silicate by Action of Fluence
The formation of a viscous FeO-SiO
2
phase, with minor amounts of MgO and metallic iron, occurs
under a gas velocity of approximately 75 m/s at the cyclone entry. This creates a deformation force
that induces thermo-viscous behavior, combined with creep.
Considering creep behavior requires knowledge of the melting temperature (T
m
) of metallic iron. The
studied temperatures ranged between 620 °C and 700 °C, which correspond to 0.3Ű0.5 T
m
. In this range,
creep behavior depends logarithmically on temperature and follows an Arrhenius-type relationship.
Using the slope-change method, activation energy for creep was calculated:
E
a
= 65 kcal/mol
When plotting the logarithm of deformation rate against the inverse of absolute temperature, a
linear relationship was obtained, resulting in:
E
a
= 62 kcal/mol
These values align with those reported for self-diffusion in this temperature range [
7].
D. Relationship Between Thermoplasticity and Creep
Since the activation energy for creep matches that of self-diffusion, the creep mechanism is controlled
by mixed diffusion. This involves the non-conservative motion of dislocations, including edge dislocations
and screw dislocations.
At the studied strain rates and temperatures, vacancy concentration remains near equilibrium, with
only minor perturbations.
Using data from [8], vacancy superheights were estimated for the range 150 °CŰ700 °C (0.23
T
m
Ű0.54 T
m
) at various creep rates. From thermodynamic considerations, the energy released by
deĄned particle sizes in the separator was quantiĄed.
Starting from CauchyŠs Ąrst law and multiplying both sides by viscosity (v):
ρ
D
Dt
v
2
2
= (∇ · T)v + f v (1)
If the body force is the gradient of a potential, f = −∇φ, then:
ρ
D
Dt
v
2
2
= (∇ · T)v + ρ
Dφ
Dt
(2)
Rearranging terms:
D
Dt
v
2
2
+ φ
= (∇ · T) · v + T : ∇v (3)
Here, the product T : ∇v represents viscous dissipation (E
V
).
The formation of cylindrical accretions above 750 °C and pressures over 10 bars is feasible when
the gas molecular weight is near 10 g/mol. These conditions validate that particle collisions release
enough energy to initiate thermoviscosity and soften the particles.
E. Effect of Temperature on Ferrous Transformations
Once the apparent viscosity and creep participation were quantiĄed, the next step was to analyze the
critical temperature for thermoplasticity onset. Partially reduced iron oxide particles heat up through
gas Ćow, creating a precondition linked to sticking tendency.
This tendency varies by mineral type and composition. Figure
2 illustrates the transition from
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Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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wustite to metallic iron, highlighting the effect of reduction rate on critical adhesion temperature.
Fig. 2. Transformation of ferrous iron into metallic iron in the studied area [9]. .
Depending on the reduction stage, hot particles exhibit varying sticking potentials, directly impacting
adhesion formation within the Ćuidized bed reactor.
The data used to develop Figure
3 were obtained from industrial tests conducted in a C.F.D. plant
using mixed Venezuelan and Australian mineral mixtures, as well as tests with 100% Australian mineral.
From this Ągure, it is possible to estimate the ranges of temperature values at which sticking of iron
particles occurs. These particles, partially metallized, exhibit adhesion behavior as a function of the
formation of metallic iron within the particle separators during their transfer into these systems. The
temperatures obtained can be assumed to represent actual working or operating conditions.
This temperature creates an activated state in the particles, predisposing them to different stages
of the sticking phenomenon (Figure
3), such as bogging or particle agglomeration in the Ćuidized
bed, crustal adherences in the upper cylindrical section of the particle separators, and sintering in the
returning particles located in the lower portion of the separator leg.
Fig. 3. Effect of the metallization rate on the critical adhesion temperature [9].
This activated adhesion potential, developed by the partially reduced iron oxide particle, enters the
particle separator along a trajectory that eventually results in collisions with the clean steel surface.
These collisions occur during the initial accretion formation or subsequent accretion development.
The kinetic behavior of this process can be mathematically expressed by Equation (
4):
EchegarayA., and Dam O. Focus on the Thermoadhesion Mechanism in the Formation of Fayalite-Type
Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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T
rop
= 3987
dFe
0
dt
!
2
− 9974
dFe
0
dt
!
+ 7027 (4)
where:
• T
rop
= Actual operating temperature (°C)
• Fe
0
= Metallic iron content
• t = Time
The correlation factor R
2
obtained for this model was 0.7684, representing a reliability of industrial
data greater than 85%, which is considered very acceptable given the inherent variability of industrial
processes.
III. METHODOLOGY
At this point, the appropriate theoretical and thermodynamic basis for the proposed mechanism has
been clearly established, as well as the empirical relationships between the critical adhesion temperature,
viscosity, and creep variables of the silicates formed during solid-particle collisions, as well as the impact
between the particles and the particle separator surfaces. Each of the steps taken to obtain the results
presented in the following section is explained below.
In the theoretical foundation of the thermos-adhesion phenomenon, this article establishes a solid
foundation of thermodynamic principles, viscosity physics, and mechanics of silicate behavior, focusing
on the formation of thermal adhesions in ceramic materials. The central hypothesis relates the relative
viscosity and plasticity of the system to the activation energy required for adhesion formation.
Sampling involved taking material samples adhering to the metal surface, speciĄcally in the cylindri-
cal area of the mechanical separator in the wustitic reactor. These samples underwent metallographic
analysis and a Bauman test to determine the stratiĄcation of the adhering layers. Additionally, chemical
composition analyses were performed to determine the initial conditions and relevant physical properties
of the samples.
In the operating conditions analysis, operational data were collected from production processes,
including temperature ranges, pressure, gas composition, working pressures, and material reduction
percentage. The impact of Ćow rate and thermal distribution within the reactor was also considered to
better understand the dynamic behavior of the system.
The process modeling was carried out using an Excel spreadsheet to simulate Ćow behavior and the
interaction between particles and surfaces in the mechanical separators. This modeling made it possible
to identify the areas of greatest adhesion and evaluate the inĆuence of variables such as temperature,
viscosity, and collision energy. The calculation of collision and adhesion energies was summarized in
a table, quantifying the contribution of each type of energy and the conditions under which adhesion
formation occurs, based on the theory of particle collisions and an adaptation of the McClean adhesion
equation.
The viscosity and plasticity analysis discussed in this study establishes a direct relationship between
the viscosity of the system and the formation of accumulations as a function of temperature and chemical
composition, applying rheological models speciĄcally developed for ceramic and silicate materials.
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 Figure
4, these samples were cut, roughened, and etched
with a 12% sulfuric acid solution to reveal the Ćow lines of the formations of the different layers in the
opposite direction of the gas Ćow entering the cyclone separator.
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Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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Fig. 4. Sample of gas flow accretion and creep lines. (a) Flow lines and layers of deposited
material attacked with 12% sulfuric acid. (b) Accelerations formed by the collision between
particles. (c) Flow lines of the adhesions in the metallic crusts, at the point where the impact
speed decreases.
This proposed mechanism meets both the thermodynamic and process conditions for accumulations
to occur.
B. Proposed coefficient for iron oxide dust
The materials, depending on the temperature range, have a thermos-adherence constant [
9] as follows:
0Ű0.3 T
M
, 0.3Ű0.5 T
M
, 0.5Ű0.9 T
M
and 0.9Ű1.0 T
M
. Here, T
M
represents the melting temperature of
pure iron, which is 1534 °C. Based on this information, the following results were obtained.
Tabla 2. Comparison of obtained calculation results
Temperature (°C) K Thermo Creep Temp. Creep (°C)
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 coefficient of adhesion 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 (Fig.
5). These
values align with those proposed by McLean for metals in a diffusion-controlled creep process, simulating
similar Ćow conditions to those of liquid metals.
This relationship assumes a combined effect of working pressure on temperature, which in turn
affects the particlesŠ velocity, gas molecular weight, and oxide properties, resulting in a plastic activated
stage responsible for the sticking tendency.
Fig. 5. Result of the thermos-adherence constant.
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K
Tc
= 0.5491 · ln(Tr) − 3.095 (6)
Where:
• K
Tc
= Adherence constant (dimensionless)
• Tr = Actual operating temperature (°C)
Using the temperature difference for the o ccurrence of thermoplasticity, in the range of 600 °C up
to the melting point of the newly formed iron, the value of K
Tc
obtained was 0.478. This represents a
modiĄcation of the McLean equation applied to ceramic systems.
The modiĄed equation to deĄne the appearance of yield stress in the studied system is represented
as:
Tc = 2.09121 · Tr − 10
−12
(7)
Where:
• Tc = Thermal adherence constant
• Tr = Actual working temperature (°C)
Fig. 6. Formation of thermal adhesion as a function of real operating temperatures.
D. Energy Activation in the Study System
The formation of adhesions as shells in the cylindrical zone, under the studied temperature and
pressure conditions, is feasible in Ćuidized bed processes when the gas molecular weight is 10 g/mol. A
temperature gradient of 30 °C between the hot gases and solid particles was assumed.
The Arrhenius equation used for modeling the activation energy is given by:
log K = log A −
E
A
R
·
1
T
(8)
Where:
• K = Reaction rate constant
• A = Molecular collision frequency
• E
A
= Activation energy (kcal/mol)
• R = Ideal gas constant
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Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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Fig. 7. Activation energy through the Arrhenius relationship. Diffusional Control (CD);
Chemical Control (CQ); Mixed Control (CM).
• T = Absolute temperature (K)
The activation energy values help identify the predominant mechanism:
1. Diffusional Control
log k = −0.013 ·
1
T
+ 0.0045 (9)
2. Mixed Control
log k = −0.052 ·
1
T
+ 0.0038 (10)
3. Chemical Control
log k = −0.0008 ·
1
T
+ 0.0028 (11)
E. Interpretation of Results
The temperatureŠs inĆuence follows particle collision theory as described by Arrhenius.
• Chemical control:Leads to bogging and particle accumulation in the bed.
• Diffusion control: Results in sintering phenomena.
• Mixed control: Affected by changes in temperature and thermal adherence constant.
The calculated activation energies are:
• Diffusional control: 5.949 kcal/mol (slope = 1.3 × 10
3
)
• Chemical control: 3.661 kcal/mol (slope = 0.8 × 10
3
)
• Mixed control: 4.805 kcal/mol (slope = 1.05 × 10
3
)
These values conĄrm the transition between different control mechanisms depending on the oper-
ating temperature and system conditions.
CONCLUSIONS
Analysis using particle collision theory reveals the energies required for adhesion in separators within
the temperature range of 600Ű700 °C. This process is fundamental for the formation of fayalite in the
presence of ferrous oxide, silica, and magnesium oxide.
The adhesion coefficients for ceramic systems such as the one studied, between 600 °C and 700
°C, range from 0.478 to 0.514, with a correlation of 0.977. These values differ from those proposed
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by McClean for metals but are consistent with the expected range and are applicable to a diffusion-
controlled creep process, analogous to the Ćow of liquid metals in thermal spraying.
Based on this theoretical principle, a yield point constant was determined, which modiĄes McLeanŠs
theory for ceramic metals. This modiĄcation is justiĄed by the energy released in the particle separator,
which, upon exceeding the transformation point from solid to liquid oxides, induces thermal adhesion
and plasticity in the oxides.
The results indicate that the energy released in the cyclone separator (660 KJ/mol) is signiĄcantly
higher than the fusion energy of silicon oxide at 2000 °C (599 KJ/mol), with an excess of 61 KJ/mol.
Finally, the application of the Arrhenius equation allowed the determination of the activation energies
for the chemical (CQ), diffusional (CD), and mixed (CM) controls, resulting in values of 5.94 kcal/mol
(CD), 4.81 kcal/mol (CM), and 3.66 kcal/mol (CQ), re spectively. The total activation energy for
fayalite formation was found to be 14.41 kcal/mol, a value very close to the theoretical prediction.
ACKNOWLEDGMENT
The authors are especially 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.
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AUTHORS
Alberto R Echegaray R, A metallurgical engineer, he graduated from Un-
expo in 2002, with advanced studies in metallurgy, simulation, energy
efficiency, and maintenance management. He also received his PhD in
Engineering Science in 2024. Since 1998, his professional career has in-
cluded positions of increasing responsibility in the steel industry (Fior de
Venezuela, Finmet/Orinoco Iron), from operations technician to process
specialist. He currently works in the Energy Management Department of
the PresidentŠs Office.
Oscar G Dam G, Metallurgical Engineer (UCV 1972) with a masterŠs degree
and Diploma (DIC) from Imperial College (1977), and a PhD in Metallurgy
(University of London 1983). He has been a Professor of Metallurgy at the
IUT Experimental de Guayana since 1978 and a Postgraduate Professor of
Materials Science at the UCV and UNEG since 1984. He is an external
postgraduate tutor at the IVIC.
EchegarayA., and Dam O. Focus on the Thermoadhesion Mechanism in the Formation of Fayalite-Type
Ceramic Deposits in Particle Separators of Fluidized-Bed Reactors
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