Coating of Refractory Surfaces with Fine TiO₂ Particles via Gas-Dynamic Cold Spraying

Abstract

Refractory materials are used worldwide in process equipment. However, gaseous and liquid process products penetrate the surface layer and deep into the volume of refractories, destroying rather expensive constructions that are complicated to repair. To address this challenge, there is a need to develop protective coatings for refractory materials that can limit the penetration of working media and extend their operational lifespan. In this work, the application of gas-dynamic cold spraying (CGDS) to produce a coating on the refractory materials using fine titanium dioxide (TiO₂) particles is explored. These particles are accelerated within a nitrogen flow, passing through a Laval nozzle, and then sprayed onto a fireclay surface. The mechanisms of particle deposition and layer formation on porous surfaces through experiments and numerical simulations were investigated. The geometry of a typical refractory pore was determined, which was then incorporated into computational fluid dynamics (CFD) simulations to model the cold spraying process of porous substrates. As a result, the influence of the particle size on its velocity and angle of penetration into pores was established. Experimental findings demonstrate the effective closure of pores and the formation of a particle layer on the refractory surface. Furthermore, the nanoindentation tests for the refractory samples showcase capabilities for checking coating thickness for porous materials.

1. Introduction

In existing industrial thermal setups, such as coke ovens, blast furnaces, heat boilers, kilns, and others, severe operating conditions prevail [1]. The main elements of these setups are heating partitions, refractory insulation, and lining, designed to transfer heat from the heating elements to the raw materials being processed and protect other structural elements from the adverse effects of high temperatures and aggressive mediums.

In these setups, thermally insulating elements are typically made from fireclay refractories, predominantly composed of SiO₂ (47%–64%) and Al₂O₃ (28%–45%), and other small inclusions of Fe₂O₂, TiO₂, CaO, MgO, and K₂O [2].

The technical state of the setup elements undergoes significant changes during the production process, leading to a notable reduction in their lifecycle [3,4]. The refractory elements are susceptible to degradation and breakdown due to a range of various external factors, including mechanical loads, exposure to diverse working environments, the formation of different corrosion products that exceed the initial volume of the refractory material, and significant temperature fluctuations [5,6,7,8,9].

Moreover, as thermal setups operate, the properties of refractory elements change due to the infiltration of gaseous and liquid byproducts formed during the processing of raw materials. These byproducts penetrate the surface layer through pores and pass deep into the refractory volume. Preventing such penetration and closing pores on the surface are essential for extending the operational lifespan of the refractory elements.

One effective approach to address this issue is to develop a protective layer on the surface of the refractory material, which reduces the penetration of the medium, and minimizes direct contact with gases, liquids, and solid substances during the operation of the equipment.

In current industrial practice, many types of coatings are employed, including ceramic coatings from viscous solutions based on thermally stable inorganic oxides [10], ceramic coatings obtained by “glazing” the outer working surface [11], adhesive insulating coatings (high-temperature adhesives) [12], bilayer alumina/mullite and mullite/alumina coatings deposited by atmospheric plasma spraying [13], coatings obtained by the crystallization of melts of high-temperature oxides [14], and coatings obtained from colloidal systems [15]. Numerous technologies for applying such coatings on the surface of refractory products are reduced to applying a liquid layer on the surface, which then crystallizes [16]. In this study [17], composite coatings based on titanium oxides were successfully prepared through a detonation spray process of the particles on fine-grained hyper-pressed concrete.

Nevertheless, obtaining hardware support for the application of these coatings poses several challenges. Moreover, highly heat-resistant coatings often exhibit low mechanical strength and high fragility. Consequently, protective coatings obtained through the mentioned methods may not entirely address the challenges related to the durability and tightness of refractories, necessitating further research and development [18].

The targeted alteration of the surface structure by particulate layers is a subject of current research [19,20,21], with cold gas-dynamic spraying (CGDS) being identified as an effective coating method [22,23]. Since its invention [22], the cold spray method has undergone continuous optimization for specific applications and is now an economically competitive method that is widely used in the industry for modifying metal surfaces. The principial advantage of CGDS lies in its relatively low operating temperatures compared to other thermal spraying methods. This characteristic makes CGDS particularly well-suited to mobile setups for repair work, where high temperatures may be impractical. Additionally, this method enables the restoration of components to their proper state by selectively applying a protective coating to the damaged surfaces [24].

Some studies demonstrated that CGDS has the potential to enhance corrosion resistance [23] and the frictional and wear-resistant properties of metal surfaces [25,26]. The authors of [27] found that for metal surfaces with a crater structure due to sandblasting, coating with ceramic particles is more effective. For Al surfaces, CGDS was successfully used by Yu et al. [28] to create resistant coatings of SiCp/Al 5056 composite.

Ma et al. [29] performed the coating of Al₂O₃ ceramic surfaces with copper particles using vacuum cold spraying and showed that this method provides a self-adaptive repair mechanism when depositing metal films onto rough ceramic substrates. In [30], the essence of the deposition mechanism of ceramic particles in cold spraying was revealed using energy analysis.

The available literature on cold spray with TiO₂ particles focuses on coatings of metal surfaces [31,32]. In our previous study [33], fine TiO₂ particles were deposited on Ti surfaces by cold spraying. In paper [34], the possibility of forming a TiO₂ layer on a sandblasted base of ceramic tiles (INAX ADM-155M) was demonstrated. Studies by Winnicki et al. [35] are devoted to the mechanical testing of TiO₂ coatings obtained by CGDS.

In contrast to the extensive research conducted on metal surfaces, the bonding mechanisms of ceramic particles to ceramic surfaces remain relatively understudied. It is assumed that due to the elastic-brittle properties of ceramic materials, the absence of plastic deformation and the possible breakage during impact make the coating of ceramics with ceramic particles ineffective. Chakrabarty et al. [36] simulated ceramic deposition and bonding in metal–ceramic composite (AlMg₃, SS304) cold spray, which demonstrated that crater depth is a critical factor in determining ceramic bonding.

In this work, CGDS was used for the coating of refractory surfaces with ceramic TiO₂ particles. Unlike metallic surfaces, refractory materials have an open pore structure and behave dominantly brittle, which can result in completely different mechanisms of the coating formation (Figure 1).

During the cold spray coating process, fine solid particles are accelerated within a supersonic gas flow generated by a Laval nozzle and collide with the porous substrate, penetrate into the pores, and fill them. Upon impact, the particle kinetic energy is converted into the deformation and heat of the particle and the substrate body. The characteristics of the coating are determined by the complex interplay of transport phenomena in the multiphase flow, including the acceleration of particles within the jet, as well as material deformation and adhesion during particle impact on the surface and on previously deposited particles.

TiO₂ powder is readily available within the desired particle size range, significantly smaller than the pore size, and is uncritical concerning safety aspects and costs. Furthermore, the thermal expansion coefficients of TiO₂ and fireclay closely align in values [2,37].

The objective of this study is to achieve the deposition of TiO₂ particles onto the porous surface of the refractory material and to analyze the properties of the resulting initial layer. This experimental investigation is supported by numerical simulations that examine the acceleration behavior of fine particles within a gas flow passing through a Laval nozzle and being subsequently sprayed onto the porous surface of the refractory. The efficacy of pore filling on the surface is also thoroughly evaluated.

2. Materials and Methods

2.1. Analysis of Spraying Particle Properties

In this work, TiO₂ particles (thermally stable rutile from Sigma-Aldrich, St. Louis, MO, USA) were employed for the coating of the refractory surface. The particle size distribution of TiO₂ powders (Figure 2a) was determined using a light-scattering method with a laser diffraction spectrometer (HORIBA LA-950V2, Retsch, Haan, Germany) in the range of 0.2–1.2 µm with a mean diameter of 0.524 µm and median size of 0.49 µm. The particle size distribution was described by the Weibull function (also known as Rosin–Rammler function simulation used in CFD to generate particles in a Laval nozzle) as follows:

$$Q_3\left(x_p\right)=1-{\exp \left(-{\displaystyle \frac{x_p}{x_0}}\right)}^n$$

(1)

where $Q_3\left(x_p\right)$ is the cumulative volume-related distribution function, $n$ is the shape parameter, and $x_0$ is the characteristic particle size, defined as the size at which 63.2% of the particles are smaller.

The fitting curve displayed in the figure is characterized by the following equation function parameters: x₀ = 0.54 µm (indicated by a red marker in Figure 2a) and n = 3.78.

As depicted in the image (Figure 2b) and captured using scanning electron microscopy (SEM) (Hitachi SU8000, FEI Helios NanoLab 650) with magnification ranging from 45 to 1,000,000×, basically the TiO₂ particles have an angular shape.

The thermophysical material properties, sourced from [37], are presented in

Table 1. Properties of TiO₂ particles.

Property	Units	Value
Density	kg·m−3	4260
Specific heat capacity (at 25 °C)	J·kg−1·K−1	683
Thermal conductivity (at 25 °C)	W·m−1·K−1	4.8

.

2.2. Analysis of Properties and Structure of the Substrate

The substrate samples were sourced from raw refractory fireclay bricks, brand SHV-42, produced at “Chasiv Yar Refractory Works” (Chasiv Yar, Ukraine). The fireclay composition contents were SiO₂ (54.8 ± 0.5%), Al₂O₃ (42.0 ± 0.5%), Fe₂O₃ (1.7 ± 0.2%), TiO₂ (0.5 ± 0.1%), K₂O (0.7 ± 0.15%), Na₂O (0.15 ± 0.01%), and CaO (0.16 ± 0.02%).

The thermophysical properties of fireclay refractories, as provided in [2], are listed in

Table 2. Properties of the fireclay.

Property	Units	Value	Ref. Temp., °C
Specific heat capacity	J·kg−1·K−1	833	100
Specific heat capacity	J·kg−1·K−1	1251	1500
Thermal conductivity	W·m−1·K−1	1.6	25
Thermal conductivity	W·m−1·K−1	1.7	200
Thermal conductivity	W·m−1·K−1	1.9	600
Thermal conductivity	W·m−1·K−1	2.0	800

.

SEM images of a fireclay surface in its initial state are depicted in Figure 3. The surface reveals cracks, craters, and medium pores (macropores) predominantly located between grains. Additionally, fine pores (micropores) are observed on the grains and along the walls of the macropores. Some areas exhibit pore channels formed by groups of pores. Notably, a distinct group of pores comprises cracks formed during the firing process of manufacture.

The bulk density of the fireclay samples was determined gravimetrically. It amounted to 1872 kg/m³. Their true density of 2404 kg/m³ was measured with a Quantachrome Ultrapyc 1000 Gas Pycnometer. The obtained values of true and bulk densities were used to estimate the porosity of samples, as described in [38]. The porosity was determined to be 0.22 ± 0.01.

For the experiments, cuboidal samples measuring 3 mm × 4 mm × 1.5 mm (as illustrated in Figure 4) were precisely cut and subsequently cleaned using compressed air.

To assess the fundamental geometric parameters of refractory pores, the substrate microstructure has been analyzed using computed microtomography (µCT). µCT of samples was performed using an X-ray device, a TomoScope L (Werth Messtechnik GmbH, Giessen, Germany, minimum voxel size of 500 nm). Figure 4 displays typical sections of the sample in both horizontal and vertical planes. The YZ plane aligns with the upper face of the sample, which is where the coating was applied.

The analysis of parameters characterizing the pores was conducted by the post-processing self-developed application “MVT µCT Analysis Tool”, which is based on the MATLAB R2021b Imaging Processing Toolbox, where the function “regionprops” evaluates pores’ properties according to a 2D image (hereinafter—2D method) and the function “regionprops3” performs it according to a 3D volumetric image (hereinafter—3D method).

Using the 2D method, pore parameters, such as projection-area-equivalent diameter and minimum and maximum Feret diameter were estimated. Meanwhile, the 3D method was employed to determine the volume-equivalent sphere diameter and porosity. Porosity was calculated as the ratio of the total volume of all pores to the volume of the sample. The obtained value of fireclay porosity, which equals 0.21, closely aligns with the previously mentioned value of 0.22 ± 0.01 (as noted in Section 2.1). The slight discrepancy of 4.6% can be attributed to the limitations of the µCT resolution with a voxel size of 0.5 µm, which restricts the accurate detection of smaller pores.

The size parameters of the pores obtained by µCT analysis are summarized in

Table 3. Pore size parameters of fireclay sample obtained from µCT images.

Pore Size	Volume-Equivalent Sphere Diameter 1, µm	Projection-Area-Equivalent Diameter 2, µm	Minimum Feret Diameter 2, µm	Maximum Feret Diameter 2, µm
Average	22.6 ± 0.7	58.8 ± 0.2	61.1 ± 0.2	107.0 ± 0.4
Median	17.5	52.2	45.1	80.0
Percentile 95%	52.5	164.2	198.7	360.2

¹ 3D analysis; ² 2D analysis.

. These dimensions were subsequently utilized to construct a geometric model of the porous surface for use in the numerical simulation of the cold spraying process, as outlined in Section 2.5.

Figure 5 presents cumulative and differential distributions of pore sizes based on various measurements: minimum and maximum Feret diameters, projection-area-equivalent diameter, and volume sphere-equivalent diameter. The ratio of the average minimum and maximum Feret diameters (Table 3) is 1.75. This shows that mainly the pores in fireclay are not round but rather elongated shapes.

In addition, it can be seen that the average value of the projection-area-equivalent diameter is slightly less than the average value of the minimum Feret diameter, which is associated with a large number of pores that are elongated in shape.

Projection-area-equivalent-diameter values are more than two times the corresponding values of the volume-equivalent sphere diameter. This occurs because the 2D method considers only one section, whereas the 3D method averages values over multiple sections. As a result, the 2D method yields a significantly higher equivalent diameter than the volume-equivalent sphere diameter calculated by the 3D method.

To construct the geometric model of pores, average values of the minimum and maximum Feret diameters, equal to 61 µm and 107 µm respectively, were employed.

2.3. Setup for the Cold Spray Experiment

The coating of the fireclay substrate surfaces with TiO₂ particles was performed with the cold spray setup shown in Figure 6. This setup was developed in our previous works for the coating of metal surfaces with TiO₂ particles [33,39].

The flow of nitrogen, used as the carrier gas, was compressed to 9 bar and submitted to a pressure tank. The TiO₂ powder was fed into the gas stream through a powder disperser (Topas SAG 409, Dresden, Germany) installed in the pressure tank. The gas mass flow was 0.85 g/s, while the mass flow of TiO₂ particles was 4 mg/s. Prior to the experiments, the powder underwent drying at 80 °C for 48 h. The gas-solids stream was heated to a temperature of 573 K at the nozzle inlet using a preheater and main heater. Subsequently, the aerosol was accelerated to supersonic velocities through the Laval nozzle and sprayed onto the substrate. The geometry of the Laval nozzle was optimized for efficient acceleration of TiO₂ particles in our previous work [40]. It possessed an orifice of 0.8 mm (throat) and 1.5 mm (outlet) in diameter and a total length of 30 mm (Figure 7). The movement of the fireclay substrate was fulfilled relative to the nozzle in the plane perpendicular to the spray direction at a distance of 5 mm using two linear motors with a velocity of 10 mm/s. The time required for one pass of the nozzle along the substrate was 7 s, with a step of 0.65 mm between each pass. The sample velocity was adjusted to prevent the formation of a solid covering layer on the surface, enabling the investigation of pore-filling mechanisms.

2.4. Analysis of Fireclay Surfaces through Nanoindentation Tests

Nanoindentation tests were conducted on refractory surfaces to examine alterations in their mechanical properties after the spraying of a TiO₂ layer. For these tests, a TI premier nanoindenter (Hysitron) with a Berkovich diamond indenter tip was utilized. For the investigation of the fireclay surface, a high-load indenter (3D OmniProbe) was used. The experiments were conducted with a maximum peak force of 1 N, with a loading time of 20 s, a holding time of 10 s, and an unloading time of 20 s, respectively. A low-load indenter (nanoDMA transducer) was employed to examine the thin TiO₂ coating. The indentations were conducted with a peak force of 5 mN, a loading time of 10 s, a holding time of 5 s, and an unloading time of 10 s.

Prior to conducting the experiments, calibration of the tip area and frame compliance was carried out on fused quartz. A minimum of five tests was conducted in order to ensure meaningful reproducibility. The Oliver and Pharr method [40] was used to determine Young’s modulus E and hardness H from the indentation load-displacement data. This method involves fitting the unloading portion of the load-displacement data to a power-law relationship derived from elastic contact theory [41]:

$$P{=\mathsf{\beta }(h-h_f)}^m$$

(2)

where $\mathsf{\beta }$ and m are empirically determined fitting parameters, $h$ is the indenter displacement, and h_f is the plastic deformation obtained from the curve fit.

The contact stiffness $S$ can be calculated by differentiating the fit of the unloading curve and evaluating the result at the maximum penetration depth $h=h_{max}$ as

$$S{={\left({\displaystyle \frac{dP}{dh}}\right)}_{h=h_{max}}=\mathsf{\beta }m(h_{max}-h_f)}^{m-1}$$

(3)

Assuming that deformation is negligible, an elastic model shows that the amount of indentation$h_s$ is given by

$$h_s={\displaystyle \frac{\epsilon P_{max}}{S}}$$

(4)

where $P_{max}$ is the maximum applied force, and $\epsilon$ is a constant that depends on the geometry of the indenter: $\epsilon$ = 0.75 for Berkovich indenters [42].

The contact depth is determined using the following equation:

$$h_c=h_{max}-h_s=h_{max}-{\displaystyle \frac{\epsilon P_{max}}{S}}$$

(5)

In nanoindentation, the hardness of the material is defined as

$$H={\displaystyle \frac{P_{max}}{A_c}}$$

(6)

where $A_c$ is the projected contact area of the indenter obtained by measuring the indentation depth $h_c$ and inserting it into the calibrated fit [43]:

$$A_c=3\sqrt{3}t{an}^2\left({\displaystyle \frac{\alpha }{2}}\right)h_c^2=24.56h_c^2$$

(7)

where $\alpha$ is the angle of the Berkovich indenter: $\alpha$ = 130.6°.

An intriguing aspect of the nanoindentation technique is its ability to calculate both the hardness and the elastic modulus of the material. The elastic stiffness $S$ of the contact is used to calculate the reduced Young’s modulus:

$$E_{red}={\displaystyle \frac{S}{2}}\sqrt{{\displaystyle \frac{\pi }{A_c}}}$$

(8)

The Young’s modulus of the sample E_s is calculated by the following relationship:

$${\displaystyle \frac{1-{\nu }_s^2}{E_s}}={\displaystyle \frac{1}{E_{red}}}-{\displaystyle \frac{1-{\nu }_i^2}{E_i}},$$

(9)

where v_i and v_s are the Poisson’s ratio of the indenter and the sample (fireclay or TiO₂ coating). The mechanical properties of the diamond indenter tip were ${\nu }_i$ = 0.07 and $E_i$ = 1140 GPa. For the investigated fireclay and TiO₂ coating, Poisson’s ratio was set to 0.2 and 0.28, respectively.

2.5. CFD Setup

To gain a deeper insight into the behavior of TiO₂ particles at the inlet of pores on the fireclay surface, simulations of fluid flow and particle motion from the Laval nozzle inlet to the collision point with the substrate’s porous surface were conducted. CFD with Lagrangian particle tracking was used to determine the velocities and penetration angles of particles into pores, as well as the temperatures of both the flow and the particles.

A model consisting of a nitrogen flow with TiO₂ particles in a Laval nozzle and a porous fireclay substrate with open pores on the surface (Figure 7) was generated.

During the calculation, the nozzle is assumed to be not movable. The geometric parameters of the model are presented in

Table 4. Geometric parameters of the model.

Parameter	Value, mm	Parameter	Value, mm
hpch	15.5	hn.1	4.5
hn	30.0	hn.2	25.5
hgap	5.0	l	0.107
dn.1	8.0	b	0.061
dn.0	0.8	h	0.107
dn.2	1.466	s	0.220
		φ	120°

. The dimensions of the Laval nozzle and the sample correspond to the experimental setup. The pore is shaped like a parallelepiped, tapering at the bottom at an angle of 120°. The pore sizes (b × l × h), as determined in Section 2.2, are 61 µm × 107 µm × 107 µm, respectively. A single row of 11 pores was simulated, arranged radially from the nozzle axis with a step (s) of 220 µm. The distance from the lower edge of the Laval nozzle to the substrate was set at 5 mm.

The influence of the nitrogen fluid on the disperse phase (TiO₂ particles) was considered in the simulation. The particles were generated at the inlet of the Laval nozzle. The initial temperature and velocity of the particles match those of the nitrogen flow at the nozzle inlet, which are 573 K and 2.85 m/s, respectively. The mass flow rate of the powder is 4 mg/s. The solid boundaries of the flow field within the Laval nozzle were defined using a constant wall roughness of 0.5 µm [39].

To establish the inlet boundary condition of the fluid flow, a pressure of 9 bar and a temperature of 573 K were specified, consistent with the experimental parameters outlined in Section 2.3. For the outlet boundary condition, an ambient pressure of 1 bar and a temperature of 298 K were employed. The k-ω SST turbulence model [44] was utilized, along with scalable wall functions and 5% turbulence intensity.

Nitrogen was modeled as compressible flow, with its density calculated according to the ideal gas law [45], and the heat capacity was assumed to vary with temperature.

Heat transfer from the flow side and the temperature gradient in the substrate were determined by solving the energy equations:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho E\right)+\nabla ·\left(\overrightarrow{v}\left(\rho E+p\right)\right)=\nabla ·\left(k_{eff}\nabla T+\left(\stackrel{̿}{\tau }·\overrightarrow{v}\right)\right)$$

(10)

where $\rho$ is the density, $\overrightarrow{v}$ is the flow velocity, $p$ is the flow pressure, $k_{eff}$ is the effective conductivity ${k+k}_t$, where $k$ is the thermal conductivity, $k_t$ is the turbulent thermal conductivity, defined according to the turbulence model being used, $T$ is the flow temperature, and $\stackrel{̿}{\tau }$ is the dissipation stress-energy tensor. The right-hand side of Equation (4) represents energy transfer due to conduction and viscous dissipation, respectively.

In Equation (4), $E$ is internal energy, which is defined as

$$E=H-{\displaystyle \frac{p}{\rho }}+{\displaystyle \frac{{\overrightarrow{v}}^2}{2}}$$

(11)

where $H$ is enthalpy.

Due to the small concentration of TiO₂ particles (2.81·10⁻⁹ g/mm³) in the flow, their impact on the flow itself can be disregarded. The trajectory of particle motion is determined by integrating the balance of acting forces in

$$m_p{\displaystyle \frac{d{\overrightarrow{v}}_p}{dt}}={\overrightarrow{F}}_g{+{\overrightarrow{F}}_b+\overrightarrow{F}}_d$$

(12)

where $m_p$ is the particle mass, ${\overrightarrow{v}}_p$ is the particle velocity, ${\overrightarrow{F}}_g$ is the gravitational force, acting on a particle in a flow, ${\overrightarrow{F}}_b$ is the buoyancy force, and ${\overrightarrow{F}}_d$ is the drag force [46].

The drag force on a particle is calculated by the following equation:

$${\overrightarrow{F}}_d={\displaystyle \frac{\rho }{2}}{C}_d{A}_p(\overrightarrow{v}-{\overrightarrow{v}}_p)\left|\overrightarrow{v}-{\overrightarrow{v}}_p\right|$$

(13)

where $C_d$ is the drag coefficient, and $A_p$ is the cross-section of the particle (the particle is assumed to be spherical).

The drag coefficient is described as a function of the particle Reynolds number, ${Re}_p,$ which is calculated by the following equation:

$${Re}_p={\displaystyle \frac{\rho \left|\overrightarrow{v}-{\overrightarrow{v}}_p\right|d_p}{\mathsf{\mu }}}$$

(14)

where $\mathsf{\mu }$ is the dynamic viscosity of the fluid, determined using the Sutherland model [47].

The drag coefficient for the Stokes regime (${Re}_p$ ≤ 0.25) is calculated by the following equation:

$$C_d={\displaystyle \frac{24}{{Re}_p}}$$

(15)

The influence of the slip on the motion of fine particles was considered with a Cunningham correction factor in the drag force according to the model described in [48]. It is assumed that the particles are evenly distributed at the entrance to the Laval nozzle.

3. Results and Discussion

3.1. SEM and µCT Analysis of the Cold Sprayed Refractory Samples

The objective of the experiment was to investigate the mechanism of pore filling. Therefore, particle flow rate, sample velocity, and the number of nozzle passes were set as to prevent the formation of a coating layer on the surface and complete closure of the pores. Spraying of the sample was carried out in five stages. During each stage, five passes of the nozzle were made along the entire surface for 35 s. Subsequently, the spraying was halted, the sample was removed from the setup, and SEM images of the surface were obtained. This process was repeated for each stage of spraying. Figure 8 shows the image of the sample before the spraying process (Figure 8a) and the images of the different sample areas obtained at each of the five stages of spraying (Figure 8b–f).

In Figure 8a, the characteristic porous structure of the refractory, as described in Section 2.2, is evident. During the first stage of spraying (Figure 8b), TiO₂ particles (depicted as white spots) enter micropores and cracks, becoming attached through mechanical interlocking within the cavities. In Figure 8c, the spraying process progresses, with particles continuing to fill the surface of larger pores. Additionally, they begin to bond with deposited particles, forming aggregates. However, no fixed particles are observed on the grains; only individual particles adhere to the inner pore walls. In Figure 8d, a layer of particles is observed on the surface, with particles attached to each other. At this stage, the closing of macropores initiates from the periphery towards the center. The particles not only fill the macropores but also form bridges over them, which are crucial for pore closure and the creation of the first particle layer. Similar mechanisms of pore filling and first-layer formation have been observed in surface filtration processes using a porous filter medium, as demonstrated by Hund et al. [49]. On the grains protruding above the surface, only the individual particles are visible.

The central area of macropores larger than about 20 µm in size remains unclosed (Figure 8e). To close these large pores, it is necessary to continue the spraying process.

Upon completion of the cold spraying process, the surface exhibits significant modification (Figure 8f), although the coating is not uniformly deposited. The post-spraying images reveal that particles are deposited both on the surface of the refractory and within the pores. Notably, fine pores (with a width of up to ~5 mean particle diameters) are effectively filled with TiO₂ powder. Interestingly, particles within a size range of 0.2–0.5 µm are observed on the surface, while larger particles penetrate deep into the pores due to their higher kinetic energy. It is assumed that the fixation of particles within pores occurs as a result of their plastic deformation upon the impact with the substrate, as well as due to high adhesive forces upon collision with each other [50,51] and with the surface of the substrate [52,53].

Figure 9 shows the µCT scan images of a fireclay sample following TiO₂ cold spraying (the position of the section is shown in Figure 4). In Figure 9a, the pink areas represent TiO₂ particles. Figure 9b illustrates three distinctive zones where the coating has formed. In the first zone, the pore features gently sloping walls, and the layer of particles entirely fills the pore cavity, resulting in an almost flat surface above it. In this zone, the coating thickness equals the pore depth. On flatter areas (zone 2), the thickness of the coating is uniform. In the third zone, characterized by pores with steep walls, particle deposition occurs, leading to gradual closure of the pore from the periphery to the center. This phenomenon may be attributed to a sharp deceleration of the gas flow in such pores, leading to the formation of a high-pressure zone and, consequently, a deceleration of the particles.

3.2. Results of Nanoindentation Tests

Several indentations were performed on both the initial fireclay sample (Figure 10a) and the coated one (Figure 10b). Crack development at the edges of the Berkovich tip imprint (Figure 10a) confirms the brittle material behavior of the sample. Figure 10b shows a layer of TiO₂ particles after nanoindentation, with no visible cracks. The geometry of the imprint on the coated sample does not correspond to the Berkovich tip shape due to the elastic recovery of the layer during unloading. This indicates that the surface layer formed by the particles is elastically–plastically deformed and adheres well to the surface of the fireclay.

Figure 11 presents force-displacement curves of both coated and uncoated fireclay samples when a nanoindenter tip penetrates a pore and grain. Each curve represents typical results of indentation measurements made at different points of the samples (twelve indentation points for the uncoated sample and eight points for the coated one).

The force curves show the presence of pop-in effects, indicating the entry of the nanoindenter into micropores and microcracks within the sample. In an experiment involving an uncovered pore, these effects are particularly noticeable. They occur when the nanoindenter disrupts the pore wall along its path and enters the next one.

The force curve corresponding to the uncoated grain (depicted in blue) shows a higher slope, suggesting a higher surface stiffness. Conversely, the force curve for the coated grain (depicted in red) exhibits a smaller slope, indicating that the nanoindenter penetrates to a greater depth under the same force. In the initial segment of this curve, the nanoindenter traverses the coating layer with minimal resistance, mainly disrupting bonds between particles rather than the particles themselves. Subsequently, in the following segment, the indenter penetrates the fireclay substrate as evidenced by the slope of this segment being similar to that of the force curve for the uncoated sample. The change in slope angle, marked by the red indicator on the red curve, corresponds to the thickness of the sprayed layer on the fireclay surface. As observed, the thickness of the sprayed layer aligns closely with the mean diameter of TiO₂ particles (0.54 μm), consistent with measurements from µCT analysis (Section 3.1).

In comparison to previously described cases, at penetration in an uncoated pore, the nanoindenter achieves greater depth at the same force, evidenced by a smaller slope in the force curve (depicted in green). The indenter traverses the pore cavity and disrupts its partitions, as indicated by the observed pop-in effects.

As a result of the tests, the elastic modulus and hardness of the coated and uncoated fireclay samples were determined. The elastic modulus for an uncoated sample (in the grain zone) falls within the range of 12.3–19.6 GPa, while the hardness is in the range of 0.6–1.05 GPa.

To determine the mechanical characteristics of a pore packed with TiO₂ particles, indentation was performed for a penetration depth up to 1.2 µm.

Figure 12 illustrates the positions of nanoindentation (a) and the results of the test (force-displacement curves for the coated pore) (b).

For all three cases of indentation, the area enclosed by the loading and unloading curves is large compared to the area under the unloading curve, indicating a significant plastic component in the deformation of a pore packed with particles. Based on the test results, the TiO₂ layer within the pore has an elastic modulus of 8.26 ± 0.5 GPa and a hardness of 0.152 ± 0.009 GPa.

The behavior of the sprayed surface of fireclay during nanoindentation, characterized by the absence of pop-in effects on the curves and their smaller slope, demonstrates the effective filling of pores already during the formation of the first layer of deposition.

3.3. CFD Simulation Results

The CFD simulations yielded distributions of overpressure and temperature (Figure 13), the Y-component (along the Laval nozzle axis), and the Z-component (tangential to the substrate surface) of gas velocity (Figure 14), along with the magnitude of particle velocity (Figure 15). Notably, the Y-velocity features negative values as per the model’s coordinate system (Figure 7).

The distributions of the pressure and temperature of the fluid flow in the expanding part of the nozzle (Figure 13) demonstrate a gradual decrease. This phenomenon occurs because thermal energy is converted into kinetic energy as the fluid expands. The gas flow after exiting the Laval nozzle begins to decelerate. Then, when it comes into contact with the substrate, it is heated to 550 K in the region of central pore #0 and to 525 K in pores #1–3 (Figure 13b). Simultaneously, the pressure in the region of the first two pores (#0, #1) reaches approximately 550 kPa (Figure 13a), decreasing rapidly after pore #3. Although the pressure at the nozzle inlet is 9 bar, the upper limit of the scale in Figure 13a is constrained to 6 bar to provide a more detailed representation of the pressure distribution at the pore inlet.

Of particular interest is the behavior of the fluid flow in the contact zone with the sample surface in the area of pores.

Over the substrate surface, along the axis of the flow, there is a notable deceleration in the Y-velocity from ~790 m/s to ~50 m/s (Figure 14a). Simultaneously, there is a significant increase in temperature from ~298 K to ~570 K (Figure 13b), coupled with a rise in pressure from ~34 kPa to ~550 kPa (Figure 13a). This can be attributed to converting a portion of the flow’s kinetic energy into thermal energy, subsequently heating both the flow and the substrate due to interaction in the stagnation zone. Such a zone, characterized by a sharp change in flow parameters, is relatively small, approximately 2 mm in diameter and around 0.6 mm high from the substrate surface along the nozzle axis, and encompasses pores #0–3.

The total velocity magnitude of the fluid flow (Figure 15a) decreases along the flow axis, similar to its Y-component (Figure 14a), over a distance of ~0.6 mm above the substrate surface, diminishing from 800 m/s to 100 m/s. Within the pores, this velocity further decreases to ~30 m/s. Upon exiting the stagnation zone, the flow proceeds along the surface of the substrate with a Z-velocity greater than a Y-velocity. The increase in fluid flow velocity in the Z direction in the boundary layer (above the substrate surface) commences after pore #1; in the region of pore #3, it achieves 460 m/s; and it peaks at its maximum (540 m/s) in the area around pore #5 (Figure 14b). Additionally, the flow maintains a high speed within the boundary layer, with its height not surpassing the extent of the stagnation zone. Notably, excessively high Z-velocity can result in the separation of particles that have settled on the surface due to significant shear forces.

In the particle velocity diagram (Figure 15b), high velocities of up to 600 m/s are observable in the central pore #0, while velocities of up to 300 m/s are evident in pores #1–3. Moreover, all particles have Re < 0.25, as was accepted in Equation (10). The density of particle trajectories indicates a reduction in the number of particles entering the offset pores.

Due to the greater inertia of the particles, their velocity above the substrate surface differs significantly from the flow velocity. Therefore, for a detailed analysis of particle motion in this zone, the data from ANSYS Fluent were stored in a separate file and analyzed with the software package “Statistica 12” (see Section 3.2).

3.4. Distribution of Sprayed Particles across the Pores

Analysis of particle trajectories calculated by the Lagrangian tracking method enabled the acquisition of parameters concerning the movement and temperature of particles penetrating the pores.

Figure 16 shows the quantitative distribution of particles over pores #0–10, radially located from the central axis of the nozzle. Out of the total 12,530 particles generated at the entrance to the Laval nozzle, 98.7% of particles successfully reached the substrate surface. The particles were considered to have penetrated the pores if their center coincided with or was below the surface.

Figure 17 shows the characteristics of the motion of particles entering pores, including the central pore #0 and the offset pores #1–4. For each pore, the following parameters are depicted: number fraction (percentage by total particle amount and by particles entering pores); particle diameters and temperature; X-, Y-, and Z- velocity components; velocity magnitude; and particle penetration angle. The colored bars represent the statistical characteristics: minimum and maximum values, median and mean values, and standard deviation (sd).

The radial distribution of the particle size within pores occurs due to the size-dependent motion of particles in the jet flow, which spreads upon collision with the surface (Figure 14 and Figure 15). The larger particles tend to move vertically and remain in the center of the jet due to their higher inertia. Indeed, the average particle diameter that enters the central pore is about 0.925 μm, with a small deviation of ±0.010 μm. Smaller particles, due to their lower inertia, tend to deviate more from vertical movement and are carried by turbulent vortices over longer distances. Consequently, they reach pores that are situated further away from the center of the nozzle. This phenomenon results in an increased fraction of fine particles in pores #1–4 compared to larger particles, which are more likely to concentrate near the center of the jet.

For the central pore, the horizontal X- and Z-components of the particle velocity are minimal, indicating negligible rotation of the flow. However, as the distance from the flow axis increases, the Z-velocity increases while the Y-velocity decreases, suggesting a change in flow direction away from the nozzle axis. By the second offset pore, the average Z-velocity exceeds 140 m/s, which is more than 70% of the Y-velocity. In pores 3 and 4, the horizontal Z-component becomes greater than the vertical Y-component.

As a particle penetration angle in the pores has been considered an angle between the resulting Y-Z particle velocity vector and the vertical axis Y (angle α in Figure 17). This angle influences the contact condition of the particle with surfaces inside the pore and the filling mechanism. A larger angle suggests a higher likelihood of the particle colliding with the side (vertical) wall of the pore. Conversely, a smaller penetration angle indicates deeper penetration of the particle into the pore, leading to a collision with its bottom.

As one moves radially away from the center axis of the nozzle, the angle at which particles penetrate the pores increases significantly. For the particles entering central pore #0, the average angle is close to zero, suggesting a nearly vertical penetration, whereas for offset pores, it ranges from 7.7° (pore #1) to 72.6° (pore #4), indicating a much more oblique penetration and predominant collision with the side walls of the pores.

The temperature of particles entering the central pore is notably lower compared to those entering pores #1–3. This distinction can be attributed to the size-dependent behavior of particles in the flow since particles entering pore #0 are larger and do not have time to heat up while passing through the elevated temperature zone near the surface. In contrast, smaller particles are transported over longer distances by turbulent vortices and have more opportunities to interact with the heated flow, leading to their faster heating.

The size distribution of particles entering the pores (Figure 18) reveals the following insights. For central pore #0 (Figure 18b), particles of large diameters predominate, since they are more inertial and can change their trajectory slowly. For pore #1 (Figure 18a), two size fractions can be distinguished: 0.2–0.6 µm (20% of particles entering the pore) and 0.6–1.2 µm (80% of particles entering the pore). The number of particles entering pores #2 and #3 is very small (3.5% and 1.4% of the total number of particles in the first four pores, respectively).

The velocity distributions of penetrated particles presented in Figure 18 and Figure 19 provide further insights into their behavior. In pore #0 (Figure 19b), particles with a Y-velocity ranging from 650 to 700 m/s dominate (69% of the particles entering the pore). Meanwhile, pore #1 (Figure 19a) exhibits a bimodal velocity distribution: particles with velocities below 500 m/s comprise 71% of those entering the pore, while particles with velocities above 550 m/s make up the remaining 29%.

In the central pore (Figure 20b), particles with a Z-velocity in the range of −2–2 m/s (88% of particles entering the pore) are prevailing, i.e., the particles penetrate pore #0 almost vertically (normal to the surface). In pore #1 (Figure 20a), for the majority of particles (86%), the Z-velocity falls within the range of 10–50 m/s. Thus, the Z-velocity distribution of particles entering pore #0 exhibits velocities with an order of magnitude lower compared to those in pore #1, as confirmed by the values of penetration angles (Figure 17). The radial distribution of the Z-component of particle velocity is nearly symmetrical due to the symmetric generation of particles at the entrance to the nozzle, generated evenly distributed along the radius.

Figure 21 shows the change in the magnitude velocities of the particles. Given that the Z-component is significantly smaller than the Y-component, the magnitude velocity distributions in the pores closely align with the Y-component.

Figure 22 illustrates the distributions of the particle penetration angle relative to the vertical axis. At the entrance to pore #0, nearly 97% of the particles exhibit an angle less than 1° (Figure 22b). Conversely, for particles entering offset pore #1 (Figure 22a), the angle value increases notably, with approximately 45% of them having 2–6° and 28% of the particles falling within the range 6–15°; the angle of the remaining 27% of particles are in the range of 15–90°.

Figure 23, Figure 24 and Figure 25 indicate the influence of particle diameter entering pores on their movement parameters and temperature. A confidence interval of 95% was used for the calculation. For the parameters of particles in the area of pore #1 compared to pore #0, the spread of the obtained values is significantly larger. This disparity arises from the flow decelerating as it moves away from the nozzle axis, causing particles to alter their motion direction and leading to increased dispersion in particle movement.

As depicted in Figure 23a, the temperature of particles decreases with an increase in their diameters. This occurs because large particles, having cooled in the nozzle flow (Figure 13), do not have sufficient time to heat up in the stagnation zone near the surface, where temperatures are high. Conversely, small particles also cool in the flow but have ample time to heat up near the surface before entering the pore. Differences in the temperature trend for particles entering pores #0 and #1 are noticeable for diameters exceeding 0.4 μm, which correlates with disparities in their velocities (Figure 23b).

Figure 23b illustrates the averaged velocity magnitude of particles entering pores #0 and #1 as a function of their diameter. For both pores, the velocity magnitude of particles with a diameter of 0.2–0.5 µm uniformly increases to 450 m/s. However, differences in the trend of the curves emerge for particles with a diameter exceeding 0.4 μm. For pore #0, as the diameter increases, the velocity rises and reaches 690 m/s (for particle diameters of 1.2 μm). In contrast, the curve profile of velocity magnitude for particles entering pore #1 peaks at 480 m/s (for particle diameters of 0.5 μm). Subsequently, a reverse trend is observed, with the velocity decreasing to 220 m/s (for particle diameters of 1.2 μm). This phenomenon can be explained by the differing behaviors of fine and large particle fractions. Fine particles (0.2–0.5 μm) accelerate quickly, approaching the gas velocity, but slow down rapidly upon reaching the pore due to the significant drop in gas velocity in that region. On the other hand, large particles (0.5–1.2 μm) accelerate less, failing to reach gas velocity, but experience minimal slowing down in the stagnation zone above the pores due to their greater inertia. It is evident that the velocity of particles with a diameter of 0.2–0.5 μm is greatly influenced by the movement characteristics of the gas flow and the velocity of particles with a diameter of 0.5–1.2 μm depends more strongly on their inertial properties.

Figure 24 shows the averaged Y- and Z-velocity of particles entering pores #0, and #1 as a function of their diameter.

Upon comparing the trend of the behavior of the Y-velocity in Figure 24a, it is noticeable that values of this velocity resemble the values of the velocity magnitude (Figure 23b) for both pores. This suggests a substantial contribution of the Y-component to the overall velocity magnitude.

The values of the Z-velocity (Figure 24b) for sprayed particles differ significantly from other components of the velocity magnitude. For pore #0, Z-velocity of the penetrating particles is very small since they almost do not move along the substrate surface (perpendicular to the axis of the nozzle). The maximum Z-velocity value for particles with a diameter of 0.2–0.5 μm is only −2 m/s, and for particles with a diameter of 0.5–1.2 μm, the value of Z-velocity is almost equal to 0. At the entrance to pore #1, the Z- velocity of the particles increases significantly because the flow abruptly changes direction and begins to move along the surface of the substrate. For fine particles (diameter range of 0.2–0.5 μm), the Z-component decreases from 120 to 40 m/s, and for large ones (diameter range of 0.5–1.2 μm), it is in the range of 40–25 m/s.

Figure 25 shows the averaged penetration angle of particles entering pores #0 and #1 as a function of their diameter. A comparison of the penetration angles of the sprayed particles in pores #0 and #1 demonstrates a significant difference in the direction of their movement. For the central pore, this angle is approximately 4° for fine particles (diameter range of 0.2–0.5 μm) and is nearly equal to zero for large ones (diameter range of 0.5–1.2 μm) (Figure 25b). Meanwhile, for the offset pore #1, the penetration angle reaches 40° for small particles and is 10° for large ones (Figure 25a).

The joint analysis of the distributions of Z-velocities (Figure 24b) and particle penetration angles (Figure 25) reveals that for pore #0, both large and small particles move toward the bottom of the pore. However, for pore #1, most of the fine particles tend to move towards the side walls.

Analysis of the behavior of particles entering the pores revealed two distinct groups: the fine particle fraction (diameter range of 0.2–0.5 μm) and the fraction of larger particles (diameter range of 0.5–1.2 μm). The movement and temperature characteristics of the fine particle fraction are primarily influenced by the parameters of the gas flow, while the behavior of the large particle fraction is influenced more by their inert properties.

It should also be noted that at a distance between the central pore #0 and offset #1 (220 μm), there are strong changes in the nature of the particle movement. Specifically, the Z-velocity increases by a factor of 30, and the penetration angle increases by a factor of 10, while the value of the magnitude velocity decreases by a factor of 1.5.

4. Conclusions

In this work, the deposition of TiO₂ particles on the porous surface of refractory (fireclay) material has been studied. The objective of this study was to investigate the mechanisms of the deposition of particles within the porous structure and the formation of adhesive layers on the surface. Fine pores (up to approximately five times the maximum particle diameter) are completely “bricked up” by deposited particles, effectively sealing the surface. The closing of larger pores occurs gradually as the layer forms from the periphery to the center of a pore, forming a particle layer on the surface.

Nanoindentation tests allowed us to determine the mechanical properties of the particle layer and demonstrated the method’s capability for testing the coating thickness on porous materials.

By CFD simulation of the cold spraying process, the main factors influencing the parameters of particle movement when they enter the pores were established:

• The radial distance between the pore and the central axis of the nozzle jet increases this distance. A significant drop in the average particle velocity and an accompanying increase in the particle penetration angle into the pores are observed.
• The diameter of the sprayed particles has a large impact since larger particles tend to enter the pores at higher velocities, while smaller particles exhibit larger penetration angles due to their higher susceptibility to changes in flow direction and turbulent effects.
• The stagnation zone is located over the substrate surface along the nozzle axis, encompassing the first four pores (radial distance of approximately 660 µm), and is characterized by a sharp change in flow parameters, causing significant changes in particle trajectories.

Based on the established trends in particle motion in the gas flow and the pore-filling mechanism, it is recommended to make a step between nozzle passes of 0.3 times the outlet nozzle diameter. This will ensure the high-quality closure of the pores with sprayed particles.

Thus, a straightforward yet deliberate alteration of the microstructure of the porous refractory surface is possible through the cold spray process. It can be used to close the pores, thereby impeding medium penetration deep into the volume of the refractory material. The presented method can be extended to other non-metallic porous materials. The process can also be combined with post-thermal treatment to increase the adhesion of the deposited particles and sinter them with the base substrate.