Multi-Physics Simulation and Optimization of Jet Electrodeposition for Ni–Diamond Composite Coatings

Abstract

This work investigated the influence of current density, plating solution flow rate, and nozzle outlet-to-cathode distance on the properties of Ni–diamond composite coatings. A multi-physics field simulation was employed to analyze the interplay between current density, plating solution flow rate, and nozzle outlet-to-cathode distance on the flow field and electric field distribution. Additionally, particle tracing simulations were incorporated into the model to evaluate the incorporation efficiency of diamond particles during composite electrodeposition. It was found that when the inlet flow rate of the electrolyte was 5 L/min, the distance between the nozzle outlet and the cathode was 3 mm, and the current density was 60 A/dm², the composite electrodeposited coating had a higher particle content and better uniformity. The simulation results were validated through experimental preparation and performance testing. This combined approach provides valuable insights for optimizing the jet electrodeposition process for Ni–diamond composite coatings with superior properties.

1. Introduction

To increase the wear resistance and corrosion resistance, as well as to improve the hardness of cutting tools, the surface of cutting tools is often coated with a diamond composite [1,2]. The jet electrodeposition method can be used to prepare composite coatings under a normal temperature and pressure environment, accurately and efficiently controlling the electrodeposition area. The content and uniformity of the incorporated diamond in the coating are related to process parameters such as current density, particle concentration, electrolyte flow rate, nozzle structure, power supply, addition of particle dispersants, and electrolyte temperature [3]. Conducting experimental research one by one will consume considerable manpower, material resources, and financial resources. Simulation methods have been used to study and optimize process parameters and to obtain good results. Using finite element analysis to simulate composite electrodeposition can facilitate parameter optimization, reduce the number of experiments, and save material and financial resources. Tognia et al. [4] developed a finite element method (FEM) model with error control and adaptive meshing using the UMFPACK solver in COMSOL Multiphysics 4.3b software. Through simulations, this model facilitated the fast and accurate determination of optimal parameters for uniform electrodeposition of various metals onto tubular coal-based carbon membranes. Pandey [5] performed a numerical study using COMSOL Multiphysics to study the effect of applied voltage and interelectrode gap on the deposition rate of nickel from an electrolyte. Cui et al. [6] simulated the jet fluid process by using FLUENT 13 software, and dynamic simulations of the jet rate of the plating solution were performed during fabrication of Ni-doped SiC nano-coatings during the JED process. Pérez [7] designed a laboratory filter-press flow cell with parallel plate electrodes for nickel electrodeposition onto mild steel from a dilute solution. Transport equations were solved in 3D by the finite element method using the commercial code COMSOL Multiphysics. Xia et al. [8] prepared Ni-doped SiC composites with a jet electrodeposition technique, in which the nozzle-fluid velocity of the plating solution was simulated by ANSYS 18.0 software. Ni/TiN composite coatings were prepared using jet pulse electrodeposition [9]. The research results indicated that flow rate was a key factor influencing the nanoparticle content in composite coatings by flow field simulation. High flow rates generate a large impact force that can dislodge loosely adsorbed particles from the surface, decreasing the nanoparticle content of the composite coating. Fu et al. [10] established a flow field and electric field model of nickel-based coating by jet electrodeposition and obtained the deposition thickness at different scanning speeds.

Some authors have simulated the deposition flow field or electric field, but simulation with particle tracing has rarely been reported. Some studies only simulated the influence of a single process parameter, and other process parameters were not studied. This work investigated the influence of current density, plating solution flow rate, and nozzle outlet-to-cathode distance on the properties of Ni–diamond composite coatings. A multi-physics field simulation was employed to analyze the interplay between current density, plating solution flow rate, and nozzle outlet-to-cathode distance on the flow field and electric field distribution. Additionally, particle tracing simulations were incorporated into the model to evaluate the incorporation efficiency of diamond particles during composite electrodeposition.

2. Simulation

2.1. Simulation Model

A 2 mm × 10 mm slot nozzle was used for composite electrodeposition. The geometry model is shown in Figure 1. The physical model and geometry of the nozzle are shown in Figure 1a and 1b, respectively. A and B are the inlet and outlet diameters of the tapering part, respectively. C is the length of tapering part, and D is the distance between the nozzle outlet and the workpiece. The nozzle model was established using COMSOL Multiphysics 6.1 software, and Figure 1c shows the model of nozzle for simulation. Due to the symmetric structure of the nozzle, a 2D axisymmetric model was employed. The anode and cathode were defined, and the inlet and outlet of the flow field are shown in Figure 1c.

For the simulation, three factor variables and three level parameters were set, namely current density (40, 50, and 60 A/dm²), the inlet velocity of electrolytes (5, 8, and 11 L/min), and the nozzle-to-cathode distance (D = 1, 2, and 3 mm). The inlet diameter was 12 mm, and the cavity height was 20 mm. The nickel density was 8.902 g/cm³, the nickel electrochemical equivalent was 1.095 g/Ah, the electrolyte conductivity was 0.5 S/cm, the electrolyte viscosity was 0.001 Pa, and the electrolyte density was 1100 kg/m³. The density of the diamond powder particles was 3510 kg/m³, and the number of charges carried was 0.

2.2. Theoretical Basis of the Multi-Physics Simulation

After the geometric model was created, mesh partitioning was performed. Multi-physics field coupling was used for simulation, which included cubic current distribution, the Nernst–Planck equation, turbulent flow field, the k − ε equation, fluid flow particle tracking, and other basic theories.

2.2.1. Electric Field Theory

In the electric field model, the preparation of metal-based diamond composite coatings used the “Tertiary Current Distribution (TCD) physical field and Nernst–Planck Equation” to study the transient electric field. The flux of each ion in the electrolyte can be calculated using the N–S equation [11]. The N–S equation can be used to describe the motion of the electric field and fluid, and it can be seen as an extension of Newton’s second law F = ma, which can be obtained as follows:

$${\displaystyle \frac{\partial c_i}{\partial t}}+\nabla ·N_i=R_{i,tot}$$

(1)

$$N_i=-D_i\nabla c_i-z_i{u}_{m,i}F{c}_i\nabla {\mathrm{\varnothing }}_l+c_{i}u=J_i+c_{i}u$$

(2)

In the formula, $N_i$ represents the total flux of i species (SI unit: mol/(m²·s)). The flux in the electrolyte is described by the Nernst–Planck equation, which involves multiple calculations of charged ion flux through diffusion, integration, and convection, as shown in Formula (2). Here, $c_i$ (SI unit: mol/m³) is the concentration of ion i, $z_i$ is the number of charges carried by the ion, $D_i$ (SI unit: m²/s) is the diffusion coefficient, $u_{m,i}$ (SI unit: (s∙mol)/kg) is the migration rate, $F$ (SI unit: As/mole) is the Faraday constant, ${\varnothing }_l$ (SI unit: V) is the electrolyte potential, $u$ (SI unit: m/s) is the velocity vector, and $J_i$ represents the molar flux relative to convective transport.

$$J_i=-D_i\nabla c_i-z_i{u}_{m,i}F{c}_i\nabla {\mathrm{\varnothing }}_l$$

(3)

Net current density describes the total flux of all types:

$$i_l=F\sum z_i{N}_i$$

(4)

where $i_l$ (SI unit: A/m²) is the current density vector.

The model simulates the electrodeposition process in a weakly acidic environment, with lower concentrations of Ni²⁺and SO₄²⁻ in the electrolyte solution. In terms of material balance, there is no need to consider the influence of proton factors. Assuming that the current is completely converted during the redox reaction process, it indicates that there will be no other reactions occurring during the model simulation process. During the electrodeposition process, the difference in cation density of the electrolyte solution gradually becomes clear because the density in the anode area is higher than that in the cathode area, forming a natural convection phenomenon. However, in this experiment, the nickel ion concentration was consumed at the negative extreme, while the positive extreme was continuously replenished. The electrolyte ion concentration changed very little, and the effect of natural convection could be neglected in the simulation model.

The simulation was for the transient change process. During the electrodeposition process, as the thickness of the deposition layer increases, the cathode boundary continuously moves, which indicates the evolution of the electrodeposition process. This model is defined by the material balance and electrical neutrality conditions of the relevant ions (Ni²⁺ and sulfate SO₄²⁻). This generates three unknowns and three model equations, with the dependent variables being nickel ion concentration, sulfate ion concentration, and ion potential. Additional variables are used to track the deformation of the mesh.

2.2.2. Flow Field Theory

In the flow field model, the preparation of metal-based diamond composite coatings requires the use of “turbulent, k − ε (SPF) physical field”, which studies the transient flow field and adopts the Navier–Stokes equation [12]. The k − ε model is a commonly used turbulence model in industrial applications. The model references the transport equation and two dependent variables, which are turbulent flow energy k and turbulent dissipation rate ε, respectively. The turbulent viscosity model is represented by the following equation:

$${\mathsf{\mu }}_{\mathrm{T}}=\mathsf{\rho }{\mathrm{c}}_{\mathsf{\mu }}{\displaystyle \frac{{\mathrm{k}}^2}{\mathsf{\epsilon }}}$$

(5)

here, ${\mathrm{c}}_{\mathsf{\mu }}$ is model constant. The transport equation for K:

$$\mathsf{\rho }{\displaystyle \frac{\partial \mathrm{k}}{\partial \mathrm{t}}}+\mathsf{\rho }\mathrm{u}·\nabla \mathrm{k}=\nabla ·\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{T}}}{{\mathsf{\sigma }}_{\mathrm{k}}}}\right)\nabla \mathrm{K}\right]+{\mathrm{P}}_{\mathrm{K}}-\mathsf{\rho }\mathsf{\epsilon }$$

(6)

$${\mathrm{P}}_{\mathrm{K}}={\mathsf{\mu }}_{\mathrm{T}}\left[\nabla \mathrm{u}:\left(\nabla \mathrm{u}+{\left(\nabla \mathrm{u}\right)}^{\mathrm{T}}\right)-{\displaystyle \frac{2}{3}}{\left(\nabla ·\mathrm{u}\right)}^2\right]-{\displaystyle \frac{2}{3}}\mathsf{\rho }\mathrm{k}\nabla ·\mathrm{u}$$

(7)

$$\mathsf{\rho }{\displaystyle \frac{\partial \mathrm{k}}{\partial \mathrm{t}}}+\mathsf{\rho }\mathrm{u}·\nabla \mathsf{\epsilon }=\nabla ·\left[\left(\mathsf{\mu }+{\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{T}}}{{\mathsf{\sigma }}_{\mathsf{\epsilon }}}}\right)\nabla \mathsf{\epsilon }\right]+{\mathrm{C}}_{\mathsf{\epsilon }1}{\displaystyle \frac{\mathsf{\epsilon }}{\mathrm{k}}}{\mathrm{p}}_{\mathrm{k}}-{\mathrm{C}}_{\mathsf{\epsilon }2}\mathsf{\rho }{\displaystyle \frac{{\mathsf{\epsilon }}^2}{\mathrm{k}}},\mathsf{\epsilon }=\mathrm{e}\mathrm{p}$$

(8)

$$\mathsf{\rho }(\mathrm{u}·\nabla )\mathrm{u}=\nabla ·\left[-\mathsf{\rho }\mathrm{l}+\mathrm{k}\right]+\mathrm{F}$$

(9)

$$\nabla ·\left(\mathsf{\rho }\mathrm{u}\right)=0$$

(10)

$$\mathrm{k}=(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{T}})(\nabla \mathrm{u}+{(\nabla \mathrm{u})}^{\mathrm{T}})-{\displaystyle \frac{2}{3}}(\mathsf{\mu }+{\mathsf{\mu }}_{\mathrm{T}})(\nabla ·\mathrm{u})\mathrm{l}-{\displaystyle \frac{2}{3}}\mathsf{\rho }\mathrm{k}\mathrm{l}$$

(11)

where k is turbulent kinetic energy, ε is the turbulent energy dissipation rate, P_k is the energy generation term, $\mathrm{u}$ (SI unit: m/s) is the average velocity vector, P (SI unit: Pa) is the pressure, µ (SI unit: N·s/m²) is the dynamic viscosity, ρ (SI unit: kg/m³) is the fluid density, F (SI unit: N) is the volumetric force, and Cµ = 0.09, C_ε1 = 1.44, C_ε2 = 1.92, σ_k = 1.0, and σ_ε = 1.3.

The k − ε equation is derived under the assumption that the flow has a sufficiently high Reynolds number. If this condition is not satisfied, then the values of k and ε are both small and exhibit chaotic behavior, as small perturbations in the flow field can lead to significant changes in the relative values of k and ε.

2.2.3. Particle Tracking Theory

In the fluid flow particle tracking model, the preparation of metal-based diamond composite coatings requires the "fluid flow particle tracking (FPT) physical field", which studies particle tracking in transient states. The combination of Brownian motion force and drag force causes particles to diffuse from areas with higher numerical density to areas with lower numerical density. The particles follow Newton’s second law, which means that the combined force acting on the object is equal to the time derivative of the linear momentum of the object in the inertial reference frame.

$${\displaystyle \frac{d\left(m_{p}v\right)}{dt}}=F_D+F_g+F_{ext}$$

(12)

$$\mathrm{v}={\displaystyle \frac{\mathrm{d}\mathrm{q}}{\mathrm{d}\mathrm{t}}}$$

(13)

where $m_p$ (SI unit: kg) is the particle mass; $v$ (SI unit: m/s) is the particle velocity; $\mathrm{q}$ (SI unit: m) is the particle position; and $F_D$, $F_g$, and $F_{ext}$ (SI unit: N) are the resistance, gravity, and other forces of particles, respectively.

In the COMSOL implementation, when the particle mass is solved as an additional degree of freedom, accretion or evaporation can occur, and the mass is moved beyond the time derivative to prevent the non-physical acceleration of the particles:

$$m_p{\displaystyle \frac{dv}{dt}}=F_D+F_g+F_{ext}$$

(14)

The flow field is calculated through the “turbulence” interface. In this model, the force exerted by particles on the fluid is ignored, so it is possible to solve the flow field in only one study and then use a separate study to calculate the particle trajectory based on the results of that flow field. There are significant transient phenomena in the model, which means that if the model is to be solved sequentially, a large number of time steps must be stored. Therefore, solving particle trajectories and flow fields in a single transient research step is a more attractive method.

2.3. Electric Field Simulation

With multi-physics software, when the current density was 60 A/dm² and the inlet velocity of electrolyte was 5 L/min, the thickness change of the coating on the brass substrate after 5 s of electroplating at different distances between the nozzle outlet and cathode was simulated. Figure 2 shows the distribution of electric field lines during the process of electrodeposition. The electric field lines were densest at the nozzle mouth, which was conducive to obtaining a thicker coating.

When the distance between the nozzle outlet and the cathode were 1 mm, 2 mm, and 3 mm respectively, the distributions of the surface coating thickness of the brass sheet under the conditions of jet electrodeposition for 0 s, 1 s, 2 s, 3 s, 4 s, and 5 s were simulated, as shown in Figure 3a–c. As a result, it was found that with the increase of jet electrodeposition time, the thickness of coating also increased. Figure 3d shows the difference in coating thickness with the distance between the nozzle outlet and the cathode when the jet electrodeposition was applied for 5 s. It was found that the shorter the distance between the nozzle outlet and the cathode was, the thicker the coating thickness, which is line with reference [13]. When the distance between the nozzle outlet and the cathode was 1 mm, the thickness of the coating reached the maximum of 0.052 μm. This is because the shorter the distance between the nozzle outlet and the cathode was, the shorter the distance for metal ions to be reduced to the cathode, which accelerated the reduction reaction, resulting in an increase in electrodeposition rate and a faster increase in coating thickness. For the case where inert diamond particles were added to the solution, with the reduction reaction acceleration, the greater the amount of diamond particles trapped and embedded on the surface of the coating.

Using multi-physics software, when the inlet velocity of electrolyte was 5 L/min and the distance between the nozzle outlet and the cathode was 3 mm, the thickness changes of the coating on brass sheets after 0 s, 1 s, 2 s, 3 s, 4 s, and 5 s of jet electrodeposition were simulated under current densities of 40, 50, and 60 A/dm², respectively. The simulation results are shown in Figure 4a–c. It can be seen that as the current density gradually increased, the thickness of the coating on the surface of the cathode brass sheet also increased. When the current density reached its maximum value of 60 A/dm², the thickest coating thickness was 0.018 μm. This was a result of an increase in current density. Figure 4d shows the difference in coating thickness with current density when jet electrodeposition was applied for 5 s. It was found that the larger the current density was, the greater the coating thickness, which is consistent with reference [14]. According to Faraday’s law, coating thickness is directly proportional to the current density.

2.4. Flow Field Simulation

2.4.1. Velocity Simulation of Flow Field

Using multi-physics software simulation, the flow field of electrodeposition was analyzed and solved, and the velocity change results of electrolyte solution on the cathode surface at different distances between the nozzle and cathode were obtained when the inlet velocity of electrolyte was 5 L/min and the current density was 60 A/dm². Figure 5a–c show the velocity distribution of the nozzle outlet at a distance of 1 mm, 2 mm, and 3 mm to the cathode when the time was 5 s. Figure 5d–f show the enlarged velocity distribution in the nozzle outlet area of Figure 5a–c, respectively. It can be observed that the velocity fluctuation on the cathode surface during the jet electrodeposition was relatively small, which helped to improve the uniformity and consistency of the coating. In order to more intuitively represent velocity fluctuation, the speed value at a distance of 0.2 mm from the surface of the cathode plate was collected to reflect the speed change of the electrolyte solution flowing through the coating surface during the electrodeposition process, as shown in Figure 6a. It was found that as the distance between the cathode and nozzle decreased, the velocity value of the electrolyte solution flowing through the surface of the brass plate increased. When the distance between the cathode and nozzle was 3 mm, the velocity at the nozzle mouth was smoother at 4.15 m/s, which was conducive to particle deposition on the surface of the coating. At different nozzle inlet flow rates, after 5 s of electrodeposition, the velocity change of the electrolyte solution on the cathode surface was simulated. Figure 6b shows the velocity at a position 0.2 mm above the cathode when the nozzle inlet flow rates were 5, 8, and 11 L/min respectively. It was found that as the nozzle inlet flow rate increased, the velocity value of the electrolyte solution flowing through the surface of the brass plate increased. When the nozzle inlet flow rate was 5 L/min, the velocity fluctuation at a position 0.2 mm above the cathode was the minimum, which was conducive to particle deposition on the surface of the coating.

2.4.2. Simulation of Pressure Distribution

Using multi-physics software simulation, the pressure distribution of electrolyte solution in the nozzle outlet area was obtained under different distances between the cathode and nozzle and different nozzle inlet flow rates when the inlet velocity of electrolyte was 5 L/min and the current density was 60 A/dm². Figure 7a–c show the pressure distribution of the nozzle outlet and cathode at distances of 1 mm, 2 mm, and 3 mm when the time was 5 s. It can be seen from this that the greater the distance between the nozzle outlet and the cathode, the smaller the pressure fluctuation on the cathode surface. The pressure fluctuation at a distance of 0.2 mm from the cathode is shown in Figure 8. It can be seen from the figure that the pressure at the nozzle was the highest, and the pressure at the outlet of the cathode plate was weakening.

From Figure 8a, it can be observed that as the distance between the cathode and nozzle decreased when the nozzle inlet flow rate was 5 L/min, the pressure value of the electrolyte solution flowing through the surface of the brass plate increased. When the distance between the cathode and nozzle was 3 mm, the pressure at the nozzle outlet was 6150 Pa, which was smoother and conducive to particle deposition on the surface of the coating. Figure 8b shows the pressure at a position 0.2 mm above the cathode after 5 s of electroplating when the nozzle outlet and cathode were at distance of 3 mm and the nozzle inlet flow rates were 5, 8, and 11 L/min, respectively. It was found that as the nozzle inlet flow rate increased, the pressure value of the electrolyte solution flowing through the surface of the brass plate increased. When the nozzle inlet flow rate was 5 L/min, the pressure fluctuation at a position 0.2 mm above the cathode was the minimum, which was conducive to particle deposition on the surface of the coating.

2.5. Multi-Physics Coupling Simulation

Figure 9 shows the tracking of diamond particles in the solution after 3 s of jet electrodeposition at different distances between the nozzle and cathode when the nozzle inlet flow rate was 5 L/min and the current density was 60 A/dm², with multi-physics software being used for simulation. When the distance between the nozzle outlet and the cathode was 1 mm, as shown in Figure 9a, most of the particles in the solution adhered to the nozzle mouth, and the particle movement speed on the surface of the cathode plate reached the maximum value of 0.0913m/s. When the distance between the nozzle outlet and the cathode was 2 mm, as shown in Figure 9b, the particles in the solution were evenly distributed within the cathode area, and the particle movement speed on the surface of the cathode plate reached the maximum value of 0.0863 m/s. When the distance between the nozzle outlet and the cathode was 3 mm, as shown in Figure 9c, the particles in the solution were uniformly dispersed within the cathode area, and the particle movement speed on the surface of the cathode plate reached the maximum value of 0.0796 m/s. It can be concluded that increasing the distance between the nozzle and cathode can slow down the speed of electrolyte of the outlet to some extent, and according to the results in Section 2.4, reducing the flow rate can increase the residence time of diamond particles near the substrate, thereby enhancing their incorporation into the coating. The simulation results, to some extent, demonstrated the effect of composite electrodeposition and provide a strong theoretical support for subsequent experiments.

3. Experimental Setup

The nozzle worktable used a cross-axis structure for movement, similar to 3D printers, with three degrees of freedom to achieve movement in X, Y, and Z directions. The equipment schematic is shown in Figure 10. A magnetic stirrer was used to provide insulation heating and stirring function for the electrolyte solution. The storage tank and electrodeposition tank were connected by a self-suction diaphragm booster pump and a hose. With the diaphragm pump, the electrolyte flowed from the storage tank to the nozzle, was sprayed onto the workpiece cathode, passed through the processing tank, and then fell back into the storage tank.

The anode was made of nickel tube with a diameter of 12 mm, a wall thickness of 1 mm, a length of 36 mm, and a purity of 99.99%. The cathode was made of a brass sheet with a size of 25 mm × 15 mm × 1 mm. The outlet size of the nozzle was 10 mm × 2 mm, and 2–4 μm diamond particles were used. Nickel and diamond were compositely electrodeposited on the brass in an electrolyte containing 280 g/L of NiSO₄·6H₂O (Xilong Scientific Co., Ltd., Shantou, China), 40 g/L of NiCl₂·6H₂O (Xilong Scientific Co., Ltd., Shantou, China), 40 g/L H₃BO₃ (Xilong Scientific Co., Ltd., Shantou, China), 5 g/L of Saccharin (Shanghai Yi En Chemical Technology Co., LTD., Shanghai, China), and 8 g/l of diamond (Zhecheng County Zhongyuan Superhard Abrasives Co., Ltd., Shangqiu, China) with a current density of 60 A/dm² [3]. The stirrer was rotated at 400 rpm, and the temperature of the solution was kept at 55 ± 3 °C. The distance between the nozzle outlet and the cathode was 3 mm. The nozzle moved back and forth at a speed of 300 mm/min. The total deposition was 900 min. The electrolyte speed of the nozzle inlet was 5 L/min, 8 L/min, and 11 L/min, respectively.

The surface morphology of the coating was observed with a JSM-6390LA scanning electron microscope (JEOL from Akishima, Japan), and the composition analysis of the coatings was conducted with the energy dispersive X-ray (EDX) in mapping mode on a 500× image. The surface friction coefficient of the coating was tested with an SFT-2M pin-on-disc friction and wear testing machine (Lanzhou Zhongke Kaihua Technology Development Co., Ltd., Lanzhou, China). The rubbing pair utilized 6 mm diameter soda-lime silicate glass balls to perform a wear test on the coating surface. The test parameters encompassed a circular wear track with a 4 mm radius, a normal load of 10 N, a rotational speed of 500 rpm, and a test duration of 5 min. A droplet of deionized water was applied to the coating surface prior to the test to serve as a lubricant between the glass balls and the coating, creating a dry-like friction condition.

4. Results and Discussion

4.1. Surface Morphology of the Coating for Composite Electrodeposition

Based on the previous research conducted by our team members, the thickness comparison between the simulation and experimental results using fixed-point jet and pure copper electrodeposition was verified [15]. Therefore, this study primarily focused on the surface morphology of the Ni–diamond composite coating. Figure 11 shows the surface morphology of the composite electrodeposited coating at nozzle-to-cathode distances of 1 mm, 2 mm, and 3 mm when the electrolyte speed of the nozzle inlet was 5 L/min. It was found that when the distance between the nozzle and cathode was 1 mm, the diamond particles on the coating surface were few and uneven, as shown in Figure 11a. When the distance between the nozzle and cathode was 2 mm, the diamond particles on the coating surface increased and the uniformity was improved, as shown in Figure 11b. When the distance between the nozzle and cathode was 3 mm, the surface of the coating had the most diamond particles and the best uniformity, as shown in Figure 11c. With a different distance between the nozzle outlet and the cathode, the diamond content in the coating was characterized by measuring the carbon content in the coating using EDX. Figure 12a shows the three positions, A, B, and C, for EDX. When D = 1 mm, the diamond weight percentage was 12.0 ± 5.4%. When D = 2 mm and 3 mm, the diamond weight percentage was 34.8 ± 3.3% and 46.4 ± 1.1%, respectively, as shown in Figure 12b. This was attributed to the reduced maximum velocity and fluctuation at the nozzle mouth as D increased from 1 mm to 3 mm, which facilitated particle deposition on the coating surface and aligned with the simulation results.

4.2. Wear Resistance of Composite Coating

The effect of electrolyte flow rate on the friction coefficient of the coating when the current density was 60 A/dm² and the distance between the nozzle outlet and cathode was 3 mm is discussed here. All samples exhibited a thickness of approximately 10 μm, aligning with the expected deposition rate of 0.018 μm per 5 s at 60 A/dm², as illustrated in Figure 4d. Sample a, b, and c corresponded to 5 L/min, 8 L/min, 11 L/min, respectively. The results are shown in Figure 13. The wearing-in process before 150 s was skipped. It can be seen that the average friction coefficient of sample c was 0.240 ± 0.020, with significant fluctuations due to the flow rate of electrolyte reaching 11 L/min, which increased the velocity of the electrolyte at the nozzle outlet and reduced the stagnation time of particles and the opportunity to embed them into the substrate, resulting in the unstable friction coefficient of the coating. The average friction coefficient of sample b was 0.220 ± 0.010, and the fluctuation of the friction coefficient was smaller, indicating a uniform distribution of diamond particles on the surface of the coating. The average friction coefficient of test piece a was 0.200 ± 0.005. The fluctuation of the friction coefficient was the smallest, indicating that the distribution of diamond particles on the surface of the coating was more uniform and the coating incorporated more diamond particles. These results were in good agreement with the summaries in Section 2.5, indicating that a nozzle inlet flow rate of 5 L/min minimized the pressure and velocity fluctuations at 0.2 mm above the cathode, thereby promoting particle deposition on the coating surface.

5. Conclusions

Ni–diamond composite coatings were prepared using jet electrodeposition in this study. A two-dimensional axisymmetric model of the nozzle was established through multi-physics software to simulate the effect of nickel-based diamond composite coatings under different parameters. The effects of current density and nozzle-to-cathode distance on coating thickness were investigated through electric field simulation. Concurrently, simulation of the electrodeposition flow field revealed that lower electrolyte inlet flow rates and increased nozzle-to-cathode distances resulted in reduced velocity and pressure fluctuations in the deposition zone. Incorporating particle tracking into the multi-physics coupled simulation demonstrated that an electrolyte inlet flow rate of 5 L/min, a nozzle-to-cathode distance of 3 mm, and a current density of 60 A/dm² yielded composite electrodeposited coatings with higher particle content and improved uniformity. The addition of particle tracking to the numerical model elucidated the composite electrodeposition process, and experimental validation confirmed its effectiveness in increasing the inert particle content within the composite electrodeposit. This approach offers a valuable design reference for the development and optimization of jet composite electrodeposition processes.