Migration and Removal of Microplastics in a Dual-Cone Mini-Hydrocyclone

Abstract

In this study, we analyzed the migration and removal of microplastics (MPs) using a dual-cone mini-hydrocyclone, thereby addressing the research gaps in flow mechanisms and separation efficiency for low-density MPs. We constructed and experimentally verified a numerical model. We discussed the velocity distribution of the flow field and the effects of the feed flow rate, feed MP volume fraction, and density on the distribution of MPs. The flow field analysis demonstrated maximum axial velocity at the cylindrical axis and peak tangential/radial velocities in the large cone section, promoting MP enrichment along the axis. The separation efficiency was improved with higher feed flow rates (e.g., 78.56% at 10 m/s for 50 μm MPs) but decreased with an increase in the MP volume fraction due to particle collisions. The MPs with densities below water demonstrated near-complete separation (98.51%), whereas those larger than water density exhibited minimal efficiency. The MPs are concentrated in the large and small cone axes, with density differences that significantly affect the migration patterns.

1. Introduction

Microplastics (MPs) are plastic particles smaller than 5 mm [1] and have emerged as a pervasive environmental pollutant in marine and freshwater systems, terrestrial soils, and even the atmosphere [2,3]. Their widespread prevalence stems from industrial discharges, plastic degradation, and consumer products such as detergents and cosmetics. Previous studies reported that MPs can accumulate in ecosystems, enter the food chain, and adversely impact aquatic organisms and human health, particularly due to their ability to adsorb toxic substances such as heavy metals and organic pollutants [4]. Furthermore, their persistence and small size make them resistant to conventional wastewater treatment methods. Figure 1 depicts the number of studies conducted on MPs in the past two decades, which represents an exponential increase in the extent of research conducted in recent years.

The use of hydrocyclones for the separation or recovery of MPs in water presents considerable potential [5,6].

Table 1. Recent studies on MP separation in water using hydrocyclones.

Authors	MP Material (Density, g/cm3)	MP Size (μm)	Hydrocyclone Diameter (mm)	Experimental Efficiencies (%)	Numerical Efficiencies (%)
Fu et al. [7]	PVC (1.22) & PET (1.31)	80	68	80	90.2
Borgia [8]	ABS, PET, PVC/(1.5)	5	29.65	/	50–98.8
Lorentzon [9]	PES /PET (1.35)	Microfibers with D = 9	15	11	/
He et al. [10]	PMMA (1.19)	5–15(D50≈10)	10	52–88	51–95
Liu et al. [11]	Nylon (1.15), LDPE (0.924)	5–50	10	45–98.1	/
Gina [12]	Nylon (1.15)	5–50	10	70–85	/
Gina [12]	LDPE (0.924)	5–50	20	77–88	/
Kulkarni [13]	PET (1.39)	Microfiber with D = 9	38.1	~50	/
Yang et al. [14]	PE (0.98)	53–63, 70–90	15	10–88	/
Liu et al. [15]	PMMA (1.19)	10	10	51–65	/
Thiemsakul et al. [16]	PET (1.25)	10	10	/	55–89.5
Bu et al. [17]	PVC (1.4)	10	10	76.85–88.53	79.97–89.82
Zhang et al. [18]	PMMA (1.19)	8	18	/	65–98.1
Chowdhury et al. [19]	PVC (1.4), PET (1.33)	300, 1	284	/	75–83
Senfter et al. [20]	HDPE (0.95)	118	100	0–99.12	/
Senfter et al. [20]	PP (0.82)	670	100	0–99.23	/
Senfter et al. [20]	PS (1.07)	85	100	3.01–93.85	/
Senfter et al. [20]	PMMA (1.2)	520	100	98.42–98.54	/

chronologically lists the recent studies conducted on MP separation in water using hydrocyclones. The MP material and size, as well as hydrocyclone diameter, were obtained, and the reported experimental and numerical separation efficiencies were depicted for comparison. The key conclusions of these studies are summarized below; however, some data that have already been presented in the table will not be repeated.

Fu et al. [7] employed a conventional hydrocyclone (CHC) to conduct separation experiments on MP mixtures containing PET and PVC. It was observed that the Newtonian efficiency exhibited a trend of first increasing and then decreasing with an increase in the cone angle. The cone angle at the highest separation purity of PET and PVC was 12° and 10°, respectively. Different sizes of cone angles can alter the flow field within the CHC, thereby affecting the separation efficiency. He et al. [10] employed a 3D printed mini-hydrocyclone (MHC) to separate the PMMA MPs with an average diameter of 10 μm. They reported that the axial and radial velocity distributions of water jointly affect the behavior of small-sized MPs in MHCs, and a larger split ratio can drive more fine particles to flow out from the underflow. Typically, hydrocyclones with diameters lower than 250 mm are referred to as MHCs, whereas those with a diameter greater than 250 mm are referred to as CHCs [21]. Liu et al. [11] reported that single-stage separation can remove over 80% of the 20 μm MPs, and the separation efficiency reaches its maximum at a split ratio of 35%. Under optimal operating parameters, the separation efficiency of the PA MPs was as high as 98.1%, whereas the separation efficiency of LDPE reached 84%. Gina [12] conducted separation tests on the same MPs, and it was observed that the separation efficiency of nylon and LDPE in synthetic stormwater increased by 7.7% and 3.8%, respectively, when compared with pure water. It indicated that ions in water can promote the aggregation of MPs, thereby enhancing the separation performance of the hydrocyclone. Kulkarni [13] reported that the average separation efficiency for a CHC performed with an open bleed line was 86%, which was much higher than that of 50% with a closed bleed line. They concluded that a hydrocyclone can be developed to filter the MPs out of the wastewater from washing machines. Liu et al. [15] achieved an increase of 14% in the separation efficiency and an increase of 0.24% in the concentration ratio in MHC using flocculation technology. However, they observed that high shear forces can damage flocs, presenting efficiencies close to those without flocculants. Thiemsakul et al. [16] reported an MP recovery rate of 76%, a water separation rate of 52%, and a pressure drop of 82,340 Pa by optimizing the structural parameters of MHC through numerical simulations. However, the Gidaspow drag model used in the numerical model was not experimentally validated. Conversely, Bu et al. [17] employed a combination of experiments and CFD simulations to verify that MHC can separate over 80% of PVC MPs. Their CFD simulations demonstrated the absence of a stable continuous air core within the MHC in the operating conditions. Zhang et al. [18] developed an innovative MHC with overflow microchannels, which can effectively redirect the particles that would typically be entrained by the short flow. The numerical results indicated that the new design structure effectively reduced the short flow by 94% compared with CHCs. The hydrocyclone with overflow microchannel demonstrated a removal improvement of 33.7% over the CHC. Senfter et al. [20] tested the separation of four different MPs in the same CHC, and the results demonstrated that high efficiency could not be achieved simultaneously. This indicates the need for targeted design of hydrocyclone structures and operating modes for different types of MPs.

In summary, the feasibility of using MHCs to remove MPs suspended in water has been confirmed by experiments and simulations. Several studies have been conducted on the effects of MHC structural parameters on separation efficiency [22]. However, its internal flow characteristics and mechanisms were not comprehensively analyzed. Recently, Liu et al. [21] analyzed the development of MHCs and reported that the centrifugal acceleration of fluids in MHC is relatively large, and the symmetry of tangential velocity is poor. Improving its application feasibility through mechanism analysis and optimization design is crucial. Our previous study [23] presented a high-efficiency MHC for MP removal from water. However, the multiphase flow field in the MHC requires further elucidation. In this study, we numerically analyzed the flow in the MHC and the migration of MPs to evaluate the feasibility of using MHC for efficient separation of MPs.

2. Mathematical Model

2.1. Governing Equations

The governing equations for the two-phase flow in an MHC are given as follows [24]:

$${\displaystyle \frac{\partial }{\partial t}}\left({\alpha }_q{\rho }_q\right)+\nabla \cdot \left({\alpha }_q{\rho }_q{\overrightarrow{u}}_q\right)=0$$

(1)

$$\begin{array}{ll}{\displaystyle \frac{\partial }{\partial t}}\left({\alpha }_q{\rho }_q{\overrightarrow{u}}_q\right)+\nabla \cdot \left({\alpha }_q{\rho }_q{\overrightarrow{u}}_q{\overrightarrow{u}}_q\right)=& -{\alpha }_q\nabla p+\nabla \cdot \left(\begin{array}{l}{\alpha }_q{\mu }_q\left(\nabla {\overrightarrow{u}}_q+\nabla {\overrightarrow{u}}_q^T\right)\\ +{\alpha }_q\left({\lambda }_q-{\displaystyle \frac{2}{3}}{\mu }_q\right)\nabla \cdot {\overrightarrow{u}}_q\overline{\overline{I}}\end{array}\right)\\ & +{\alpha }_q{\rho }_q\overrightarrow{g}+{\displaystyle \sum _{q=1}^n{\overrightarrow{R}}_{sq}}+\left({\overrightarrow{F}}_q+{\overrightarrow{F}}_{td,q}\right)\end{array}$$

(2)

where ${\overrightarrow{u}}_q$, ${\alpha }_q$, and ${\rho }_q$ denote the velocity, volume fraction, and density of the phase, q, respectively. ${\mu }_q$ and ${\lambda }_q$ denote the shear and bulk viscosities of phase q. ${\overrightarrow{R}}_{sq}$ denotes the interaction force between the phases. ${\overrightarrow{F}}_q$ denotes the external body force, and ${\overrightarrow{F}}_{td,q}$ denotes the turbulent dispersion force.

The fluid flow inside the hydrocyclone includes a strong outer vortex toward the underflow and an inner vortex toward the overflow, and neither the standard k-ε model nor the RNG k-ε model can accurately predict the strong vortex. The Reynolds stress model (RSM) solves the Reynolds stress transport equation and dissipation rate equation without closing the equations with the assumption of eddy viscosity. Therefore, the RSM model does not have the isotropic assumption of other RANS models to accurately predict the internal swirling motion of hydrocyclones. The Reynolds stress transport equation is expressed as follows:

$${\displaystyle \frac{\partial \left(\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)}{\partial t}}+{\displaystyle \frac{\partial \left(\rho u_k\overline{u_i^{\prime }{u}_j^{\prime }}\right)}{\partial x_k}}=D_{T,ij}+D_{L,ij}+P_{ij}+G_{ij}+{\phi }_{ij}+{\epsilon }_{ij}+F_{ij}$$

(3)

The right-hand side of the equation represents terms expressing the turbulent diffusion, molecular diffusion, stress production, buoyancy production, pressure strain, dissipation, and rotational system production. They are expressed as follows:

$$D_{T,ij}=-{\displaystyle \frac{\partial }{\partial x_k}}\left[\overline{\rho u_i^{\prime }{u}_j^{\prime }{u}_k^{\prime }}+\overline{p^{\prime }\left({\delta }_{kj}{u}_i^{\prime }+{\delta }_{ik}{u}_j^{\prime }\right)}\right]$$

(4)

$$D_{L,ij}={\displaystyle \frac{\partial }{\partial x_k}}\left(\mu {\displaystyle \frac{\partial }{\partial x_k}}\left(\overline{u_i^{\prime }{u}_j^{\prime }}\right)\right)$$

(5)

$$P_{ij}=-\rho \left(\overline{u_i^{\prime }{u}_k^{\prime }}{\displaystyle \frac{\partial u_j}{\partial x_k}}+\overline{u_j^{\prime }{u}_k^{\prime }}{\displaystyle \frac{\partial u_i}{\partial x_k}}\right)$$

(6)

$$G_{ij}=-\rho \beta \left(g_i\overline{u_j^{\prime }\theta }+g_j\overline{u_i^{\prime }\theta }\right)$$

(7)

$${\phi }_{ij}=p\prime \overline{\left({\displaystyle \frac{\partial u_i^{\prime }}{\partial x_j}}+{\displaystyle \frac{\partial u_j^{\prime }}{\partial x_i}}\right)}$$

(8)

$${\epsilon }_{ij}=-2\mu \overline{{\displaystyle \frac{\partial u_i^{\prime }}{\partial x_k}}{\displaystyle \frac{\partial u_j^{\prime }}{\partial x_k}}}$$

(9)

$$F_{ij}=-2\rho {\Omega }_k\left(\overline{u_j^{\prime }{u}_m^{\prime }}{\epsilon }_{ikm}+\overline{u_i^{\prime }{u}_m^{\prime }}{\epsilon }_{jkm}\right)$$

(10)

2.2. Interphase Interactions

We employed the Euler–Euler model to track the particle movement. Water is the primary phase, and the MPs form the secondary phase. The interphase forces between the primary phase and the secondary phase include drag, lift, turbulent diffusion, and virtual mass forces and can be expressed as follows:

$${\displaystyle \sum _{q=1}^n{\overrightarrow{R}}_{sq}}={\displaystyle \sum _{q=1}^n{K}_{sq}}\left({\overrightarrow{u}}_s-{\overrightarrow{u}}_q\right)$$

(11)

The drag force between the dispersed phase, s, and continuous phase, q, can be calculated as follows:

$$F_D=K_{qs}\left({\overrightarrow{u}}_q-{\overrightarrow{u}}_s\right)$$

(12)

where K_sq denotes the interphase momentum exchange coefficient, and K_sq = K_qs.

The Euler multiphase flow model provides various drag models, and the applicable scenarios, corresponding drag coefficients, and phase exchange coefficients of different drag models vary.

Table 2. Phase exchange coefficients of different solid–liquid drag models.

Drag Models	Phase Exchange Coefficients
Wen–Yu [25]	$K_{sq}={\displaystyle \frac{3}{4}}{C}_D{\displaystyle \frac{{\alpha }_s{\alpha }_q\left|{\overrightarrow{u}}_s-{\overrightarrow{u}}_q\right|}{d_s}}{\alpha }_q^{-2.65}$
Gidaspow [26]	${\alpha }_q>0.8,K_{sq}={\displaystyle \frac{3}{4}}{C}_D{\displaystyle \frac{{\alpha }_s{\alpha }_q{\rho }_q\left|{\overrightarrow{u}}_s-{\overrightarrow{u}}_q\right|}{d_s}}{\alpha }_q^{-265}$ ${\alpha }_q\le 0.8,K_{sq}=150{\displaystyle \frac{{\alpha }_s\left(1-{\alpha }_q\right){\mu }_q}{{\alpha }_q{d}_s^2}}+1.75{\displaystyle \frac{{\rho }_q{\alpha }_s\left|{\overrightarrow{u}}_s-{\overrightarrow{u}}_q\right|}{d_s}}$
Syamlal–O’Brien [27]	$K_{sq}={\displaystyle \frac{3{\alpha }_s{\alpha }_q{\rho }_q}{4v_{r,s}^2{d}_s}}{C}_D\left({\displaystyle \frac{R{e}_s}{v_{r,s}}}\right)\left|{\overrightarrow{u}}_s-{\overrightarrow{u}}_q\right|$
Huilin–Gidaspow [28]	$K_{sq}=\psi K_{sq-Ergun }+(1-\psi )K_{sq-Wen\&Yu}$ where $\psi ={\displaystyle \frac{1}{2}}+{\displaystyle \frac{\arctan \left(262.5\left({\alpha }_s-0.2\right)\right)}{\pi }}$

lists the commonly used drag models between the solid–liquid phases.

The drag coefficients for the Wen–Yu, Gidaspow, and Hulin–Gidaspow models in Table 1 can be calculated as follows:

$$C_D={\displaystyle \frac{24}{{\alpha }_{q}R{e}_s}}\left[1+0.15{({\alpha }_{q}R{e}_s)}^{0.687}\right]$$

(13)

The drag coefficients for the Syamlal–O’Brien model can be calculated as follows:

$$C_D={\left(0.63+{\displaystyle \frac{4.8}{\sqrt{R{e}_s/v_{r,s}}}}\right)}^2$$

(14)

When the volume fraction of the dispersed phase is low, the drag force between it and the continuous phase must be corrected. The drag force correction model proposed by Brucato et al. [29] is adopted, which assumes that the drag coefficient increases with the turbulence of the liquid phase. The calculation formula for the drag force correction coefficient is as follows:

$$\eta =1+K{\left({\displaystyle \frac{d}{\lambda }}\right)}^3$$

(15)

where K = 6.5 × 10⁻⁶, and the Kolmogorov scale, $\lambda$, can be determined as follows:

$$\lambda ={\left({\displaystyle \frac{{\nu }_l^3}{\epsilon }}\right)}^{1/4}$$

(16)

where ν_l denotes the viscosity of the liquid phase and ε denotes the turbulent dissipation rate (m²/s³).

The turbulent dispersion force of multiphase flow significantly affects the distribution and motion of particles. The turbulent dispersion force is a fluctuation component generated by the average process of instantaneous resistance, which demonstrates the influence of velocity fluctuations on the moving particles. Therefore, the turbulent dispersion force must be considered in numerical simulation. In this study, we employed the Burns model for turbulent dispersion force [30]:

$${\overrightarrow{F}}_{td,s}=-{\overrightarrow{F}}_{td,q}=-C_{TD}{K}_{qs}{\displaystyle \frac{{\mu }_{tq}}{{\sigma }_{qs}{\rho }_q}}\left({\displaystyle \frac{\nabla {\alpha }_s}{{\alpha }_s}}-{\displaystyle \frac{\nabla {\alpha }_q}{{\alpha }_q}}\right)$$

(17)

where C_TD denotes the turbulence dispersion coefficient, which is a parameter between 0 and 1 and corresponds to the turbulence intensity; its default value is 1. σ_qs and μ_tq denote the turbulent Prandtl number and turbulent viscosity, respectively.

3. Numerical Method

3.1. Computational Domain and Mesh Generation

We employed an optimized dual-cone MHC to analyze the asymmetry migration and removal of MPs [23]. Figure 2 and

Table 3. Geometrical parameters of MHC.

Geometrical Parameters	Values
Diameter of the cylindrical body Ds	20 mm
Length of the cylindrical body Ls	36 mm
Nominal diameter D	12 mm
Upper cone angle θ1	25°
Lower cone angle θ2	1.5°
Diameter of the vortex finder Do	2 mm
Diameter of the spigot Du	7 mm
Width and height of the entrance W × H	3.8 mm × 4.2 mm

present the schematic and geometric parameters of the MHC, respectively. The MHC has smaller dimensions, presenting a swirling flow with poorer symmetry when compared with the CHC. The hydrocyclone was designed with dual tangential inlets to enhance the radial symmetry of its flow field.

The flow field within the hydrocyclone was discretized using the ANSYS ICEM CFD 2022 software. We selected a hexahedral mesh to optimize the computational efficiency and accuracy. We evaluated the grid independence based on four different grid schemes and selected a grid of 450,000 units (Figure 3) corresponding to the grid medium. A boundary layer was created on the wall of the cyclone, considering the calculation accuracy and time cost.

3.2. Parameters and Boundary Conditions

The material in the continuous phase was water with a density of 998.2 kg/m³ and viscosity of 1.003 × 10⁻³ Pa∙s; the density of PE MPs was 930 kg/m³. The hydrocyclone inlet was set as a velocity inlet, wherein the MPs and water exhibit the same velocity. The wall of the MHC was set as a no-slip condition. The overflow and underflow outlets were set as the pressure outlets. The overflow outlet pressure was set at 0 Pa, and the bottom outlet pressure was adjusted based on the split ratio and inlet flow velocity. When the diversion ratio was 0.1 and the inlet flow velocity was 5 m/s, the outlet pressure at the underflow was set to 40,000 Pa.

3.3. Numerical Schemes

The simulations were performed using ANSYS Fluent 2022 software. The phase-coupled SIMPLE algorithm was used to solve the velocity–pressure coupling, and

Table 4. Discrete schemes for different terms.

Spatial Discretization	Discrete Schemes
Gradient	Least Squares Cell-Based
Pressure	PRESTO!
Momentum	QUICK
Volume fraction	Modified HRIC
Turbulent kinetic energy	Second Order Upwind
Turbulent dissipation rate	Second Order Upwind
Reynolds stress	Second Order Upwind

presents the discrete schemes. To improve the accuracy of the calculation and reduce the computation time, we employed the result of 8000 iterations of the steady-state calculation as the initialization value for the unsteady-state calculation. The time step for unsteady-state calculation was set to 0.001 s, and the calculation result after 2 s of unsteady-state calculation was considered as the numerical result.

4. Results and Discussion

4.1. Calculation Verification

To determine the appropriate solid–liquid drag model, we compared the separation efficiencies obtained from the four different models presented in Table 2. Figure 4 depicts the separation efficiency of 50 μm MPs at different feed volume fractions under the conditions of a feed velocity (V_in) of 5 m/s and a split ratio (S) of 0.1. The separation efficiency decreases with an increase in the volume fraction of MPs in all the drag models. This phenomenon can be attributed to the fact that random collisions between MPs increase with an increase in the initial volume fraction of MPs, whereas the separation efficiency decreases with an increase in the MP concentration. Therefore, the feed concentration for hydrocyclones with fixed structural dimensions must be limited within an appropriate range to ensure high separation efficiency.

Among the four drag models, the separation efficiency under the Gidaspow model was almost identical to that under the Hui–Lin Gidaspow model. The separation efficiency obtained by the Syamlal–O’Brien model was slightly higher than the calculation results of the Gidaspow model, and the separation efficiency under the Wen–Yu model was significantly higher than the calculation results of the other three models. Based on the applicable conditions of each model, the Wen–Yu model was more suitable for conditions where the volume fraction of the secondary phase is much smaller than that of the main phase. This condition is more appropriate for the separation of MPs in this study. Therefore, we employed the Wen–Yu model to calculate the separation efficiency of MPs with different diameters in the next sections.

Figure 5 depicts the grade efficiency obtained from the experimental measurements and numerical results based on the Wen–Yu model. The experimental methods represent our previous work [23]. The calculation results of this model are typically consistent with the trend of experimental data. The calculated values of particle grade efficiency for MPs with a diameter of 10–70 μm have a certain deviation from the experimental values, while the calculated values of particle grade efficiency for MPs with a diameter greater than 70 μm are relatively close to the experimental values. The overall consistency between the numerical simulation results and experimental results is high; therefore, the numerical model can be used to describe the multiphase flow in the MHC.

4.2. Velocity Distribution of Flow Field

The velocity field was obtained under a feed velocity of 5 m/s and a split ratio of 0.1. Figure 6 depicts the velocity contours of the longitudinal section. The velocity field exhibits high symmetry, which corresponds to the dual tangential inlets design of the MHC. The axial velocity at the wall of the MHC was downward, whereas the axial velocity near the axis was upward, which concurs with the characteristics of the external rotation direction moving toward the underflow and the internal rotation direction moving toward the overflow inside the hydrocyclone. The diameter of the overflow tube was small, and the fluid entering the overflow tube was accelerated, presenting a large axial velocity. Subsequently, the axial velocity of the fluid decreased along the extension of the overflow tube. Along the direction of the wall toward the axis, the tangential velocity exhibits a trend of first increasing and then decreasing. In the axial direction, as the distance from the top of the cylindrical segment increases, the maximum tangential velocity gradually decreases during the movement of the fluid toward the bottom flow direction. The radial velocity is much lower than the maximum values of axial velocity and tangential velocity, and the fluctuation range is very small; therefore, the changes displayed under the same legend are not obvious. The characteristics of the velocity field of the MHC used in this study are generally similar to those of the light-dispersed phase hydrocyclone used for oil–water separation. The cylindrical section (Z = 20 mm), upper cone (Z = 44 mm), upper end of the lower cone (Z = 60 mm), and middle end of the lower cone (Z = 160 mm) of the MHC were selected as sample sections, as illustrated in Figure 7. The velocity components at these sections were plotted in Figure 8, and the flow pattern was analyzed.

4.2.1. Axial Velocity

Figure 8a depicts the axial velocity distribution along the radial distance. A positive axial velocity indicates fluid movement toward the overflow, whereas a negative axial velocity indicates fluid movement toward the underflow. The axial velocity distribution indicates that the internal swirling flow at the axis of the MHC flows upward, whereas the fluid near the wall moves toward the underflow with the external swirling flow. There are regions with zero axial velocity at all four cross-sectional positions; additionally, there are three positions with zero axial velocity at the Z = 20 mm position of the cylindrical section. These positions with zero axial velocity are the locations of the zero axial velocity envelope surface. The closer to the overflow outlet, the greater the fluid velocity at the inner core. This indicates that the pressure gradient generated by the continuously contracting lower cone drives the MP particles to flow out of the overflow with the fluid.

4.2.2. Tangential Velocity

Figure 8b depicts the radial distribution of tangential velocity at four cross-sectional positions. Along the direction of the wall toward the axis, the tangential velocity gradually increased with a decrease in the radius. The tangential velocity reached its maximum value at a certain radius, exhibiting the law of quasi-free vortices. Subsequently, the tangential velocity rapidly decreased and reached its minimum value at the axis, exhibiting the law of forced vortices.

The tangential velocity was the highest at the large cone section (Z = 44 mm). The presence of a large cone angle caused the diameter of the flow section to rapidly decrease with an increase in the axial distance, thereby accelerating the fluid velocity passing through this section. Simultaneously, the cone angle guided the direction of the fluid motion, and the tangential velocity reached its maximum value at a specific radius at this section location. The tangential velocity significantly affected the centrifugal acceleration generated by the vortex field. Based on the location of the maximum tangential velocity, it can be inferred that the large cone section contributes significantly to centrifugal separation.

4.2.3. Radial Velocity

Figure 8c depicts the radial velocity distribution curves at four selected cross-sectional positions. A positive radial velocity indicated that the fluid velocity pointed from the axis to the wall, whereas a negative radial velocity indicated that the fluid velocity pointed from the wall to the axis. In the direction from the wall to the axis, the absolute value of the radial velocity exhibits a trend of first increasing and then decreasing. The radial velocity was larger at the wall of the large cone section because the diameter at the large cone section rapidly decreased, and the fluid in the cylindrical section rapidly approached the axis. The radial velocity distribution at the two cross-sections of the small cone section exhibits a similar trend. The radial velocity near the wall of the hydrocyclone was negative, and the radial velocity at the wall points toward the axis. The radial velocity near the axis exhibits a phenomenon of alternating positive and negative values. This indicates that even symmetrical geometric structures have instability in the core. An unstable inner core can cause more lightweight particles to return to the outer core, potentially reducing separation efficiency. Hence, it is necessary to ensure the stability of the turbulent flow field by optimizing the design of MHC.

The velocity distribution of MPs was similar to that of the liquid phase, with only numerical differences. Therefore, instead of comprehensively analyzing the velocity distribution of the MPs, we evaluated the concentration distribution and migration characteristics to analyze the laws for achieving higher separation efficiency in terms of flow mechanism.

4.3. MP Distribution and Migration

4.3.1. Effect of the Feed Flow Rate

To analyze the MP distribution characteristics at different feed flow rates, we conducted numerical calculations based on different feed velocities.

Table 5. Separation efficiencies at different feed velocities.

Feeding Velocities	Separation Efficiencies
6 m/s	56.41%
7 m/s	61.14%
8 m/s	66.24%
9 m/s	71.89%
10 m/s	78.56%

presents the separation efficiencies of 50 μm MPs at different feed velocities within the range of 6–10 m/s. The data in the table indicate that the separation efficiency of 50 μm MPs increased with an increase in the feed flow rate, which concurs with the experimental data.

Figure 9 depicts the contours of the MP volume fraction at different feed velocities. As the feed velocity increases, the MP volume fraction near the axis of the MHC and the overflow gradually increase. The MP volume fraction at the connection between the overflow and the cylindrical section, as well as near the axis of the large cone section and the upper end of the small cone section, presents the most significant change.

To further analyze the MP distribution pattern presented in Figure 9, the curves of the MP volume fraction at four cross-sections along the radial distance were plotted as shown in Figure 10. Within the same cross-section, the MP volume fraction near the wall always remained at a low value. The MP volume fraction near the axis increased rapidly with an increase in the feed flow rate. The amount of MPs and water entering the MHC per unit time increased with an increase in the feed flow rate, presenting an increase in the swirling velocity. At the same feed velocity, the upper end of the small cone section (Z = 60 mm) represents the position with the highest MP volume fraction among the four sections. Combining Figure 9, it can be observed that the MPs at this position are highly enriched and form a core area with a larger volume fraction. Within 2 mm of the radial distance at the upper end of the small cone section, the MP volume fraction exhibits the most significant variation with the radial distance. Under the action of the large cone section, MPs rapidly migrate toward the axis of the MHC. The MP volume fraction in the middle of the small cone section was much lower than in the other positions, and most of the MPs are enriched in the axis of the MHC and move toward the overflow at the upper end of the small cone section.

According to the MP volume fraction at the middle end of the small cone section (Z = 160 mm), the MP volume fraction at the wall decreased with an increase in the feed velocity, whereas the difference in the MP volume fraction near the axis was minimal. The increase in the inlet flow velocity caused a decrease in the average volume fraction of the MPs at that cross-sectional position, thereby reducing the proportion of the MPs escaping from the underflow outlet. Consequently, this phenomenon explains that with an increase in the inlet flow velocity, the MPs near the wall were more likely to accumulate toward the axis of the MHC above the upper end of the small cone, thereby reducing the proportion of MPs escaping from the underflow outlet.

4.3.2. Effect of Feed MP Volume Fraction

Figure 11 depicts the MP volume fraction contours under different feed volume fractions (α_s). The area near the upper axis of the cylindrical section, large cone section, and small cone section was always the region with a higher MP volume fraction. This phenomenon indicates that MPs with a density lower than water accumulate toward the axis of the MHC under the action of centripetal buoyancy during the cyclonic separation process. The enrichment of MPs in the axial area of the MHC gradually increased with an increase in the feed volume fraction, and the areas with higher volume fractions extend toward the underflow and the wall of the MHC. MPs primarily accumulated near the axis of the large cone section and the axis of the upper end of the small cone section. The large and small cone angles of the MHC contributed significantly to the aggregation of MPs toward the axis.

Figure 12 depicts the radial distributions of the MP volume fractions at the feed inlet when they are 0.01 and 0.03, respectively. For cross-sections at the same axial position, the MP volume fraction on the axis of the MHC was the highest, whereas the amount of MPs on the wall was lower. MPs migrate toward the axis under the action of centripetal buoyancy. The smaller the value of axial distance, the closer the selected cross-sectional position is to the overflow of the MHC. Under the same feed volume fraction, the concentration of MPs near the axis of the MHC exhibits a trend of first increasing and then decreasing with an increase in the axial distance. Conversely, the volume fraction of MPs near the wall always exhibits a gradually decreasing trend. The diameter of the MHC decreases rapidly with an increase in the axial distance in the large cone section (Z = 44 mm), as shown in Figure 11, and MPs accumulate toward the axis of the MHC with the fluid. At the upper end of the small cone section (Z = 60 mm), the MP volume fraction at the axis reached its maximum value, and the MP volume fraction near the wall was lower than that at the cylindrical and large cone sections.

Figure 13 depicts the radial distributions of MPs under different volume fractions of feed MPs. The larger the volume fraction of MPs fed, the greater the MP volume fraction at the same radial distance on the same section. As the feed MP volume fraction increases, the distribution of MPs exhibits a relatively uniform increase in the same section. The MP volume fraction at the four cross-sectional positions, from highest to lowest, is as follows: upper end of the small cone section > large cone section > cylindrical section > middle end of the small cone section. Among them, the MP volume fraction at the upper end of the small cone section (Z = 60 mm) exhibits the largest gradient with radial distance. Due to the uniform increase in volume fraction from 0.01 to 0.06, a larger interval between adjacent curves indicates a greater degree of concentration enrichment. From the graph, it can be seen that as the volume fraction of MP in the feed increases, the growth of particle concentration at the axis position will gradually slow down. This indicates that the feed concentration should not be too high, which may cause blockage of the overflow outlet.

Figure 14 depicts the grade efficiency curves for three different feed MP volume fractions. The numerical results indicated that the grade efficiency of MPs was affected by the feed concentration. The grade efficiency of MPs smaller than 30 μm exhibited minimal variation with the feed MP volume fraction. The separation efficiency of MPs with a diameter of 30–90 μm decreased significantly with an increase in the volume fraction. The grade efficiency of MPs larger than 90 μm was almost completely separated at a feed volume fraction of 0.01. The size of MP with a grade efficiency approaching 100% increased with an increase in the volume fraction. The decrease in the grade efficiency of MPs in the diameter range of 30–90 μm can be attributed to the increased MP volume fraction, which exacerbates the collisions between MPs and reduces the separation efficiency.

4.3.3. Effect of MP Density

The density of the MP significantly affects the separation performance. However, the density of common MPs is close to that of water, presenting significant challenges to the cyclonic separation method. We numerically simulated four particle densities to evaluate the effect of different dispersed phase densities on the separation efficiency.

Table 6. Separation efficiencies at different feed MP densities.

Feeding Densities	Separation Efficiencies
800 kg/m3	98.51%
930 kg/m3	50.32%
998 kg/m3	10.78%
1100 kg/m3	2.97%

presents the separation efficiency of 50 μm MPs at four densities with a feed velocity of 5 m/s, split ratio of 0.1, and volume fraction of 0.03. Figure 14 depicts the volume fraction contours of the MPs in the longitudinal section. Almost all the feeding MPs with a density of 800 kg/m³ can be separated, whereas separating 1100 kg/m³ MPs using MHC presents a considerable challenge. The separation efficiency at a density of 998 kg/m³ is very close to that at the water split ratio.

MPs with a density of 930 kg/m³ were primarily enriched in the axis and overflow tube between the large and small cone sections, as shown in Figure 15. The enrichment effect of MPs with a density of 800 kg/m³ in the MHC was significantly higher than that of MPs with other densities. An MP cylindrical core was formed between the overflow tube and the small cone section, and the volume fraction of this enrichment area exhibits a large upper end and a small lower end. MPs with a density of 998 kg/m³ were uniformly dispersed throughout the entire MHC, indicating that MPs of this density cannot be effectively separated by the MHC (without a density difference between MP and water). MPs with a density of 1100 kg/m³ belong to heavy particles, and theoretically, the separation effect of using a light-dispersed phase hydrocyclone was poor. They were primarily concentrated on the wall of the MHC, and the volume fraction of MPs at the axis of the cylindrical section was close to 0. With an increase in the axial distance, the MP volume fraction at the axis exhibits an increasing trend. MPs with this density move toward the underflow along with the external cyclone.

Figure 16 depicts the MP distribution under different feed MP densities. MPs with densities of 800 kg/m³ and 930 kg/m³ exhibit low volume fraction near the wall and high volume fraction near the axis. The volume fraction of MPs with a density of 800 kg/m³ near the axis gradually decreased with an increase in the axial distance, and the particle enrichment area with this density was located at the upper end of the cylindrical section of the MHC. The volume fraction of MPs with a density of 930 kg/m³ near the axis exhibits a trend of gradually increasing and then rapidly decreasing with an increase in the axial distance. The increase in density presents a downward shift in the enrichment area of MPs, which is located between the large and small cone sections. The MPs with a density of 980 kg/m³ were uniformly distributed across four cross-sections, and the volume fraction remains identical to that of the inlet MP volume fraction. The volume fraction of MPs with a density of 1100 kg/m³ exhibits a high wall surface and low axis at four cross-sections. The cross-sectional area of the MHC gradually decreased with an increase in the axial distance, forcing particles to migrate toward the axis, presenting an increase in the MP volume fraction near the axis in the small cone section.

In the cylindrical section (Z = 20 mm) and the large cone section (Z = 44 mm), the volume fraction of MPs with a density of 800 kg/m³ on the wall was lower than that on the axis, and the volume fraction of MPs with a density of 930 kg/m³ on the axis was significantly lower than that of MPs with a density of 800 kg/m³. The density significantly affected the migration efficiency of MPs toward the axis at the positions of the cylindrical section and the large cone section. At the upper end of the small cone section (Z = 60 mm), the volume fraction of 800 kg/m³ particles was higher than that of the 930 kg/m³ particles within a small radius range. Overall, the volume fraction of 800 kg/m³ MPs was lower than that of the 930 kg/m³ MPs. At the same radial position at the middle end of the small cone section (Z = 160 mm), the MP volume fraction of 800 kg/m³ was lower than that of 930 kg/m³.

5. Conclusions

In this study, we numerically analyzed the solid–liquid two-phase flow in the separation of MPs using an MHC. The fluid calculation domain of the hydrocyclone was discretized, and a numerical model was constructed to evaluate the migration and removal of MPs in a dual-cone MHC. Furthermore, we discussed the velocity distribution of the flow field and the effects of feed flow rate, feed MP volume fraction, and density on the distribution of MPs. The main conclusions of this study are as follows:

(1) The maximum deviation between the calculated grade efficiency using the Wen–Yu drag model and the experimental data was within 10%, which indicated that the numerical model can be used to describe the two-phase flow.

(2) The maximum axial velocity of continuous phase water was located at the axis position of the cylindrical section, whereas the maximum tangential and radial velocities were observed in the large cone section, which contributes significantly to the aggregation of MPs along the axis.

(3) During the cyclonic separation process, MPs are primarily enriched in the axis of the large and small cone sections of the hydrocyclone and the overflow. An increase in the volume fraction of MPs in the feed reduced the separation efficiency. The larger the feed flow rate, the greater the enrichment and concentration of MPs along the axis, and the higher the separation efficiency (e.g., 78.56% at 10 m/s for 50 μm MPs).

(4) The density of MPs was lower than that of water, and the greater the density difference with water, the higher the degree of enrichment and concentration at the axis of the cylindrical section of the hydrocyclone. A near-complete separation (98.51%) can be achieved for 800 kg/m³ MPs. MPs with a density greater than or equal to water are difficult to separate using the hydrocyclone used in this study.

In summary, this paper’s innovations lie in its optimized dual-cone MHC design, validated numerical model for flow simulation, detailed mechanistic insights into MP migration, and parameter-driven efficiency enhancements. These contributions advance the field by providing a reliable, high-efficiency approach for removing low-density microplastics, with validated models enabling further research and application. The findings fill critical gaps in understanding flow dynamics and separation performance, paving the way for more effective environmental remediation technologies.