Microplastic separation and enrichment in microchannels under derivative electric field gradient by bipolar electrode reactions

The decomposed plastic products in the natural environment evolve into tiny plastic particles with characteristics such as small size, lightweight, and difficulty in removal, resulting in a significant pollution issue in aquatic environments. Significant progress has been made in microplastic separation technology benefiting from microfluidic chips in recent years. Based on the mechanisms of microfluidic control technology, this study investigates the enrichment and separation mechanisms of polystyrene particles in an unbuffered solution. The Faraday reaction caused by the bipolar electrodes changes the electric field gradient and improves the separation efficiency. We also propose an evaluation scheme to measure the separation efficiency. Finite element simulations are conducted to parametrically analyze the influence of applied voltages, channel geometry, and size of electrodes on plastic particle separation. The numerical cases indicate that the electrode-installed microfluidic channels separate microplastic particles effectively and precisely. The electrodes play an important role in local electric field distribution and trigger violent chemical reactions. By optimizing the microchannel structure, applied voltages, and separation channel angle, an optimal solution for separating microplastic particles can be found. This study could supply some references to control microplastic pollution in the future.

www.nature.com/scientificreports/factor.Section "Conclusions" discusses the relevant characteristics of the model and presents the conclusions of this study.

Fundamental of microchannel
The method of separating particles in an unbuffered solution can achieve the separation of microplastic particles without the addition of other solutions.This method can prevent secondary pollution in the aquatic environment in practical applications.The method offers advantages such as low cost and long lifespan, providing a more feasible solution for the separation of microplastic particles.The separation principle of microplastic particles is illustrated in Fig. 1.
When the fluid flows through the microchannel, the microchannel walls carry a negative charge.The ions in the diffusion layer undergo directed movement and the conductor produces induced charges to maintain the same potential within the conductor after an electric voltage V is applied.Due to the viscosity of the fluid, the ions induce electroosmotic flow.Since the diffusion layer has a local positive charge, the direction of the electroosmotic flow is the same as the movement direction of the cations.
The potential near the conductor is illustrated in Fig. 2a.At the interface of the bipolar electrode, the potential difference drives redox reactions.The redox reaction involves water electrolysis under unbuffered conditions, producing H + at the anode and OH − at the cathode.The generation of ions creates a significant gradient change in electric field strength near the bipolar electrode in the solution.This change causes a redirection of microplastic particles at this location, achieving the separation effect.
The electric field strength near the cathode of the bipolar electrode is illustrated in Fig. 2b.Under a zeropressure gradient flow, negatively charged microplastic particles are influenced by the opposing effects of electroosmotic flow and electromigration.The electroosmotic flow effect is dominant at position A, causing the microplastic particle to move leftward.Conversely, when the particles are at position C, these cause the microplastic particle to move rightward.Particles eventually reach position B where electrophoresis and electroosmotic flow reach a balance.

Governing equation
The analysis of microchannel issues involves the coupling of multiple physical fields such as fluid flow, electrostatic field, and mass transfer.The corresponding equations for this are the Navier-Stokes equations, the Poisson equation, and the Nernst-Planck mass transfer equations.The Navier-Stokes equations are described as: where u represents fluid velocity; η stands for fluid dynamic viscosity; ρ is the fluid density; F is the Faraday constant; V is the applied voltage across the microchannel; z i and c i represent the charge number and concentration of i species, respectively.Due to the simulation of microfluidic, fluid flows slowly and Reynolds number Re is small at the steady condition in the channel.Therefore, Eq. (1) simplifies to the following form: We use the Poisson equation to solve for electrostatic fields, which is described as follows: where ε is the relative permittivity; ρ is the space charge density in the solution, which is ρ = n i=1 Fz i c i ; due to the channel in the micrometer or millimeter range, the electric double layer has little influence on the solution.therefore, we can assume the electrical neutrality in the solution.The Poisson equation can simplify the Laplace equation: We utilize the Nernst-Planck equation to solve concentration distribution in the Runners: where D i represents the diffusion coefficient of i species, respectively; J i represents the flux of i species, u m,i is the electrophoretic mobility of i species; R i stands for the reaction source term for i species.In the unbuffered solution, we consider the reaction source term arising from the electrolysis of water.The equation of the chemical reaction is shown below: the reaction source terms R for H + and OH − in Eq. ( 6) can be determined through reaction rates.The equations are expressed as: where ] represent the chemical reaction rates for OH − and H + , respectively.k f and k b are the forward and reverse reaction rate constants for the electrode reaction.

Model simplification
The intricate nature of solving differential equations involves strongly coupled multi-physics phenomena in numerical simulations of microfluidics.This model often entails challenging convergence and computational difficulties.We choose to judiciously simplify the microchannel model before embarking on the numerical simulations.
The electric field and potential generated by the bipolar electrode reaction is shown in Fig. 3.The electric field varies the most at the ends of the bipolar electrode and changes relatively slowly at other positions of the bipolar electrode 47 .The potential in Fig. 3 shows that the overpotential is highest at positions adjacent to the bipolar electrodes.
The electric field and current density distribution within the microchannel are depicted in Fig. 4.These results show that the electric field is highest at positions adjacent to the bipolar electrodes, and the current density induced by the reaction is also maximized corresponding to the locations.It can be seen that the oxidation-reduction reaction occurs most intensely at the ends of the bipolar electrode from these results.Therefore, (1) we model the ends of the bipolar electrode to replace the entire bipolar electrode, which can reduce model complexity.
The structure of the separation channel is shown in Fig. 5.The OH − generated by the cathodic reaction increases the conductivity near the cathode.The electric field gradient is changed by increased conductivity, which alters the magnitude and direction of the electric migration.As a result, the plastic particles flow out of the upper channel to achieve the separation effect.The influence of parameters such as the applied voltage, the separation channel angle, and the distance of the bipolar electrode on the separation efficiency of plastic microbeads is investigated.

Boundary conditions
Concerning the schematic diagram of the bifurcated channel in Fig. 5, the main boundary conditions for this system are the surfaces of the bipolar electrodes.The oxidation reactions occur at the anode of the bipolar electrode producing H + .The electrode reaction equation is shown below: The current density generated at the anode reaction obeys the Butler-Volmer equation shown below 48 :  In Eqs. ( 10) and ( 11), i loc represents the local current density for the anodic reaction; i 0 denotes the exchange current density for the anodic reaction; α and β are the transfer coefficients for the anodic and cathodic reactions, respectively; R is the universal gas constant; T stands for temperature; η a denotes the overpotential at the anode of the bipolar electrode; ϕ s represents the potential of electrode and ϕ l is the potential of the solution near the bipolar electrode; E eq,a represents the electrode potential at the temperature T solved by Nernst equation.The equation is shown below: In Eq. ( 12), E 0,a represents the standard electrode potential for the anodic reaction; F is the Faraday constant; n is the number of electrons involved in the reaction transfer; C [H + ] is the surface H + concentration at the bipolar electrode, and C 0,[H + ] is the H + concentration in the bulk solution.
The rate of chemical reaction of the H + follows Faraday's law: In Eq. ( 13), v [H + ] represents the stoichiometric number of H + in the anodic reaction.The chemical reaction equation for producing OH − at the cathode of the bipolar electrode is as follows: The cathodic reaction at the bipolar electrode also follows the Butler-Volmer equation and Faraday's law: where i 0,c represents the exchange current density for the cathodic reaction, η c is the overpotential for the cathodic reaction; E eq,c is the electrode potential for the cathodic reaction at the temperature T; E 0,c is the standard electrode potential for the cathodic reaction; C [OH − ] and C 0,[OH − ] represent the OH − concentration near the cathodic electrode and in the bulk solution, respectively; n is the stoichiometric number of OH − .The boundary conditions applied at the inlet of the microchannel: (1) specified ion concentration c 0,i ; (2) specified voltage V 0 ; and (3) pressure is set to 0: The boundary conditions applied at the outlet of the microchannel: (1) zero diffusion flux, (2) zero voltage, and (3) pressure is set to 0: The boundary conditions imposed at the microchannel walls: (1) zero flux, (2) electrical insulation, and (3) the velocity of electroosmotic flow within the microchannel follows the Helmholtz-Smoluchowski equation 49 : where ζ represents the potential difference between the diffusion layer and the bulk solution, E is the electrical field strength inside the microchannel, E = − ∇V, and V is the applied potential within the solution.

Model verification
We use the straight channel model commonly used in the field of microfluidics to verify the feasibility of the simulation method to ensure that the simulation results are real and valid.The results of the simulations are compared with the experimental results of other researchers to prove that the simulation method is feasible.
Ionic current density is depicted in Fig. 6.Because of the electrode reaction of the model, the result of ionic current density can vary along the length of the channel.These variables changed most significantly around the bipolar electrodes.Therefore, the values of current density near the three bipolar electrodes are extracted and compared with the experimental data.The results of the simulation show an almost equal effect to those of other researchers 46 , which means a correct simulation model.
The ionic current density is measured at three positions in the experiments of other scientific researchers, which are 500 μm of the electrode cathode (upstream of BPE), 1500 μm downstream of the electrode cathode (between BPE poles), and 1000 μm downstream of electrode anode (downstream of BPE).These results are shown in Table 1.The results show that the simulation results are not much different from the experimental data within the allowable range of error, and the results obtained by the simulation model are valid.

Particle separation in the channel
The separation microchannel structure is shown in Fig. 5.A solution of KCl with a concentration of 5 mol/m 3 ( z .033 × 10 -9 m 2 /s, D H + = 9.103 × 10 -9 m 2 /s, D OH − = 5.28 × 10 -9 m 2 /s) is used at the inlet of the channel.In order to ensure the validity of the model and to be able to implement the simulation function, we assume microplastics are evenly distributed in solution.A polystyrene microplastic particle is used and its concentration is 3 × 10 -12 mol/m 3 .Although environmental factors lead to different charges of microplastic particles, we choose a special kind of polystyrene microplastic, whose charge is − 2 (z Bead = − 2).Microbeads can be affected by diffusion in this simulation, so the diffusion coefficient is considered, which is 7.85 × 10 -8 m 2 /s (D Bead = 7.85 × 10 -8 m 2 /s).Additionally, the diameter of particles is 0.99 μm.The relative permittivity of the solution is 80, and the zeta potential is − 80 mV.The governing Eqs. ( 2), (3), ( 5), (19)    (6) and ( 7) are solved using the commercial finite element software Comsol Multiphysics V6.0.By varying the applied voltage V 0 , separation channel angle θ, and position of the bipolar electrode d, the microfluidics separation mechanism and the impact on the efficiency of microchannel separation are investigated.
The geometry of the used microfluidic channel is depicted in Fig. 7. Upon applying a voltage V 0 on both sides of the separation channel, the bipolar electrodes at the bottom of the channel become activated.Microplastic particles flow out from the top of the channel, while purified water flows out from the bottom of the channel.

Effect of applied voltage on separation efficiency
When the applied voltage V 0 is varied, the magnitude of the overpotential on the bipolar electrode is changed, which affects the oxidation-reduction reaction rate.Finally, the reaction rate impacts the separation efficiency of microparticles.
The concentration distribution of microplastic particles is illustrated in a partial model of the bifurcation channel in Fig. 8, indicated by the red dashed box in Fig. 7. c m,avg is the average concentration of microplastics in the top channel.The electrochemical reaction rate near the cathode accelerates as the voltage V 0 increases, which leads to a change in the nearby electric field strength.This alteration impacts the force experienced by microplastic particles in the solution and results in a decrease in particle concentration in the bottom channel and an increase in concentration in the top channel.
We simulated the distribution of flow and electric fields to consider the convection and electromigration of microplastics.The flow rate of electroosmotic flow is accelerating with the increase of the applied voltage V 0 , which is depicted in Fig. 9a.Electroosmotic flow is predominant in the motion of particles away from the bipolar electrode.Additionally, the properties of fluid flow become complex near the electrode for the changing electric field.
We can also observe the changing electric field in Fig. 9b.The reaction of the electrode affects the electric field in the bipolar electrode cathode region, which generates a large electric gradient.the direction and magnitude of electroosmotic flow and electromigration in this region, therefore, they can affect the motion trajectory of microplastics.
To study the factors affecting the electric field, the simulation was conducted to model the ion concentrations at different voltages.Figure 10 illustrates the distribution of OH − ion concentration along the centerline of  The curves represent the electric field strength at x = 1900 μm in Fig. 12, as indicated by the black dashed line in the schematic of Fig. 7.With the increase in the applied voltage V 0 , the overall electric field near the cathode rises.This phenomenon enhances the electric migration effect experienced by microplastic.The initial equilibrium is disrupted because of the increasing electric migration effect.The microplastic particles move toward the lower electric field direction.
Figure 13 depicts the distribution of microplastic concentration at the same location.Due to the alteration in electric field strength, the forces acting on microplastic particles are modified and influence the concentration of microparticles near the cathode.Lastly, the force affects the trajectory of the particles.
To investigate the influence of different voltages on the separation factor of plastic, we define the separation factor r as the ratio of the concentration of the tiny plastic in the top channel to that in the bottom channel.The variation of the separation factor under different voltages is illustrated in Fig. 14.As the voltage V 0 increased from 30 to 50 V, the separation factor increases by up to about 50%.The relationship between voltage and separation factor is as follows: Due to the large electromigration effect of the accelerated reaction electrochemical reaction rate, this phenomenon indicates an improved separation efficiency with the development of voltage.However, with the increase in voltage, more secondary reactions occurred on the bipolar electrodes.These reactions can render the separation of microplastic particles uncontrollable.Simultaneously, escalating the voltage leads to an increase in the temperature within the microchannels because of the generation of more heat.Therefore, it is imperative to comprehensively consider the influence of voltage based on the actual application scenario.

Effect of separation channel angle on separation efficiency
The varying angle θ of the separation channel alters the flow patterns of the fluid, which causes a shift in the locations where H + and OH − accumulate.This change affects the magnitude of the electric and the trajectory of the microplastic particles field within the microchannel.The microplastic concentration and flux near the cathode are depicted in Fig. 15.The average concentration of the upper channel is almost constant, and the flux changes very little at angles between 5° and 30°.When the angle is greater than 30°, the flux of microplastic particles changes significantly.
To further explore the above changes, we simulate the electric field inside the microchannel.The distribution of the electric field is illustrated along the midline of the bottom channel in Fig. 16.The conductivity of the solution changes very little because the overall concentration in the solution barely changes at angles between 5° and 30°.Therefore, the electric field does not change much in this range.However, the local electric field strength changes due to the change in particle flux at more than 30°.
The relationship between the angle and the separation factor is depicted in Fig. 17.The relationship between angle and separation factor is as follows: (23)  r=3.017 + 0.001θ  As the angle θ of the bifurcation channel continuously increases, the electric field strength remains relatively constant.Therefore, the magnitude of the separation factor ranges from 3.02 to 3.06, showing a subtle variation in the separation efficiency.It manifests that the varying angle has little effect on separation efficiency.

Effect of bipolar electrode distance on separation efficiency
The cathode position of the bipolar electrode represents the most dynamically changing region of the electric field.In this simulation, we keep the position of the anode fixed while altering the distance d between the two electrodes to change the cathode position.Altering the cathode position leads to variations in the most dynamically changing region of electric field strength.Consequently, the electro-migration effect experienced by microplastic particles is altered and affects the trajectory of plastic microbead motion.
The concentration distribution of microplastic particles is presented in the channel for different cathode positions of the bipolar electrode in Fig. 18. Figure 18 shows that the concentration of microplastic particles rises in the bottom channel and decreases in the top channel as distance d between the two electrodes increases.The phenomenon indicates a weakening of the separation efficiency.
To further analyze the results of the microplastic concentration distribution, we conduct additional simulations involving electric field and microplastic particle concentration.Figure 19 shows the electric field at the centerline position of the bottom channel.
It is evident that the electric field near the bipolar electrode increases significantly from 7.5 to 7.9 kV/m when the cathode of the bipolar electrode moves towards the positive voltage side.This increase is attributed to an increased potential near the inlet of the runners.The rate of chemistry reaction is increased by elevated potential, which leads to increased solution conductivity.Significant variations in the electric field gradient occur near the bipolar electrode.
However, due to the premature change in the electric field gradient within the microchannel, microplastic particle concentrations become re-mixed after separation.It fails to achieve the desired separation effect.When the bipolar electrode is close to the bifurcation point of the channel (x = 2000 μm), the electric field is the highest near the bifurcation point.Microplastic particles experience a substantial electro-migration effect, resulting in more thorough separation.
Figure 20 represents the microparticle concentration at x = 1900 μm.It is observable that the curve becomes smoother for the increasing distance d, indicating a poorer separation efficiency.When the distance d is 2900 μm, the ratio of the highest concentration to the lowest concentration can reach 7.95, which shows an effective separation.
Figure 21 illustrates the relationship between the separation factor r and the distance d between the bipolar electrodes.The expression of this relationship is as follows: The separation factor exhibits an exponential decay as distance increases in Fig. 21.The electric field is highest near the bifurcation point in the smallest distance, resulting in the strongest electro-migration effect and better  www.nature.com/scientificreports/separation efficiency.Conversely, the overall increased field strength is unable to achieve effective separation due to being far from the bifurcation point, which leads to a decrease in the separation factor.To further confirm the separation effect of the microchannels, the separation factor without bipolar electrode action is calculated in Fig. 21.The results show that the separation factor without bipolar electrodes (BPE inactive) is always 1, which means that there is no significant separation effect without bipolar electrodes.On the contrary, the separation factor with the bipolar electrode (BPE active) is higher than 1.This phenomenon  indicates that the concentration of the top channel is higher than that of the bottom channel, which means a good effect of separation.
The outlet concentration of microplastics is measured to clearly illustrate the effect of microchannel separation.These results depicted in Table 2 show that the outlet concentration is consistent under the condition of no bipolar electrode.In addition, the top outlet concentration is greater than that of the bottom outlet concentration under the influence of bipolar electrodes.The concentration of the lower channel is reduced to less than half of the original level when the separation factor reaches more than 2, which means an acceptable range in this study.

Conclusions
In this study, we utilized the redox reactions at the bipolar electrode to separate microplastic particles.We employed commercial finite element software to simulate the behavior of microplastic particles in the separation channel.By varying the applied voltage and the separation channel angle, we investigated the influencing factors on microplastic particle behavior.Additionally, we proposed a performance evaluation scheme for separation efficiency.
(1) Based on the original separation channel, we propose an improved simplified model of a bifurcated channel utilizing Faradaic electrode reactions under buffer-free solution conditions.(2) Utilizing the finite element method to simulate variations in different parameters, we propose a performance evaluation metric to measure the efficiency of microplastic separation.(3) The simulation results demonstrate that the microchannel can effectively separate microplastic particles under the condition of no buffering solution.Furthermore, with an increase in the applied voltage V 0 from 30 to 50 V, the oxidation-reduction reaction rate at the bipolar electrode increases.The concentration of OH − near the cathode increases by approximately 20%, from 4.5 to 5.5 mol/m 3 .Consequently, the separation factor of microplastics also increases by 50%.( 4) With an increase in the separation channel angle, there is a slight improvement in the microplastic particle flux in the top channel.However, the separation factor of microplastic particles remains relatively stable with little variation.(5) As the distance d between the bipolar electrodes increases, the separation factor r exhibits exponential decay.When the distance increases from 2700 to 3500 μm, the separation factor decreases from 6.14 to 1.47, indicating a gradual deterioration in the separation efficiency.

Figure 2 .
Figure 2. Distribution of electric potential and electric field near bipolar electrodes.(a) Solution potential and bipolar electrode potential.(b) Changes in electric field strength near the bipolar electrode and force acting on microplastic particles.

Figure 3 .
Figure 3. Electric field and potential distribution within the microchannel.

Figure 4 .
Figure 4. Current density and electric field distribution within the microchannel.

Figure 5 .
Figure 5.The separation principle in the bifurcation channel.

Figure 8 .
Figure 8. Concentration and flux distribution of microplastic particles in partial microchannels at different voltages (unit: mol/m 3 ).

Figure 9 .
Figure 9. Distribution of flow and electric fields at different voltages.(a) Velocity distribution in the microchannel (unit: mm/s).(b) Electric fields distribution in the microchannel (unit: kV/m).

Figure 10 .
Figure 10.Concentration of hydroxide ions at different voltages.

Figure 11 .
Figure 11.Electric field distribution at different voltages.

Figure 12 .
Figure 12.Electric field along the y-direction at different voltages.

Figure 13 .
Figure 13.Microplastic particle concentration along the y-direction at different voltages.

Figure 14 .
Figure 14.The relationship between separation factor and voltage variation.

Figure 15 .
Figure 15.Concentration and flux distribution of microplastic particles in partial microchannels at different angles (unit: mol/m 3 ).

44 Figure 16 .
Figure 16.Distribution of electric field strength at different angles.

Figure 17 .
Figure 17.The relationship between separation factor and angle variation.

Figure 18 .
Figure 18.Concentration and flux distribution of microplastic particles in partial microchannels at different bipolar electrode distances (unit: mol/m 3 ).

Figure 19 .
Figure 19.Distribution of electric field at different bipolar electrode distances.

Figure 20 .
Figure 20.Microplastic concentration along the y-direction at different bipolar electrode distances.

Figure 21 .
Figure 21.The relationship between separation factor and bipolar electrode distance variation.

Table 1 .
Ionic current density (unit: A/m 2 ).Position A Position B Position C