Changes In Field Intensity Research Articles

Resonance scattering generated by rotating bodies

Abstract The scattering of rotating bodies to a polarized plane wave, including the dielectric cylinder and sphere, is studied. The resonance caused by rotation is emphasized. Numerical results prove that the resonance scattering caused by rotation can be realized in the optical range. It is sensitive to the rotation dimensionless parameter γ. The internal Mie mode corresponding to the electromagnetic field intensity changes with γ, and the resonant mode appears when the particle rotates at a specific speed. Moreover, the resonant mode changes with γ. It causes resonance scattering to appear in the same particle at different speeds. Inside particles, resonant rings are composed of a series of array points and are determined by γ. Under resonance conditions, the energy near the rotating cylinder is consistent with its rotation direction. In contrast, the direction of energy flow in the rotating sphere model is opposite to the direction of particle rotation. This work provides a novel idea for the design of ultra-sensitive sensors and resonators. It has promising applications in optical communication, optical microscopy, and optical signal processing.

A novel electric field-assisted material extrusion process for clean additive manufacturing

Material extrusion (MEX) is a type of additive manufacturing technique that is widely used in a variety of applications. However, the issue of reduced quality of printed parts caused by degraded polymer debris accumulation on the nozzle surface during the MEX process has received very limited attention. This work presents a novel electric field-assisted MEX (E-MEX) method to solve the quality issue by significantly reducing the accumulations of polymer debris on the nozzle. By applying a high-voltage power source between the nozzle and the build plate, an electrostatic force was generated to overcome the which showed great potential to reduce the accumulation of molten thermoplastic material on the nozzles. Both the E-MEX and conventional MEX methods were used to print test specimens for specific amounts of time to confirm the efficacy of the E-MEX method. 3D scanning was used to quantify the volumes of debris that had accumulated on the nozzle. Compared to the conventional MEX method, the E-MEX printing reduced debris accumulation by 47 % after about 5 h and over 80 % after about 15 h of the printing process. The changes in electric field intensity over orienting height were analyzed using numerical simulations. The relationship between electric field intensity and time spent by the nozzle during the printing process at a specific height was established. The polymer accumulation in the E-MEX process was found to be dependent on the electric field intensity and the continuous time spent by the nozzle in the weaker electric field enhanced polymer debris accumulations on the nozzle surfaces. The presented study integrates experimental observations with simulation results, revealing the mechanism of debris accumulation on the nozzle when the electric field decreased to a certain level during printing process. A numerical simulation model was developed to understand the traveling of accumulated polymer debris from the nozzle's outer surface to the printing layer under the influence of electrostatic force. The simulation results showed that the dragging of polymer debris towards the build plate occurs when the electric force acting in the tangential and normal direction is sufficient to overcome the viscous force and normal force in the polymer debris. The simulation results also showed some part of the debris remained in the crease area of the nozzle surface due to the viscous and surface tension forces prevailing over the electric force.

Paleoenvironmental Controls on the Abundances of Magnetofossils in the Southwestern Iberian Margin

AbstractMagnetofossils are nanosized magnetic fossil remnants of magnetotactic bacteria (MTB) that are widely distributed in marine and freshwater sediments. Past studies have revealed that changes in the morphology and abundance of magnetofossils are linked with diverse paleoenvironmental changes, such as glacial‐interglacial variation, redox conditions associated with primary productivity and organic matter supply, chemical weathering and diagenesis. Besides, it has long been speculated that changes in geomagnetic field intensity could also affect the abundance of magnetofossils. However, it is not yet clear, how these environmental factors controlled past MTB populations in combination. To answer this question, we studied magnetofossils‐rich sediments from cores MD01‐2443 and 2444 off the Southwest Iberian Margin. The paleomagnetic records of our samples reveal geomagnetic excursions corresponding to the Laschamp, Blake, Iceland Basin, and Pringle Falls events. We estimated the relative abundance of magnetofossils in the samples based on isothermal remanent magnetization unmixing and found it to increase during warmer periods and decrease during colder periods, while not covary with changes in the geomagnetic field intensity. To further distinguish the role of different paleoenvironmental factors, we compared magnetofossil abundance with planktonic δ18O, δ13C of organic matter, K/Al and Si/Al, which indicate continental ice volume (paleotemperature), organic matter origin, run‐off intensity and productivity, respectively. The results indicate that less continental ice volume (higher paleotemperature), enhanced productivity and run‐off intensity are closely related and jointly promoted magnetofossil production and preservation. Our study offers a comprehensive approach to understanding how magnetofossil assemblages relate to paleoenvironmental changes off the SW Iberian Margin.

Biphasic Regulation of Apoptosis Following Gastric Irreversible Electroporation Using Tissue Immunohistochemistry of Activated Caspase-3 with TUNEL Method.

The regulation of apoptosis is the primary goal of ablation therapy. Irreversible electroporation (IRE) is a promising non-thermal tissue ablation-based therapy that induces apoptosis by manipulating electrical conditions. This study aimed to investigate IRE-induced gastric tissue apoptosis in response to changes in the electric field intensity, followed by the repair process. Among the 52 rats used in this study, 24 were used to explore apoptosis, and 28 were used to study regeneration. The apoptosis-to-necrosis ratio of the electrical field strength was evaluated using terminal deoxynucleotidyl transferase-mediated deoxyuridine triphosphate nick-end labeling and caspase-3 immunohistochemistry. The size of IRE-induced ulcers in the gastric tissue continuously increased with increasing electrical intensity (r2 = 0.830, p < 0.001). The level of apoptosis gradually decreased after peaking at 200 V (1000 V/cm). The size of the 400 V-ablated ulcers continued to decrease, and they were not visible by day 14. The proliferation and migration of epithelial cells with fibroblasts were observed on day 3 and augmented on day 7 post-ablation. This investigation demonstrated the biphasic activation of apoptosis with respect to the electrical field strength. Visually and histologically, IRE-induced gastric ulcers demonstrated complete tissue regeneration after two weeks.

Rapid Changes in Strength and Direction of Earth's Magnetic Field Over the Past 100,000 Years

AbstractPrevious studies of rapid geomagnetic changes have highlighted the most extreme changes in direction and field strength found in paleomagnetic field models over the past 100 ky. Here we study distributions of rates of change in both time and space. Field models based on direct observations provide the most accurate values for rates of change, but their short duration precludes a complete description of field behavior. Broader representation is provided by time‐varying paleofield models, here including GGF100k, GGFSS70, LSMOD.2, CALS10k.2, HFM.OL1.A1, pfm9k.2, and SHAWQ‐iron age although variability across models and lack of temporal and spatial resolution of fine scale variations make direct comparisons difficult. For the paleofield we define rapid changes as exceeding the peak overall value of 0.4° yr−1 for directional changes and 150 nT yr−1 for intensities as established by the gufm1 model spanning 1590–1990 CE. We find that rapid directional changes are associated with low field strength and can spread across all latitudes during such episodes. Distributions of directional rates of change exhibit high skewness for models that include excursions. Rates of change in field intensity exceeding 150 nT yr−1 arise in brief intervals during the Holocene particularly associated with the strong field Levantine Iron Age Anomaly. Around the Laschamp excursion there are also rare localized occurrences of rapid intensity change. Limitations in current models make it difficult to define absolute rates for past changes, but we see that rapid changes are essential field characteristics not observed in the modern field that should nevertheless be regarded as an essential for Earth‐like dynamo simulations.

Effects of the applied fields' strength on the plasma behavior and processes in E × B plasma discharges of various propellants. II. Magnetic field

The effects of magnetic field intensity on the properties of the plasma discharge and on the underlying phenomena are studied for different propellants' ion mass. The plasma setup represents a 2D radial–azimuthal configuration with perpendicular electric and magnetic fields. The electric field is along the axial direction, and the magnetic field is along the radial direction. The magnetic field intensity is changed from 5 to 30 mT, with 5 mT increments. The studied propellant gases are xenon, krypton, and argon. The simulations are carried out using a reduced-order particle-in-cell code. It is shown that, for all the propellants, the change in the magnetic field intensity yields two distinct plasma regimes, where either the modified two-stream instability (MTSI) or the electron cyclotron drift instability (ECDI) are dominant. A third plasma regime is also observed for cases with moderate values of the magnetic field (15 and 20 mT), where the ECDI and the MTSI co-exist with comparable amplitudes. This described variation of plasma regime becomes clearly reflected in the radial distribution of the axial electron current density and the electron temperature anisotropy. At the relatively low-magnetic-field intensities (5 and 10 mT), the MTSI is mitigated. At relatively high magnitudes of the magnetic field (25 and 30 mT), the MTSI becomes strongly present, a long-wavelength wave mode develops, and the ECDI becomes suppressed. An exception to this latter observation was noticed for xenon, for which the ECDI was observed to be detectable with a notable strength up to the magnetic field value of 25 mT.

Mathematical modeling of the magnetic field in the vicinity of narrow capillaries

A mathematical model of the magnetic field, which is generated by negative charges located on the outer side of the red blood cell (RBC) membrane, has been constructed. When modeling, the geometric (area, volume) and physical (speed, number of revolutions per second, charge, number of charges on the membrane) characteristics of a red blood cell in a narrow capillary are taken into account. Computer calculations made it possible to find the magnetic field strength near a single RBC rolling along a narrow capillary. Calculations were also carried out to determine the magnetic field strength in the vicinity of a capillary through which several RBCs move. The dependence of the maximum magnetic field strength on the distances between RBCs (hematocrit) was found. In particular, it is shown that at distances from the capillary equal to 8 capillary diameters, the maximum magnetic field intensity changes on average by 1.3 times with an increase in hematocrit by 1.5 times (from 12.27% to 18.25%).

Simulation analysis of enhanced fluidization leaching process and geothermal synergy in deep ground metal mines

Based on the mining of deep metal mineral resources and the current in-situ leaching mining process of uranium ore, combined with the technological characteristics of ?fluidized mining of metal ore? and ?deep geothermal development?, an innovative concept of strengthening the fluidized leaching process of deep metal ore - geothermal co mining is proposed, A numerical simulation method was used to analyze the turbulent flow and heat transfer characteristics of a new type of heat transfer enhancement element - a swirl plate as a support between tubes. The renormalization two equation turbulence model was used for numerical simulation, and the SIMPLEC algorithm was used for pressure and velocity coupling, and the enhanced wall treatment method was used for wall treatment. The periodic changes in the cross-sectional flow field and turbulence intensity of the unit flow channel were analyzed, as well as the synergistic relationship between the flow field and temperature field on the cross-section. The corresponding variation trends of the average Nusselt number and the average synergy angle of the cross-section were compared. The experimental results show that the 270-4.25 cyclone sheet can more fully utilize the enhanced heat transfer of the spin flow, and the overall average Nusselt number is higher than 180-2.0, which is consistent with the experimental results. That is, ?m is low where high Nub and ?m is high where low Nub is low, indicating that the changing trend of the two is fully consistent with the field synergy principle. This paper systematically analyzes the basic theoretical bottleneck, key technical problems and future development trend in the process of geothermal joint mining of deep metal mine, and aims to provide reference for the strengthening of geothermal joint mining and geothermal joint mining of deep metal ore.

Electric field and force characteristic of dust aerosol particles on the surface of high-voltage transmission line

High-voltage transmission lines play a crucial role in facilitating the utilization of renewable energy in regions prone to desertification. The accumulation of atmospheric particles on the surface of these lines can significantly impact corona discharge and wind-induced conductor displacement. Accurately quantifying the force exerted by particles adhering to conductor surfaces is essential for evaluating fouling conditions and making informed decisions. Therefore, this study investigates the changes in electric field intensity along branched conductors caused by various fouling layers and their resulting influence on the adhesion of dust particles. The findings indicate that as individual particle size increases, the field strength at the top of the particle gradually decreases and eventually stabilizes at approximately 49.22 kV/cm, which corresponds to a field strength approximately 1.96 times higher than that of an unpolluted transmission line. Furthermore, when particle spacing exceeds 15 times the particle size, the field strength around the transmission line gradually decreases and approaches the level observed on non-adhering surface. The electric field remains relatively stable. In a triangular arrangement of three particles, the maximum field strength at the tip of the fouling layer is approximately 1.44 times higher than that of double particles and 1.5 times higher compared to single particles. These results suggest that particles adhering to the transmission line have a greater affinity for adsorbing charged particles. Additionally, relevant numerical calculations demonstrate that in dry environments, the primary adhesion forces between particles and transmission lines follow an order of electrostatic force and van der Waals force. Specifically, at the minimum field strength, these forces are approximately 74.73 times and 19.43 times stronger than the gravitational force acting on the particles.

Magnetic field caused enhanced absorption and circular dichroism of an achiral plasmonic nanostructure.

In this paper, modulation of light-matter interactions by a magnetic field is used to generate circular dichroism (CD) from an achiral plasmonic nanostructure. Theoretical investigations show an increase in light absorption by the nanostructure in the presence of a magnetic field. The achiral nanostructure exhibits CD in external magnetic field parallel to circularly polarized light (CPL) incidence. The CD emergence is caused by modulation of electron motion to reduced/enhanced frequencies under CPL incidence. Compared to previous studies, in this paper the mechanism of CD emergence, and the physical reasoning behind the change in CD due to change in magnetic field direction and intensity, are explained. CD intensity increases with increasing magnetic field intensity, while CD sign changes on magnetic field direction reversal. Varying structural parameters significantly influences CD intensity. This study can be helpful in magneto-optics and in magneto-chiral applications.

Electric Field Characteristics of HDPE-NR Biocomposite Under Breakdown Condition

It is critical to develop new insulating materials that can improve the performance of next generation high voltage cables for creating future electrical networks. The high electric field reduces the resistance of solid insulation and produces partial discharge through imperfections in a dielectric, causing the dielectric to age and eventually fail. Thus, this project seeks to analyse the electric field intensity of High Density Polyethylene (HDPE) in breakdown condition when added with 10g, 20g and 30g of different types of bio-filler such as coconut coir fibre, pineapple leaves fibre, and oil palm empty fruit bunch. This can be achieved by creating a two-dimensional (2D) axisymmetric electrostatic model by using the Finite Element Method Magnetics (FEMM) 4.2 software. The results showed that the unfilled HDPE biocomposites have a higher electric field intensity than 10g, 20g, and 30g biocomposite. This indicates that the maximum electric field intensity changes according to the permittivity and voltage of the bio-filler under breakdown conditions. As a result, the maximum electric field intensity was much lower for HDPE added with a 20g of the pineapple leaves fibre. Hence, pineapple leaves fibre was the best composition as it tends to improve the dielectricproperties since it has a lower electric field intensity at the top electrode as compared to other compositions.

A symmetric bar chart-shape microwave sensor with high Q-factor for permittivity determination of fluidics

AbstractThis paper introduces a symmetric bar chart-shape (SBCS) microwave sensor for measuring permittivity of fluidic samples. For designing purposes, the introduced sensor was used based on the field changes between the SBCS and rectangular loop microstrip (RLM) structure. When a sample is placed on the sensing location, interaction between SBCS and RLM varies the field intensity. The vinegar samples were combined with water and then they are placed on the sensor. The change in field intensity changes the resonance frequency. However, there is a relationship between the permittivity of samples and the resonance frequencies. The proposed sensor is implemented on the substrate of RO4003C. The relative permittivity of samples changed from 59 to 77 and the resonance frequencies changed from 2.3 to 1.4 GHz. The quality factor is 3544 and the sensitivity is 2.2%.

Numerical Analysis and Structure Optimization of Concentric GST Ring Resonator Mounted over SiO2 Substrate and Cr Ground Layer

Since the introduction of Metal-Insulator-Metal (MIM) absorbers, most of the structures demonstrated a narrowband absorption response which is not suitable for potential applications in photovoltaic systems, as it requires higher energy to enhance its performance. Very little research is being conducted in this direction; to address this issue, we exhibit a broadband solar absorber designed using a concentric GST ring resonator placed upon a silicon dioxide substrate layer with chromium used as a ground plane. It was analyzed using the finite element method. The design is also optimized by using a nonlinear parametric optimization algorithm. Comparatively less work has been focused on solar absorbers designed with the help of GST material, and here we have compared the effect of two different phases of GST, i.e., amorphous (aGST) and crystalline (cGST); the results indicate the higher performance of aGST phase. Parametric optimization has been adapted to identify the optimal design to attain high performance at minimal resources. The absorption response is angle insensitive for 0 to 60 degrees, and at the same time for both TE and TM modes, the design provides identical results, indicating the polarization-insensitive properties. The electric field intensity changes at the six peak wavelengths are also demonstrated for the authentication of the high performance. Thus, the proposed concentric GST ring resonator solar absorber can present a higher solar energy absorption rate than other solar structure designs. This design can be applied for improving the performance of photovoltaic systems.

Numerical simulation of streamer discharge with different electrode shapes in C4F7N

In recent years, the environmentally friendly gas, C4F7N, has been recognized as a potential SF6 alternative gas due to its excellent insulation. To study the streamer discharge characteristics of different electrode shapes in C4F7N, a fluid model was established by COMSOL, and simulations were performed. Streamer discharge as a function of varying electrode shapes was analyzed, and the variation law of electric field intensity and photon flux was obtained, which serves as a theoretical basis for optical detection and reliable diagnosis of partial discharge. Simulation results demonstrate that under the same discharge conditions, the electric field inhomogeneity of the needle–plane model, rod–plane model, and ball–plane model decreased successively and the breakdown difficulty increased. With the increase in the applied voltage, the peak electric field intensity of the streamer head was found to increase, whereas an increase in the electrode spacing was found to decrease this property. The change in photon flux was found to be similar to the change in the electric field intensity.

Temperature-compensated balloon-like fiber magnetic field sensor with F-P structure based on PDMS

A highly sensitive balloon-like fiber interferometer based on magnetic fluid (MF) nanomaterial for magnetic field measurement is proposed in this paper. The Mach-Zehnder interferometer (MZI) was formed by bending the single-mode fiber (SMF) nested in Teflon tubes, and then MF was filled into the tube of the balloon-like fiber interferometer by using the capillary effect. When the external magnetic field intensity changes, the refractive index (RI) of MF changes, resulting in the change of the difference in optical path. The change of magnetic field intensity can be detected by the shift of interference spectrum. Besides, a Fabry-Perot interference (FPI) by filling the SMF with polydimethylsiloxane (PDMS), which is only sensitive to temperature, is proposed to compensate the temperature during sensing of magnetic field. The transmission signal of the MZI and the reflection signal of FPI are cascaded together to the circulator, optical switch and other components, so that the magnetic field intensity and temperature can be measured simultaneously. The temperature sensitivity of the MZI and the FPI is –0.919 nm/℃ and1.559 nm/℃, respectively. FPI could be used to offset the effect of temperature. Consequently, the sensitivity of the magnetic field sensor can reach 0.683 nm/mT in the range of 0 to 10 mT, and the linear coefficient is 0.987. The system could be widely employed in lots of applications of magnetic field and temperature monitoring.

Electric field distribution around asymmetric agglomerate model reconstructed from FIB–SEM images of epoxy nanocomposite

AbstractThis study focussed on determining the electric field distribution formed by asymmetric agglomerates in order to elucidate the mechanism by which large agglomerates reduce the dielectric breakdown strength of nanocomposites. Epoxy nanocomposite sample was prepared by adding 2.5 vol% of TiO2nanoparticles with a primary particle size ranging from 30 to 50 nm. The three‐dimensional (3D) structure of the epoxy nanocomposites with a thickness of 5 μm was analysed via focussed ion beam and scanning electron microscopy. The 3D reconstruction was performed using 250 observation images, and a 3D model of the particle in the observational range was obtained. The electric field distribution for the 3D model of the agglomerate with the largest size was determined using the finite element method. In addition, we constructed a calculation model that effectively accommodate changes in the direction of the applied electric field. Subsequently, we examined the changes in the maximum electric field intensity around the agglomerate.

Endogenous electric field accelerates phenol degradation in bioelectrochemical systems with reduced electrode spacing.

Reducing the electrode spacing in bioelectrochemical systems (BESs) are widely reported to improve power output, which was mainly attributed to the decrease of ohmic resistance (Rohm) for a long time. Here we found the change of endogenous electric field (EF) intensity was the key to improve electroactivity in response to a reduced electrode spacing, which also accelerated phenol biodegradation. Correlation and principal components analysis revealed that the microbial community of electroactive biofilm (EAB) was independent of Rohm, while the EF intensity was found closely related to most of predominant genera. A strong EF selectively enriched phenol-degrading bacteria Comamonas in suspension and Geobacter in EAB, contributed to the improvement of degradation efficiency. EF also induced the secretion of extracellular polymeric substances, protected EAB from being inactivated by phenol. Our findings highlighted the importance of EF intensity on BESs performance, providing new insights into the design and application of BESs in wastewater treatment.

Archaeomagnetism in the Levant and Mesopotamia Reveals the Largest Changes in the Geomagnetic Field.

Our understanding of geomagnetic field intensity prior to the era of direct instrumental measurements relies on paleointensity analysis of rocks and archaeological materials that serve as magnetic recorders. Only in rare cases are absolute paleointensity data sets continuous over millennial timescales, in sub-centennial resolution, and directly dated using radiocarbon. As a result, fundamental properties of the geomagnetic field, such as its maximum intensity and rate of change have remained a subject of lively discussion. Here, we place firm constraints on these two quantities using Bayesian modeling of well-dated archaeomagnetic intensity data from the Levant and Upper Mesopotamia. We report new data from 23 groups of pottery collected from 18 consecutive radiocarbon-dated archaeological strata from Tel Megiddo, Israel. In the Near East, the period of 1700-550BCE is represented by 84 groups of archaeological artifacts, 55 of which were dated using radiocarbon or a direct link to clear historically dated events, providing unprecedented sub-century resolution. Moreover, stratigraphic relationships between samples collected from multi-layered sites enable further refinement of the data ages. The Bayesian curve shows four geomagnetic spikes between 1050 and 600BCE, with virtual axial dipole moment (VADM) reaching values of 155-162ZAm2, much higher than any prediction from geomagnetic field models. Rates of change associated with the four spikes are ∼0.35-0.55μT/year (∼0.7-1.1ZAm2/year), at least twice the maximum rate inferred from direct observations spanning the past 180years. The increase from 1750 to 1030BCE (73-161ZAm2) depicts the Holocene's largest change in field intensity.

Using molecular dynamics simulations to study the non-thermal effects of microwave radiation on the mechanism of char gasification

Studying the chemical effects of alternating electric fields on char gasification is key to exploring the non-thermal effects of microwaves on the reaction mechanism. The gasification mechanism of char in the presence of an electric field was explored through molecular dynamics (MD) simulations and quantum chemical calculations. The results show that the promotion effect of 0.02 V/Å alternating electric field on the gasification reaction rate of char is about 8 times that of non-electric field, and the square wave electric field and static electric field are 6.79 times and 5.39 times respectively, this effect increases exponentially as the field intensity increases. Interestingly, the use of alternating electric fields showed, for the first time, that the changes in the electric field intensity and direction also have a significant effect. In terms of the adsorption process during gasification, the electric field promotes the formation of O and OH free radicals (about 5 times of no electric field) and increases the polarity of the char edge, both of which are conducive to adsorption. The electric field can weaken the curling of char macromolecules and expose more active carbon sites, thus increasing the overall reaction rate. For the desorption process during gasification, the presence of the electric field promotes the deformation and tear of char, which destroys its aromaticity, loosening the carbon-oxygen compounds at the carbon edge, which facilitates the desorption of CO, the desorption rate is about 10 times that of non-electric field system. Further, the change in direction of the electric field also promotes the desorption process. The results from this study suggest that the remarkable effects of alternating electric fields on char molecules can have an impact on the field of solid fuel gasification.

Effect of electrode geometry on the flow structure induced by plasma actuators

Pulsed surface arc discharge (PSAD) is one of the essential techniques in flow control. In this paper, the effects of electrode configuration on heat transfer characteristics of PSAD and disturbance characteristics of PSAD on the flow field were investigated by thermal imaging technology and high-speed photography technology. By defining the curvature of curve (COC) of the electrode, we investigated the physical mechanism of the electrode configuration, affecting the PSAD disturbed flow field. The results show that the COC has the optimal solution COCopt. When COC ≤ COCopt, the smaller the COC, the more concentrated the PSAD disturbances to the flow field. When COC &amp;gt; COCopt, the electrode configuration will have an end point effect, resulting in a deviation between the theoretical COC and the real COC. The larger the COC, the stronger the end point effect, and the more concentrated the PSAD disturbances to the flow field. The COC affects the disturbance degree of PSAD to the flow field by distorting the electric field intensity distribution. The change in the electric field intensity causes the fluctuation frequency of the flow field to be inconsistent with the discharge frequency of the PSAD. The stronger the distortion degree of the electric field intensity, the stronger the high-frequency characteristics of the fluctuating frequency of the flow field, and the stronger the high-frequency characteristics of the flow mode of the flow field. In addition, we obtained the value range of COCopt within 0.5–0.7 through theoretical derivation and established a mathematical model of electrode structure's effect on the flow field's flow structure.