Direct Current Electric Field Research Articles

Laboratory study on the transformation of oil-water interface properties under direct current electric field

Interface tension is one of the important mechanisms that affect crude oil recovery and plays an important role in the development of tight oil reservoirs. Electrical-enhanced oil recovery can be used as a technology to reduce interfacial tension and improve crude oil recovery. In the previous research process of Electrical-enhanced oil recovery, the focus was more on the influence of electric field on wettability, and the understanding of the changes in interfacial tension under electric field action is not yet comprehensive. This article designs an orthogonal experiment to study the effect of electric field on oil-water properties. The degree of influence of three factors, namely sodium chloride solution concentration (C), direct current voltage (V), and voltage action time (t), on interfacial tension is studied. Gas chromatography, four component analysis, and Fourier transform infrared spectroscopy are combined to discuss the mechanism of the influence of changes in solution pH, crude oil components, and oil phase functional groups on interfacial tension. The results show that an external electric field can effectively reduce the interfacial tension between oil and water, and the maximum change in interfacial tension after the experiment can be reduced from 23.21 mN/m to 0.37 mN/m; Through range analysis, it can be concluded that the concentration of sodium chloride solution has the greatest impact on interfacial tension, followed by DC voltage and voltage action time. The optimal experimental conditions are 0.5mol/L sodium chloride solution, 10V DC voltage, and a voltage action time of 18 hours, and the change in interfacial tension is related to the increase in pH value. The change in crude oil composition is also an important reason for the decrease in interfacial tension under external electric fields. Finally, Fourier transform infrared spectroscopy was used to determine that under the action of an electric field, the increase in pH of the sodium chloride solution resulted in the formation of carboxylate salts through chemical reactions between alkaline substances of solution and acidic substances of the oil, which were the key factors in reducing interfacial tension. This study helps to understand and explore the principles and mechanisms of Electrical-enhanced oil recovery in improving oil recovery, with the aim of contributing to the development and promotion of Electrical-enhanced oil recovery technology.

Hemocompatibility and Preangiogenic Attributes of SiBxCyNzOm Coatings for Biomedical Applications.

In current clinical practices related to orthopedics, dental, and cardiovascular surgeries, a number of biomaterial coatings, such as hydroxyapatite (HAp), diamond-like carbon (DLC), have been used in combination with metallic substrates (stainless steel, Ti6Al4V alloy, etc.). Although SiBCN coatings are widely explored in material science for diverse applications, their potential remains largely unexplored for biomedical applications. With this motivation, the present work reports the development of SiBxCyNzOm coatings on a Ti6Al4V substrate, employing a reactive radiofrequency (RF) magnetron sputtering technique. Three different coating compositions (Si0.27B0.10C0.31N0.07O0.24, Si0.23B0.06C0.21N0.22O0.27, and Si0.20B0.05C0.19N0.20O0.35) were obtained using a Si2BC2N target and varying nitrogen flow rates. The hydrophilic properties of the as-synthesized coatings were rationalized in terms of an increase in the number of oxygen-containing functional groups (OH and NO) on the surface, as probed using XPS and FTIR analyses. Furthermore, the cellular monoculture of SVEC4-10 endothelial cells and L929 fibroblasts established good cytocompatibility. More importantly, the coculture system of SVEC4-10 and L929, in the absence of growth factors, demonstrated clear cellular phenotypical changes, with extensive sprouting leading to tube-like morphologies on the coating surfaces, when stimulated using a customized cell stimulator (StimuCell) with 1.15 V/cm direct current (DC) electric field strength for 1 h. In addition, the hemocompatibility assessment using human blood samples revealed clinically acceptable hemolysis, less erythrocyte adhesion, shorter plasma recalcification, and reduced risk for thrombosis on the SiBxCyNzOm coatings, when compared to uncoated Ti6Al4V. Taken together, the present study unambiguously establishes excellent cytocompatibility, hemocompatibility, and defines the preangiogenic properties of SiBxCyNzOm bioceramic coatings for potential biomedical applications.

Spatiotemporal dynamic temperature variation dominated by ion behaviors during groundwater remediation using direct current

Direct current (DC) electric field has shown promising performance in contaminated site remediation, in which the Joule heating effect plays an important role but has been previously underappreciated. This study focuses on the spatiotemporal characteristics and mechanism of temperature change in heterogeneous porous media with applied DC. The heating process can be divided into four phases: preferential heating of the low permeability zone (LPZ), rapid heating in the middle region, temperature drop and hot zone shift, and reheating. The dynamic ion behaviors with complex interplays among reactions, electrokinetic-driven migration, and mixed convection induced an uneven redistribution of ions and dominated the heating rate and temperature distribution. The concentration of major ions near the pH jump decreased to 1% of the initial value, even though ions were continuously pumped into the heating zone. This ion depletion caused a drop in current, heating rate, and temperature. Here ions cannot be delivered rapidly into the ion-depleted zone by electromigration due to the potential flattening in the surrounding region. The presence of LPZ intensified the nonuniformity of ion redistribution, where a regional focusing of water-soluble ions was observed, and weakened the temperature rebound compared with that using homogeneous sand. These results provide a new perspective on the regulation of DC heating in site remediation.

Electromechanical properties and domain evolution of a tetragonal Er3+-doped Pb(Mg1/3Nb2/3)O3–PbTiO3 ferroelectric single crystal

Herein, a tetragonal Er3+-doped Pb(Mg1/3Nb2/3)O3–PbTiO3 single crystal is comprehensively investigated. The actual composition of the studied crystal is Pb(Mg1/3Nb2/3)O3–36PbTiO3 doped with 0.17-mol% Er3+ (PMN–36PT: 0.17-mol% Er3+). The crystal exhibits a high shear piezoelectric constant of ∼936 pC/N, approximately three times the longitudinal piezoelectric constant when poled along [001]c, as well as a higher Curie temperature of ∼170 °C and large coercive field of ∼4.58 kV/cm. At room temperature, the crystal presents a mass of domain walls along the <110>c direction and extinction is observed four times within a 360° rotation, showing typical domain features of the tetragonal phase. Under a direct current–electric field along the [010]c direction, the extinction rule remains unchanged; however, changes in the domain configuration can be observed. In addition, the orientation dependence of the piezoelectric constant, dielectric coefficient, elastic compliance constant, and electromechanical coupling factor is calculated using the coordinate transformation method. The findings of this study are of considerable importance for the fundamental studies and device design of tetragonal ferroelectric crystals.

Inactivation of polyphenol oxidase by low intensity DC field: Experiment and mechanism analysis via molecular dynamics simulation and molecular docking

In this study, inactivation of mushroom polyphenol oxidase (PPO) by low intensity direct current (DC) electric field and its molecular mechanism were investigated. In the experiments under 3 V/cm, 5 V/cm, 7 V/cm and 9 V/cm electric fields, PPOs were all completely inactivated after different exposure times. Under 1 V/cm, a residual activity of 11.88 % remained. The inactivation kinetics confirms to Weibull model. Under 1–7 V/cm, n value closes to a constant about 1.3. The structural analysis of PPO under 3 V/cm and 5 V/cm by fluorescence emission spectroscopy and molecular dynamics (MD) simulation showed that the tertiary structure was slightly changed with increased radius of gyration, higher potential energy and rate of C-alpha fluctuation. After exposure to the electric field, most of the hydrophobic tryptophan (TRP) residues turned to the hydrophilic surface, resulting the fluorescence red-shifted and quenched. Molecular docking indicated that the receptor binding domain of catechol in PPO was changed. PPO under electric field was MD simulated the first time, revealing the changing mechanism of the electric field itself on PPO, a binuclear copper enzyme, which has a metallic center. All these suggest that the low intensity DC electric field would be a promising option for enzymatic browning inhibition or even enzyme activity inactivation.

Electroosmotic flow in soft clay and measures to promote movement under direct current electric field.

Electroosmosis has been proposed as a technique to reduce moisture and thus increase the stability of soft clay. However, its high energy consumption and uneven reinforcement effect has limited its popularization and application in practical engineering. This paper presents the results of some electrokinetic tests performed on clayey specimens with different electrification time and anode boundary conditions. The results indicate that the timing of the formation of electroosmotic flow (EF) by the water originally contained in different soil cross sections, from the anode to the cathode, varies. The measuring soil cross section nearest the anode first reached the limiting water content of 22%±3% and electroosmosis had to be stopped. Water injection into the anode during electroosmosis enhanced further drainage of other four measuring soil cross sections until the second soil cross section from the anode reached the limiting water content of 30%±2%. Electroosmosis with water injection into the anode technique provides more uniform reinforcement, increasing EF, and environmental protection. The experimental results highlighted the relevant and expected contribution of water injection into the anode on the effectiveness of the electroosmotic treatment as a soft clay improvement technique.

Migration of human T cells can be differentially directed by electric fields depending on the extracellular microenvironment

T cell migration plays an essential role in the immune response and Tcell-based therapies. It can be modulated by chemical and physical cues such as electric fields (EFs). The mechanisms underlying electrotaxis (cell migration manipulated by EFs) are not fully understood and systematic studies with immune cells are rare. In this invitro study, we show that direct current EFs with strengths of physiologically occurring EFs (25-200mV/mm) can guide the migration of primary human CD4+ and CD8+ Tcells on 2D substrates toward the anode and in a 3D environment differentially (CD4+ Tcells show cathodal and CD8+ Tcells show anodal electrotaxis). Overall, we find that EFs present a potent stimulus to direct Tcell migration in different microenvironments in a cell-type-, substrate-, and voltage-dependent manner, while not significantly influencing Tcell differentiation or viability.

Falling, deformation, and coalescence of droplet in model waxy oil under an electric field

Electrocoalescence technology can efficiently dehydrate waxy crude oil but the mechanisms are still unclear. Herein, the continuous microscopic behaviors of droplet falling, deformation, and coalescence were experimentally investigated to clarify the dynamic response mechanism of droplet in waxy oil under an electric field. The results showed the droplet falling under both gravity and electrostatic attraction to deform by the electric field force. Moreover, the expansion and clamping of the liquid bridge resulted from the competition between electric field force and capillary force. However, the precipitated wax crystals reduced the kinetic energy of the droplet and affected its external circulation, thus delaying the falling time. In addition, the wax crystals with interfacial activity adsorbed on the oil-water interface and cross-linked to form a spatial network structure, thereby weakening droplet deformation, hindering liquid film drainage, and inhibiting liquid bridge expansion. Importantly, the droplet adsorbed wax crystals exhibited interfacial elasticity, which makes them more inclined to partial coalescence. The low-frequency pulsed direct current (PUDC) electric field with high strength intermittent effect displayed the most obvious inhibition effect on the wax crystals. Overall, these findings look promising for future design and optimization of high-efficiency electric dehydrators and related fields.

Recovery of biochar particles laden with lead in saturated porous media by DC electric field

The co-transport behavior of environmental pollutants with biochar particles has aroused great interests from researchers due to the concerns about pollutant diffusion and environmental exposure after biochar is applied to soil. In this work, the recovery and co-transport behavior of biochar micron-/nano-particles (BCMP and BCNP) and lead (Pb2+) in saturated porous media were investigated under different ionic strength conditions (IS = 1, 5 and 10 mM) under a direct current electric field. The results showed that the electric field could significantly enhance the mobility of Pb adsorbed biochar particles, particularly BCNP. The recovery of Pb laden biochar particles was improved by 1.8 folds, reaching 78.8% at maximum under favorable condition at +0.5 V cm−1. According to the CDE (Convection-Dispersion-Equation) model and DLVO (Derjaguin-Landau-Verwey-Overbeek) theory analysis, the electric field facilitated the transport of Pb carried biochar mainly by increasing the negative charges on biochar surface and improving the repulsive force between biochar and porous media. High IS was favorable for biochar transport under the electric field, but inhibited desorbing Pb2+ from biochar (18% by maximum at IS = 10 mM). By switching the electric field power, a two-stage strategy was established to maximize the recovery of both biochar particles and Pb, where BCNP and Pb recovery were higher than electric field free case by 90% and 35%, respectively. The findings of this study can help build a biochar recovery approach to prevent potential risks from biochar application in heavy metal contaminated soil remediation.

Microstructural analysis of flash-healed Vickers-indented microcracks near positive/negative electrodes on the (001) surface of cubic zirconia single crystals under direct current electric fields

Flash healing is a technique that uses power spikes to rapidly repair microcracks on ceramic surfaces. In this study, the microstructures of flash-healed Vickers-indented microcracks near the positive/negative electrodes under a DC electric field were examined by scanning transmission electron microscopy. The microstructural morphology near the positive electrode was almost identical to that of the microcracks located between both electrodes, as previously reported. However, a decrease in the degree of healing was observed near the negative electrode. This was attributed to the insufficient recovery of dislocations generated at the indentation state, which should have occurred in the initial stage of healing. The delay in dislocation recovery prevented contact between the inner surfaces of the microcracks and is possibly related to the increase in oxygen vacancies near the negative electrode.

Characterization of electric field distribution in valve-side casing of 500 kV converter transformer considering AC and DC mixed voltage

The converter transformer, as one of the indispensable core devices in the ultra-high voltage direct current (UHVDC) transmission system, exhibits highly complex electric field distribution characteristics within the valve-side bushing. In-depth research into the electric field distribution characteristics and variation patterns of the valve-side bushing under both alternating current (AC) and direct current (DC) voltage conditions is crucial for ensuring the reliable operation of the transmission system. This study focuses on investigating the electric field distribution of the valve-side bushing under AC and DC voltage excitations. A full-scale finite element model of the valve-side bushing of the converter transformer is constructed using finite element simulation software for modeling and research purposes. The results indicate that the internal electric field distribution of the bushing is generally similar under both AC and DC voltage excitations. However, in the SF6-filled region, a steeper voltage drop is observed under DC excitation compared to AC. The space charges generated in the DC electric field due to field polarization have a significant impact on the distortion of the electric field on the inner and outermost layer electrode plates. These conclusions provide theoretical guidance for the insulation design of the valve-side bushing in converter transformers at the 500 kV voltage level and similar ratings.

Wetting and evaporation behavior of dilute sodium dodecyl sulfate droplets on soft substrates under a direct current electric field

Wetting and evaporation behavior of dilute sodium dodecyl sulfate (SDS) droplets on planar polydimethylsiloxane (PDMS) surfaces under a direct current (DC) electric field were experimentally investigated. Two characteristic voltages—actuation voltage and saturation voltage were observed in the electrowetting of dilute SDS droplets on PDMS surfaces. It was found that for dilute SDS droplets with a fixed SDS concentration substrate elasticity has an obvious influence on actuation voltage, and saturation voltage increased with the increase of mass ratio of PDMS surfaces. SDS concentration was also found to obviously influence actuation voltage and saturation voltage when SDS concentration was in a certain range. For the case of evaporation of sessile dilute SDS droplets on PDMS surfaces with the application of a DC electric field, substrate elasticity, SDS concentration and the magnitude of applied voltage were all found to have an influence on the duration of CCR stage. Moreover, contact angle hysteresis for dilute SDS droplets on a planar PDMS 10:1 surface under different applied voltage was measured and it was found that the magnitude of applied voltage greatly influenced contact angle hysteresis, which also depends on SDS concentration and KCl concentration.

Electroosmosis and electrophoresis in soft clay under direct current electric field

The demand for innovative and cost-effective in-situ consolidation technologies in soft clay stimulated the effort to employ electrokinetic phenomena in soils under an electric field. This work explains the principles of electrophoresis and electroosmosis in soft clay under an electric field and discusses the implacations of these results for field implementation of the technique. The experimental work reported here was carried out to shed light on the principles by considering various influencing factors. The results show that there is a threshold current (about 15 mA) for electroosmosis and electrophoresis in soft clay. Below the threshold current, electrophoresis plays a major role and is accompanied by weak electroosmosis. The particle size, dry density, and boundary rise height of electrophoretic soil in anode chamber are mainly affected by soil moisture content, electrode in electrolyte length, and bottom of electrode to soil surface distance. The closer the soil moisture content is to the average value of the liquid limit and plastic limit, the denser the electrophoretic soil will be. Above the threshold current, almost only electroosmosis occurs. The greater the current, the greater the electroosmosis. In practical engineering application, electrodes are usually directly inserted into the soft clay. This results in the current usually being much greater than the threshold current, meaning the electrophoretic phenomenon in the soil can be negligible.

Glioblastoma U-87 cell electrotaxis is hindered by doxycycline with a concomitant reduction in the matrix metallopeptidase-9 expression

Electric fields (EF) play an essential role in cancer cell migration. Numerous cancer cell types exhibit electrotaxis under direct current electric fields (dcEF) of physiological electric field strength (EFs). This study investigated the effects of doxycycline on the electrotactic responses of U87 cells. After EF stimulation, U87 cells migrated toward the cathode, whereas doxycycline-treated U87 cells exhibited enhanced cell mobility but hindered cathodal migration. We further investigated the expression of the metastasis-correlated proteins matrix metallopeptidase-2 (MMP-2) and MMP-9 in U87 cells. The levels of MMP-2 in the cells were not altered under EF or doxycycline stimulation. In contrast, the EF stimulation greatly enhanced the levels of MMP-9 and then repressed in doxycycline-cotreated cells, accompanied by reduced cathodal migration. Our results demonstrated that an antibiotic at a non-toxic concentration could suppress the enhanced cell migration accelerated by EF of physiological strength. This finding may be applied as an anti-metastatic treatment for cancers.

Nanoparticle-laden droplet-liquid film electrocoalescence behaviors: A molecular dynamics simulation

Electrocoalescence is an efficient and environmentally friendly process for separating water-in-oil (W/O) emulsions. In this paper, molecular dynamics (MD) simulation method was used to study the electrocoalescence behaviors of nanoparticle-laden (NP-laden) droplet-liquid film. The results showed that the coalescence behaviors successively exhibited three modes, i.e., complete coalescence (CC) mode, critical state, and partial coalescence (PC) mode, with increasing direct current (DC) electric field strengths. The alternating current (AC) electric fields tended to promote the CC mode, and the coalescence efficiencies increased with increasing frequencies. Compared with the pure water droplet, the NP-laden droplets had greater tendencies to exhibit PC mode. In addition, the droplet with large We numbers produced strong impact force, and thus promoted rapid coalescence process. In the two-droplets system, due to the large number of water (H2O) molecules, droplet polarization phenomena were much significant under electric fields, hence resulting in PC mode at small field strengths. It is noteworthy that, at the absence of electric fields, the huge initial kinetic energy (EK) carried by the two droplets could overcome the surface energy (ES) at small We, and thus the droplet was detached from the liquid film. This work can provide theoretical guidance for designing compact and efficient oil–water separators.

Effect of electric and electromagnetic fields on energy consumption, texture, and microstructure of dried black garlic

Drying is one of the most energy-intensive food processing technologies and can contribute to greenhouse gas (GHG) emissions. Therefore, novel nonthermal pretreatment methods can be used to affect the plant tissue and decrease the drying time. A pulsed electric field (PEF), direct current electric field (DCEF), and electromagnetic field (EMF) were applied to black garlic cloves which were subsequently subjected to convective pre-drying followed by a vacuum-microwave finishing drying. The effect of these pretreatments on the physical properties, energy consumption, attributes of texture profile analysis (TPA), as well as microstructure determined by the use of X-ray computed tomography is presented. The application of pretreatments reduced the porosity of the material and resulted in an increased hardness compared to the unpretreated sample. Overall, nonthermal pretreatments proved beneficial in reducing the drying time and minimizing the energy consumption as well as greenhouse gas emissions during processing while maintaining a high quality of dried black garlic.

Comparison of simulations of the gas conduction in HVDC GIL by application of nonlinear conductivity model and ion-drift-diffusion model

Purpose Gas insulated systems, such as gas insulated lines (GIL), use insulating gas, mostly sulfur hexalfluoride (SF6), to enable a higher dielectric strength compared to e.g. air. However, under high voltage direct current conditions, charge accumulation and electric field stress may occur, which may lead to partial discharge or system failure. Therefore, numerical simulations are used to design the system and determine the electric field and charge distribution. Although the gas conduction shows a more complex current–voltage characteristic compared to solid insulation, the electric conductivity of the SF6 gas is set as constant in most works. The purpose of this study is to investigate different approaches to address the conduction in the gas properly for numerical simulations. Design/methodology/approach In this work, two approaches are investigated to address the conduction in the insulating gas and are compared to each other. One method is an ion-drift-diffusion model, where the conduction in the gas is described by the ion motion in the SF6 gas. However, this method is computationally expensive. Alternatively, a less complex approach is an electro-thermal model with the application of an electric conductivity model for the SF6 gas. Measurements show that the electric conductivity in the SF6 gas has a nonlinear dependency on temperature, electric field and gas pressure. From these measurements, an electric conductivity model was developed. Both methods are compared by simulation results, where different parameters and conditions are considered, to investigate the potential of the electric conductivity model as a computationally less expensive alternative. Findings The simulation results of both simulation approaches show similar results, proving the electric conductivity for the SF6 gas as a valid alternative. Using the electro-thermal model approach with the application of the electric conductivity model enables a solution time up to six times faster compared to the ion-drift-diffusion model. The application of the model allows to examine the influence of different parameters such as temperature and gas pressure on the electric field distribution in the GIL, whereas the ion-drift-diffusion model enables to investigate the distribution of homo- and heteropolar charges in the insulation gas. Originality/value This work presents numerical simulation models for high voltage direct current GIL, where the conduction in the SF6 gas is described more precisely compared to a definition of a constant electric conductivity value for the insulation gas. The electric conductivity model for the SF6 gas allows for consideration of the current–voltage characteristics of the gas, is computationally less expensive compared to an ion-drift diffusion model and needs considerably less solution time.

Unraveling Partial Coalescence Between Droplet and Oil-Water Interface in Water-in-Oil Emulsions under a Direct-Current Electric Field via Molecular Dynamics Simulation.

When the electric field strength (E) surpasses a certain threshold, secondary droplets are generated during the coalescence between water droplets in oil and the oil-water interface (so-called the droplet-interface partial coalescence phenomenon), resulting in a lower efficiency of droplet electrocoalescence. This study employs molecular dynamics (MD) simulations to investigate the droplet-interface partial coalescence phenomenon under direct current (DC) electric fields. The results demonstrate that intermolecular interactions, particularly the formation of hydrogen bonds, play a crucial role in dipole-dipole coalescence. Droplet-interface partial coalescence is categorized into five regimes based on droplet morphology. During the contact and fusion of the droplet with the water layer, the dipole moment of the droplet exhibits alternating increases and decreases along the electric field direction. Electric field forces acting on sodium ions and the internal interactions within droplets promote the process of droplet-interface partial coalescence. High field strengths cause significant elongation of the droplet, leading to its fragmentation into multiple segments. The migration of hydrated ions has a dual impact on the droplet-interface partial coalescence, with both facilitative and suppressive effects. The time required for droplet-interface partial coalescence initially decreases and subsequently increases as the field strength increases, depending on the competitive relationship between the extent of droplet stretching and the electric field force. This work provides molecular insights into the droplet-interface coalescence mechanisms in water-in-oil emulsions under DC electric fields.

Electrical Conduction Mechanisms in Ethyl Cellulose Films under DC and AC Electric Fields.

This work reports the dielectric behavior of the biopolymer ethyl cellulose (EC) observed from transient currents experiments under the action of a direct current (DC) electric field (~107 V/m) under vacuum conditions. The viscoelastic response of the EC was evaluated using dynamic mechanical analysis (DMA), observing a mechanical relaxation related to glass transition of around ~402 K. Furthermore, we propose a mathematical framework that describes the transient current in EC using a fractional differential equation, whose solution involves the Mittag-Leffler function. The fractional order, between 0 and 1, is related to the energy dissipation rate and the molecular mobility of the polymer. Subsequently, the conduction mechanisms are considered, on the one hand, the phenomena that occur through the polymer-electrode interface and, on the other hand, those which manifest themselves in the bulk material. Finally, alternating current (AC) conductivity measurements above the glass transition temperature (~402 K) and in a frequency domain from 20 Hz to 2 MHz were carried out, observing electrical conduction described by the segmental movements of the polymeric chains. Its electrical properties also position EC as a potential candidate for electrical, electronics, and mechatronics applications.

Lagrangian dynamics of multiscale vortices in electromagnetically driven two-dimensional turbulence

We experimentally investigate the dynamics of decomposed multiscale vortex cores (VCs) as singular objects of the two-dimensional (2D) turbulence driven by the Lorentz force from a direct current electric field and 2D magnetic lattice array. It is found that, in the xyt space, VCs of each mode (i.e., vortex spatial scale) appear as a zoo of unstable wiggling filament arrays with spatially alternating signs of vorticities. VC interaction and the chaotic external Lorentz force for vorticity injection and retraction lead to: (a) the spatial bunching of the VCs of adjacent modes, and the decaying position correlation of VCs with their separation and increasing mode number; (b) single VC dissociation and VC pair recombination, and in turn stretched exponential distributions of VC lifetimes of all modes; (c) similar persistent (super) diffusions of VCs of all modes, associated with persistent changes of the mean square vorticity fluctuations of VCs of the corresponding modes; and (d) the positively correlated instantaneous energy (enstrophy) variations between two neighboring VCs of modes 3 (the scale of the magnetic array for external vorticity injection and retraction) and its harmonics mode 4, and two-way instantaneous energy (enstrophy) exchange of the flow field surrounding VCs of modes 1–2 and modes 2–3.