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The partial discharge (PD) event in high-voltage insulation releases energy, exerts mechanical pressure, and generates elastic waves. Detecting and locating these PD events through short-duration acoustic pulses is well established, particularly in gas-insulated systems and oil-insulated transformers. However, its full potential remains untapped in solid insulation systems, where the propagation capability of the acoustic pulse and the acoustic reflections pose fundamental challenges to the acoustic emission (AE) detection technique. This study investigates the influence of reflections and multiple paths on the propagating acoustic pulse in polymeric insulating materials using a finite element method (FEM) in COMSOL. It was observed that the reflections from the boundary influence the propagating pulse's shape, peak magnitude, and arrival time. An analytical MATLAB model further quantifies the impact of multiple propagation paths on the shape, magnitude, and arrival time of the pulse travelling in a cylinder. Additionally, a Perfect Matched Layer (PML) was implemented in the COMSOL model to eliminate the reflections from the boundary, and it revealed that the acoustic pulse magnitude decreases with distance following the inverse square law. In essence, the models aid in measuring how reflections contribute to the observed signals, facilitating the precise identification of the source of the PD event in the tested system. [ABSTRACT FROM AUTHOR]

Insulation resistance (IR) is an essential metric indicating insulation conditions of extruded power cables. To deliver reliable IR simulation as a reference for practical cable inspection, in this paper, four IR degradation models for cross-linked polyethylene-insulated cables under thermal ageing are presented. In addition, the influences of methodologies and temperature profiles on IR simulation are evaluated. Cable cylindrical insulation is first divided into sufficiently small segments whose temperatures are simulated by jointly using a finite volume method and an artificial neural network to model the thermal ageing experiment conditions. The thermal degradation of IR is then simulated by dichotomy models that randomly sample fully degraded segments based on an overall insulation (layer) ageing condition estimation and discretization models that estimate the gradual degradation of individual segments, respectively. Furthermore, uniform and non-uniform temperature profiles are incorporated into dichotomy and discretization models, respectively, for a comparison. The IR simulation results are not only compared between different models, but also discussed around the sensitivity of IR simulation to segment sizes and degradation rates. This provides cable assessment engineers with insights into model behaviour as a reference for their selection of appropriate IR degradation models. [ABSTRACT FROM AUTHOR]

Impulsive underwater discharges have been investigated for many decades, yet the complex pre-breakdown processes that underpin their development are not fully understood. Higher pre-breakdown energy losses may lead to significant reduction in the magnitude and intensity of the pressure waves generated by expanding post-breakdown plasma channels. Thus, it is important to characterize these losses for different discharge types and to identify approaches to their reduction. The present paper analyses thermal pre-breakdown processes in the case of free path and wire-guided discharges in water: fast joule heating of a small volume of water at the high-voltage electrode and joule heating and the melting of the wire, respectively. The energy required for joule heating of the water and metallic wire have been obtained from thermal models, analysed and compared with the experimental pre-breakdown energy losses. Pressure impulses generated by free path and by wire-guided underwater discharges have also been investigated. It was shown that wire-guided discharges support the formation of longer plasma channels better than free path underwater discharges for the same energy available per discharge. This results in stronger pressure impulses developed by underwater wire-guided discharges. It has been shown that the pressure magnitude in the case of both discharge types is inversely proportional to the observation distance which is a characteristic of a spherical acoustic wave. [ABSTRACT FROM AUTHOR]

Gas-filled plasma closing switches (PCSs) are essential components of high energy density pulsed power systems used to generate short, high-power (tens MW to several GW) impulses. In practical applications, PCSs are required to operate in high-current (tens kA), high-voltage (10s–100s kV) regimes, to produce fast-rising ns and sub-ns HV impulses. The transient impedance of a PCS affects the rise time of the generated impulses and the power delivered to the load. Thus, the design and optimization of PCSs require detailed information on the dynamic plasma resistance. This article is focused on an investigation of the time-dependent resistance of the plasma channel(s) formed between the electrodes of a multielectrode PCS. Experimentally measured underdamped current and voltage waveforms were used to obtain the transient plasma resistance of the PCS. The PCS was filled with different gases: dry air, CO2, N2, and a 90%/10% Ar/O2 mixture, in the pressure range from 0 up to 10 bar (gauge). It was found that the plasma resistance drops rapidly from a few hundreds of ohms to a few hundreds of milliohms due to the Joule heating of the breakdown channel. The methods proposed by Braginskii and Kushner to model the transient postbreakdown resistance were used to obtain analytical plasma resistances for all of the gases. These resistances have been compared with the transient resistance obtained using a Kirchhoff analysis of the lumped-element, postbreakdown RLC circuit. Based on this comparison, the suitability of the chosen analytical methods to determine the transient breakdown resistance in gases is discussed. The obtained results will help in the optimization of the operational performance of PCSs filled with environmentally friendly, low environmental impact gases. [ABSTRACT FROM AUTHOR]

This article reports and discusses the results of impulse breakdown study of different insulating liquids under highly divergent electric field conditions. Samples of a natural ester (Envirotemp FR3), a synthetic ester (MIDEL 7131), and a naphthenic mineral oil (Shell Diala S4 ZX) at different levels of relative humidity were exposed to HV impulses with a nominal 7- $\mu \text{s}$ rise time and 150-kV peak voltage of both positive and negative polarity. A strong dependence of the breakdown voltage and time to breakdown of the investigated dielectric liquids was observed with respect to the polarity of the applied HV impulses. It was shown that the FR3 natural ester liquid has a higher dielectric strength when exposed to positive impulse than when under negative impulse stress. The opposite breakdown behavior was observed for the synthetic ester MIDEL 7131 and the naphthenic oil Shell Diala S4 ZX which exhibited lower breakdown voltage under positive energization as compared with the negative energization. The breakdown voltage and prebreakdown time obtained in the present tests of the naphthenic oil, Shell Diala S4 ZX, lie between that of the ester liquids irrespective of impulse polarity. It has been established that no statistically significant variations exist in the breakdown parameters (breakdown voltage and time to breakdown) of the studied dielectric liquids as their relative humidity is increased under either impulse polarity. The obtained results will help in coordination of practical applications of low environmental impact dielectric fluids in power and pulsed power systems and components. [ABSTRACT FROM AUTHOR]

Comprehensive knowledge and understanding of the breakdown behavior of solid–gas interfaces are important for the development, optimization, and coordination of insulation in practical high-voltage (HV) gas-insulated systems (GISs) that are widely used in the power and pulsed power industries. However, despite significant research efforts focused on the characterization of the breakdown parameters and properties of complex gas-filled HV systems, the basic mechanisms that underpin the development of discharges in such solid–gas topologies are not fully understood. This lack of knowledge is particularly noticeable in the case of solid–gas interfaces stressed with HV impulses. This study is aimed at the experimental investigation of the breakdown behavior of solid–gas interfaces, formed between solid dielectrics and common gases: dry air, N2, and CO2 at atmospheric pressure. Four different solid-dielectric materials, PTFE, HDPE, Delrin, and Macor, with relative permittivities in the range from 2.1 to 6.3, were used in this work. The solid–gas interfaces formed by these dielectric materials and the surrounding gases were stressed with positive and negative HV impulses. The breakdown voltage and time to breakdown were obtained for all combinations of solid–gas interfaces using both positive and negative impulses, with a nominal rise time of $\sim 1.9~\mu \text{s}$. A digital camera operated in the open-shutter regime was used to obtain images of the breakdown spark channels that were classified according to their propagation paths. The results obtained in this study will help in further understanding of the breakdown behavior of solid–gas interfaces and can be used in the development and optimization of dielectric topologies for use in GISs. [ABSTRACT FROM AUTHOR]

The dielectric performance of gases in insulation systems used in high voltage power and pulsed power applications is a subject of intensive theoretical and experimental investigations. Transient breakdown processes in gases stressed with short, high-field impulses, have been studied for many decades. However, there are still significant gaps in the understanding of the main breakdown processes and mechanisms associated with fast transient breakdown processes in gases. This knowledge is important for the optimization of gaseous insulating systems and for the coordination of gaseous insulation in power and pulsed power apparatuses. This information is also required for the development of gas-filled components such as circuit breakers and plasma closing switches. This article is aimed at the analysis of the field-time breakdown characteristics of air, N2, CO2, and SF6, using kinetic and drift-diffusion approaches. The kinetic approach is based upon the avalanche-to-streamer transition criterion, while the fluid drift-diffusion model requires self-consistent numerical solution of the continuity equations for charged species, and the Poisson equation for the electric field. The time to breakdown as a function of the applied field was obtained for all investigated gases. The obtained analytical results agree well with the experimental data reported in the literature, which suggests that both approaches can be used for insulation coordination, and for the development of gas-insulated power and pulsed power systems and components. [ABSTRACT FROM AUTHOR]

Samples of polypropylene and high density polyethylene have been exposed to partial discharge activity at elevated temperatures under the influence of combined AC and DC stresses in the range of 1 and 2.5 kHz. Based on FTIR-ATR and dielectric spectroscopy data values for the carbonyl index (CI), the low frequency conductivity (σ 0) and a proposed new index the susceptibility index (χI) have been calculated to characterize the degree of ageing in the samples. The susceptibility index reflects changes in the number of dipoles and the distribution of dipole moments in the system as a result of ageing. The rate of energy delivery from the partial discharge activity has also been calculated and has been found to be dependent on the frequency of the AC component of the stress. Strong correlations are observed between the behavior of the individual indices and the rate of energy delivery. Possible reasons for these observed correlations are discussed and the observed differences in the behavior of the ageing under different experimental conditions are considered. [ABSTRACT FROM AUTHOR]

Characterization of a corona-stabilized switch in the single-shot regime, including triggering range, delay times, and jitter, is reported over the pressure range 0–3 bar gauge, as a continuation of work from similar characterization with this switch filled with SF6 with different gap spacings. When filled with mixtures of 1,3,3,3-tetrafluoropropene (HFO-1234ze) and N2, the breakdown voltage can be increased by up to ~306% and ~191% under negative and positive polarities, respectively, of that using 100% N2. These results were achieved with gas mixtures consisting of 80% N2 and 20% HFO-1234ze, by pressure. The maximum negative polarity triggering range was 13.6 kV, comparable to that achieved previously using SF6. The measured delay time and calculated jitter were generally found to increase with increasing pressure, and with increasing percentage (from 5% to 20%) of HFO-1234ze in the gas mixtures. von Laue statistical analysis of time-to-breakdown data showed that both the formative time and statistical time increased with increasing pressure, and with increasing percentage of HFO-1234ze in the gas mixtures. The formative time under negative polarity was significantly longer than that for positive polarity. The results indicate that HFO-1234ze may be considered as a suitable candidate to replace SF6 for switching applications, although there are some operational observations that require further investigation. [ABSTRACT FROM AUTHOR]

This paper is focused on investigation of the electrical, hydrodynamic, and acoustic parameters of underwater plasma discharges, stabilized with thin copper wires. The experimental current and acoustic waveforms have been obtained using different combinations of the circuit capacitance, charging voltage, and wire length. The resistances of plasma discharges have been calculated for all combinations of electrical and topological parameters, based on the constant resistance approach. Phenomenological scaling relationships that link the plasma resistance and the total energy delivered to the plasma, the period of discharge cavity oscillation and the peak magnitude of the acoustic impulse have been obtained. These relationships can be used in optimization of the acoustic output from the wire-guided discharges for different practical applications. [ABSTRACT FROM PUBLISHER]

A statistical analysis has been undertaken to determine the statistical and formative times associated with breakdowns along a polymer-oil interface under impulse conditions. Early analysis was based on an assumption that the breakdown data followed the von Laue Distribution. However, it was found that in the Laue plots there were deviations from the expected straight line behavior at short times to breakdown, which may be due to a normal distribution in values of the formative times. In addition, the plots showed multiple straight line sections, which suggested that changes were occurring to the breakdown processes during the experimental run, or that more than one mechanism of breakdown was occurring. Values of the statistical time ts and the formative time tf were determined from the data by making choices on the straight line section to be considered, and ignoring the effects of the normal distribution on the derived values of ts and tf. The present paper is focused on further development of this statistical method, including a rigorous analysis of the experimental data, taking into account the effect that a normal distribution of the formative times has on the derived values of ts and tf. Optimal fits in terms of three parameters: ts, tf, and ?f (the standard deviation of the formative time) have been derived using Kolmogorov-Smirnov statistics to quantify the quality of fit. The quality of these fits and the applicability of this approach is discussed. [ABSTRACT FROM AUTHOR]

One of the challenges on the increasing reliance on isolated renewable generation sources is the transmission of power from these sources to centers of power demand. One possible approach is the use of high voltage direct current (HVDC) transmission. The power electronic converters are key components in HVDC transmission system. The converters produce the intended DC voltage for transmission but there may also be AC harmonics superimposed. The superimposed harmonics on the HVDC may have synergistic effects and may lead to further degradation in the cable insulation. Previous research has shown that partial discharge was the main cause of degradation in polymeric insulation under AC stress. However, few publications have demonstrated the effect of combined stress on cable insulation degradation. Additionally, the most popular cable insulation material, cross-linked polyethylene (XLPE), cannot be recycled. Alternative materials which can be recycled have been proposed and one such solution could be thermoplastic materials. In this study, HDPE was investigated as a reference material for thermoplastics and their potential use as insulation in HVDC cables. In this paper the effect of frequency on HDPE degradation under superimposed stresses was studied using the following approaches; equivalent phase resolved partial discharge (PRPD) plots, fourier transform infrared spectroscopy ? attenuated total reflection (FTIR-ATR) and dielectric spectroscopy (DS) measurements were carried out. The results show that during aging and with a frequency increase, the voltage of PD events increased which in turn created more polar molecule groups on the surface. The amount of polar molecule groups was found to affect ?' and tan?, with both increasing when more polar molecules were created. The results show that applying a higher AC frequency enhances polymer degradation. [ABSTRACT FROM PUBLISHER]

Beyond on remarkable progresses in a technology of high-voltage pulse, it is considered to apply the high-voltage pulsed electric field to an inactivation of a microorganism. In particular, the method of the high-voltage pulse has advantage in the inactivation of bacteria in foods, since conventional methods such as heat disinfectant, X-ray or gamma-ray are expected to induce negative secondary effects, changes of flavor, taste, texture of the foods, and so on. In the treatment of the microorganism by the high-voltage pulse, the microorganism is destroyed by pure mechanical stress force created by externally applied electric field, and therefore there are no negative secondary effects. However, it should be carefully evaluated how much strong stress force can be produced by reasonable voltage and pulse duration of the high-voltage pulse for the inactivation of the microorganism. Then, evaluation of the stress force for cases of complete sphere and axis-symmetric shapes of the microorganism were presented by using an analytical formula or 2-D FEM. In this paper, an electrostatic field analysis by using 3-D BEM with a thin layer approximation for a membrane of the microorganism is presented to aim to evaluate the stress force for arbitrary shape microorganism. [ABSTRACT FROM AUTHOR]

Underwater spark discharges are used in multiple practical applications including plasma closing switches, water treatment, plasma channel drilling and mineral processing, waste recycling, treatment of metals, and medical lithotripsy. Spark discharges in water have been studied for several decades; however, despite significant research efforts and progress in this area, further investigation into the efficiency of plasma acoustic sources and their optimization is required in order to expand their practical application. This paper is aimed at investigation of the electrical and hydrodynamic parameters of underwater plasma-generated cavities, including plasma resistance, energy delivered into the plasma cavity, period of cavity oscillations, and characteristics of pressure impulses. Different energy levels, breakdown voltages, and gap distances were used in the present study to allow systematic analysis of these electrical and hydrodynamic parameters. Empirical scaling relations that link the maximum acoustic pressure and the period of cavity oscillations with the energization parameters and the resistance of plasma have been obtained. These empirical functions can be used for optimization of the plasma acoustic sources and for tailoring their parameters for specific practical applications. [ABSTRACT FROM AUTHOR]

Pulsed microdischarges produced by dielectric barrier discharges (DBDs) in a submillimeter gap were investigated under 200 cycles of sinusoidal ac voltage at 5 kHz in this paper. The impulsive current in the external circuit was accurately measured by an oscilloscope with a bandwidth of 2.5 GHz and a maximum sampling rate of 40 GS/s to calculate the filamentary current in the discharge gap. The amplitude, pulse duration, and transferred charge of a single filamentary current and the microdischarge energy acquired over the 200 voltage cycles were statistically analyzed for different discharge gaps and gas pressures. The microdischarge parameters and ozone generation efficiencies for different conditions were compared. The ozone production efficiency was found to increase with increasing pressure from 1 to 2 bar absolute, and the gap length from 0.2 to 0.5 mm. The maximum ozone production efficiency achieved in the paper was 217 g/kWh, with a gap length of 0.5 mm, an absolute pressure of 2.0 bar, and an applied voltage of 5.5 kV at 5 kHz. [ABSTRACT FROM AUTHOR]

Chemical oxidation and the bactericidal capabilities of nonthermal plasma discharges can be used in different practical applications, such as biodecontamination, sterilisation of medical equipment, waste water treatment, syn-gas treatment, and others. In this paper, the oxidation and biodecontamination effects of impulsive plasma discharge, which propagate across a liquid sample/air interface (surface discharges), and through the bulk of a liquid sample (direct discharges), have been investigated. The oxidizing capability was analyzed by measuring the degree of decolorization of indigo carmine dye in water solutions. Gram-negative and gram-positive bacterias, E. coli and S. aureus, respectively, were used as model microorganisms in the investigation of the biocidal effects of plasma discharges. Surface and direct plasma discharges were generated by high-voltage impulses of both polarities, with the magnitudes of 20, 24, and 28 kV, and the chemical oxidation and biodecontamination capabilities of such discharges have been obtained and analyzed. It has been established that the defining factor in the chemical and biological effects of plasma discharges is the normalized delivered charge (dose). The results obtained in this paper show that surface discharges have greater biodecontamination capability as compared with direct transient plasma discharges. Also, it was shown that the decontamination rate of E. coli is more than double than that of S. aureus. [ABSTRACT FROM AUTHOR]

This paper presents an analysis of energy partition among various physical processes during the formation of an electrical arc. The experimental work was conducted to accurately determine the energy delivered into the discharge. The transient voltage and current waveforms have been measured. An analytical model was developed that allows estimation of energy partition in the discharge to be performed in order to evaluate risks associated with different energy components: thermal, kinetic acoustic, and light. Approximately 60% of the electrical energy is converted into mechanical work, subsequently contributing to the pressure rise. The results obtained will help in studies of safety considerations regarding hazards associated with plasma discharges in transient faults/sparks and during the onset of arcing faults (flash and blast hazards). [ABSTRACT FROM AUTHOR]

Pulsed electric field (PEF) treatment can be used to facilitate microbial cell lysis. The aim of this paper is to investigate this effect of PEF treatment on microalgae. The PEF system used in this paper consists of a pulse generator and treatment cell with parallel-plane metallic electrodes. The PEF treatment of microalgae, Spirulina, was conducted using 33.3- and 66.7-kV/cm electric field impulses. The efficiency of the PEF treatment for inactivation of microalgae was assessed by comparison of the growth curves of PEF-treated and untreated samples. Results showed that growth of microalgae can be stopped by the application between 100 and 500 high-field impulses with field magnitude 33.3 kV/cm. When the field is increased to a magnitude of 66.7 kV/cm, the growth of microalgae can be stopped by application of 50 impulses. Overall, this paper confirms that PEF treatments can be used for the inactivation of algae and the energy consumption of the PEF process can be reduced using suspensions with lower electrical conductivity. [ABSTRACT FROM PUBLISHER]

Air-borne micrometer and submicrometer particles produced by anthropogenic sources contaminate atmospheric air, especially in large cities where both population and industrial activities are higher leading to a reduced air quality. Recent research has pointed out particles less than 2.5 \mum in diameter (PM2.5) as a potential health hazard. To address this issue, stricter legislation has been put into force to reduce PM2.5 emissions. This paper is focused on the development of an impulsive microelectrostatic precipitation technology for charging and removal of fine air-borne particles in an economically feasible way. In this paper, a compact coaxial precipitator has been developed for possible indoor air cleaning applications. High-voltage impulses together with dc voltage have been used for energization of the reactor as it has been shown to enhance the precipitation efficiency. This precipitation system has been used for removal of fumes and fine air-borne particles from ambient air. In addition to the experimental part, analytical work has been conducted to optimize the electrostatic precipitation process and to reduce its power consumption. [ABSTRACT FROM PUBLISHER]

It is shown that high-voltage corona discharges in atmospheric air have significant potential for bacterial inactivation. Neutral reactive oxygen and nitrogen species and ions generated by the corona discharges act upon the target liquid or solid surfaces and produce chemical or biological effects. The concentration of ions and reactive species including ozone generated by these discharges defines the efficiency of the corona treatment. In this paper, the chemical (oxidation) effect of direct corona discharges (where ions act upon the target surface) and indirect corona discharges (where ions are screened by a grounded metallic mesh) in atmospheric air is studied by measuring the degree of decolorization of a blue dye dissolved in water. The biological effects of the direct and indirect discharges are studied by observing the degree of bacterial inactivation of gram-negative and gram-positive microorganisms, Escherichia coli and Staphylococcus aureus, seeded on agar plates. The relationship between the ozone concentration and biological efficiency of the corona treatment is evaluated. The obtained results can be used for optimization of cleaning and inactivation treatment processes based on the use of nonthermal plasma produced under dc energization conditions. [ABSTRACT FROM AUTHOR]

Particles with dimensions less than 2.5 \mum (PM2.5) have been identified as being potentially hazardous to human health. The electrostatic precipitation process, which is mainly used in industrial applications, displays a drop in the precipitation efficiency for particles in the range 0.1–1 \mum. This paper is focused on the development of an impulsive microelectrostatic precipitation (\mu-ESP) technology for indoor air cleaning applications. Short (microsecond) high-voltage impulses are used in this technology, which allows the magnitude of the electric field that particles experience to be increased without complete spark breakdown occurring and also reduces the energy consumption compared to that of dc-energized systems. The charging process of particles in the impulsive electric field used in the reactor has been analyzed. Ambient laboratory air and air-diluted cigarette smoke, which contain a significant proportion of PM2.5 particles, were used in the precipitation tests. In order to optimize performance for the \mu-ESP process, different energization modes of the developed precipitation reactor were studied: dc energization, impulsive energization, and their combination. It has been shown that combined dc and impulsive energization of the two stage \mu-ESP reactor produces the maximum precipitation effect. In both cases, ambient laboratory air and diluted smoke, 100% precipitation efficiency has been achieved for fine (250 nm and above) particles; in the tests with diluted smoke, a fine mesh filter was incorporated in the precipitation system to achieve this level of performance. [ABSTRACT FROM AUTHOR]

Surface discharges along oil-immersed solids used as insulators and supports in high-voltage pulsed-power equipment can lead to catastrophic system failures. To achieve reliable compact pulsed-power systems, it is important to quantify the electrical fields at which surface flashover, or other types of breakdown event, will occur for different dielectric materials. This paper reports the observed behavior of samples of polypropylene, low-density polyethylene, ultrahigh-molecular-weight polyethylene, Rexolite, and Torlon, which were subjected to impulse voltages of peak amplitude of 350 kV and a rise time of 1 \mu\s. The cylindrical samples were located between pairs of electrodes immersed in insulating oil. Breakdown events were studied under both nonuniform- and uniform-field conditions, with sample lengths being chosen so that the breakdown events occurred on the rising edge of the impulse. Ultrahigh-molecular-weight polyethylene showed the highest average breakdown field, which is 645 kV/cm, in uniform fields, and the corresponding breakdown field was reduced to \sim400 kV/cm in the nonuniform fields. Weibull plots of the various sets of results are presented, providing comparative data for system designers for the appropriate choice of dielectric materials to act as insulators for high-voltage pulsed-power machines. [ABSTRACT FROM PUBLISHER]

The impulse dielectric behavior of insulating liquids is of significant interest for researchers and engineers working in the field of design, construction, and operation of pulsed power systems. Analysis of the literature data on transformer oils shows that potentially there are several different physical processes that could be responsible for dielectric breakdown by submicrosecond and microsecond impulses. While for short submicrosecond impulses ionization (plasma streamer) is likely to be the main breakdown mechanism, for longer impulses, the thermal effects associated with Joule heating start to play an important role. This paper provides a theoretical analysis of the latter mechanism in dielectric liquids of different degrees of purity stressed with high-voltage (HV) impulses with duration sufficient to cause local heating, evaporation, and formation of prebreakdown gas bubbles. The proposed model is based on the assumption that dielectric breakdown is developed through percolation channels of gas bubbles, and the criterion of formation of these percolation chains is obtained. To test the developed model, the breakdown field-time characteristics have been calculated for the liquid with chemical composition close to that of transformer oils but with known thermodynamic characteristics (n -hexane). Its dielectric strength has been obtained as a function of externally applied pressure and temperature. The analytical results show good agreement when compared with the experimental data available in the literature. [ABSTRACT FROM PUBLISHER]