Reaction–diffusion system

30 year-old Entertainer or Range Artist Wesley from Drumheller, really loves vehicle, property developers properties for sale in singapore singapore and horse racing. Finds inspiration by traveling to Works of Antoni Gaudí. Template:Use British English Dielectric-barrier discharge (DBD) is the electrical discharge between two electrodes separated by an insulating dielectric barrier. Originally called silent (inaudible) discharge and also known as ozone production discharge or partial discharge, it was first reported by Ernst Werner von Siemens in 1857.

Typical construction of DBD device

Process

The process normally uses high voltage alternating current, ranging from lower RF to microwave frequencies. However, other methods were developed to extend the frequency range all the way down to the DC. One method was to use a high resistivity layer to cover one of the electrodes. This is known as the resistive barrier discharge. Another technique using a semiconductor layer of gallium arsenide (GaAs) to replace the dielectric layer, enables these devices to be driven by a DC voltage between 580 V and 740 V.

Construction

DBD devices can be made in many configurations, typically planar, using parallel plates separated by a dielectric or cylindrical, using coaxial plates with a dielectric tube between them. In a common coaxial configuration, the dielectric is shaped in the same form as common fluorescent tubing. It is filled at atmospheric pressure with either a rare gas or rare gas-halide mix, with the glass walls acting as the dielectric barrier. Due to the atmospheric pressure level, such processes require high energy levels to sustain. Common dielectric materials include glass, quartz, ceramics and polymers. The gap distance between electrodes varies considerably, from less than 0.1 mm in plasma displays, several millimetres in ozone generators and up to several centimetres in CO₂ lasers.

Operation

A multitude of random arcs form in operation gap exceeding 1.5 mm between the two electrodes during discharges in gases at the atmospheric pressure . As the charges collect on the surface of the dielectric, they discharge in microseconds (millionths of a second), leading to their reformation elsewhere on the surface. Similar to other electrical discharge methods, the contained plasma is sustained if the continuous energy source provides the required degree of ionization, overcoming the recombination process leading to the extinction of the discharge plasma. Such recombinations are directly proportional to the collisions between the molecules and in turn to the pressure of the gas, as explained by Paschen's Law. The discharge process causes the emission of an energetic photon, the frequency and energy of which corresponds to the type of gas used to fill the discharge gap.

I-V characteristic of DBD

Fig. 1. Electric diagram of DBD device

The electrical diagram of the DBD device at the absence of discharge can be presented in the form shown in Fig. 1 where $C_1$ is capacitance of dielectric adjacent to one of two electrodes and $C_g$ is capacitance of the air (or gas) gap between the dielectric within the adjacent electrode footprint and the ground electrode. $C_p$ and $R_p$ are capacity and resistance modeling electric response of plasma. If a switch $S$ connects the capacitors $C_1$ and $C_2$ shown in Fig. 1 (there is no electrical breakdown), the voltage generator is connected to a circuit comprising two capacitors $C_1$ and $C_2$ connected in a series circuit. A capacitance of this circuit can be expressed as

$C_s=\frac{C_1{C}_2}{C_1+C_2}$, (1)

and the electric current $I(t)$ through this circuit can be expressed in the form

$I(t)=C_s\frac{dU}{dt}$, (2)

Fig. 2. Typical oscillograms of DBD voltage U(t) and current I(t)

where $U(t)$ is a generator voltage. Oscillograms$U(t)$ and $I(t)$ obtained in the case of the electrical breakdown of the operating gap, switch $S$ in Fig. 1 is connected to $R_p$, are presented in Fig. 2. We are going to describe, in a first order of approximation, the plasma response to voltage $U_g(t)$ applied to the gap in the same way as a series circuit of two invariable components $R_p$ and$C_p$. To proof this assumption valuability, let us express the value $U_g(t)$ in the form

$U_g(t)=U(t)-\frac{1}{C_1}\underset{t}{\overset{0}{\int }}I(t_1)d{t}_1+U_0$, (3)

where the second term on the right hand side is a drop in potential on the capacitor $C_1$, and $U_0$ is the integration constant. The current $I(t)$ can be expressed in terms of the voltage $U_g(t)$ and values $R_p$ and $C_p$. For this purpose, let us present the value $U_g(t)$ in the form of sum

$U_g(t)=U_{Rp}+U_{Cp}$, (4)

where $U_{Rp}(t)$ and $U_{Cp}(t)$ represent the drops in potential on the resistor $R_p$ and capacitor$C_p$ respectively. Taking into account that the electric current through the circuit can be expressed as $I(t)=C_p(d{U}_{Cp}/dt)$ and consequently,

$U_{Rp}(t)=R_{p}I(t)=R_p{C}_p(d{U}_{Cp}/dt)$,

the equation (4) can be rewritten as the standard linear differential equation

$\frac{d{U}_{Cp}(t)}{dt}+\frac{1}{R_p{C}_p}{U}_{Cp}(t)=\frac{1}{R_p{C}_p}{U}_g(t)$, (5)

which solution is

$U_{Cp}(t)=\frac{1}{R_p{C}_p}\exp (-t/R_p{C}_p)(\underset{0}{\overset{t}{\int }}{U}_g(t_1)\exp (t_1/R_p{C}_p)d{t}_1+C_{int})$, (6)

where $C_{int}$ is the integration constant. Differentiating Equation (6) with respect to $t$ and substituting the result in Equation (5), one can express the current $I(t)$ in terms of the voltage $U_g(t)$ and values $R_p$ and $C_p$:

Fig. 3. Actual (black curve) and theoretical (grey curve) currents I(t) through DBD

$I(t)=\frac{1}{R_p}[U_g(t)-\frac{\exp (-t/R_p{C}_p)}{R_p{C}_p}(\underset{0}{\overset{t}{\int }}{U}_g(t_1)\exp (t_1/R_p{C}_p)d{t}_1+C_{int})]$, (7)

where

$U_g=U_p+\Delta U$, (8)

$U_p$ is drop in potential on plasma, and $\Delta U$ is the constant near-electrode drop in potential. Four parameters: $R_p$, $\tau =R_p{C}_p$,$\Delta U$ , and $C_{int}$ can be found by procedure of fitting of the theoretical function $I(t)$ , calculated from the experimental value $U_g(t)$ by equation (7), with the actual electric current $I(t)$ measured in experiment. Results of the least square fitting, corresponding to some particular case, are shown in Fig. 3. For detail of the equation (7) derivation and possibilities to analyse DBD parameters, see Ref. The equation (7) represents the I-V characteristic of DBD in a most general form.

Applications

Usage of generated radiation

DBDs can be used to generate optical radiation by the relaxation of excited species in the plasma. The main application here is the generation of UV-radiation. Those excimer ultraviolet lamps can produce light with short wavelengths which can be used to produce ozone in industrial scales. Ozone is still used extensively in industrial air and water treatment. Early 19th-century attempts at commercial nitric acid and ammonia production used DBDs as several nitrogen-oxygen compounds are generated as discharge products.

Usage of the generated plasma

The plasma itself is used to modify or clean (plasma cleaning) surfaces of materials (e.g. polymers, semiconductor surfaces), that can also act as dielectric barrier, or to modify gases applied further to “soft” plasma cleaning and increasing adhesion of surfaces prepared for coating or gluing (flat panel display technologies).

Since the 19th century, DBDs were known for their decomposition of different gaseous compounds, such as NH₃, H₂S and CO₂. Other modern applications include semiconductor manufacturing, germicidal processes, polymer surface treatment, high-power CO₂ lasers typically used for welding and metal cutting, pollution control and plasma displays panels. The relatively lower temperature of DBDs makes it an attractive method of generating plasma at atmospheric pressure.

Medicine

Dielectric barrier discharges were used to generate relatively large volume diffuse plasmas at atmospheric pressure and applied to inactivate bacteria in the mid 1990s. This eventually led to the development of a new field of applications, the biomedical applications of plasmas. This field is now known as plasma medicine.

Water treatment

An additional process when using chlorine gas for removal of bacteria and organic contaminates in drinking water supplies. Treatment of public swimming baths, aquariums and fish ponds involves the use of ultraviolet radiation produced when a dielectric mixture of xenon gas and glass are used.

Industry

A dielectric barrier discharge is one method of plasma treatment of textiles at atmospheric pressure and room temperature. The treatment can be used to modify the surface properties of the textile to improve wettability, improve the absorption of dyes and adhesion, and for sterilization. DBD plasma provides a dry treatment that doesn't generate waste water or require drying of the fabric after treatment. For textile treatment, a DBD system requires a few kilovolts of alternating current, at between 1 and 100 kilohertz. Voltage is applied to insulated electrodes with a millimetre-size gap through which the textile passes.

An excimer lamp can be used as a powerful source of short-wavelength ultraviolet light, useful in chemical processes such as surface cleaning of semiconductor wafers. The lamp relies on a dielectric barrier discharge in an atmosphere of xenon and other gases to produce the excimers.

Properties

Due to their nature, these devices have the following properties:

• capacitive electric load: low Power Factor in range of 0.1 to 0.3
• high ignition voltage 1 - 10 kV
• huge amount of energy stored in electric field - requirement of energy recovery if DBD is not driven continuously
• voltages and currents during discharge event have major influence on discharge behaviour (filamented, homogeneous).

Operation with continuous sine waves or square waves is mostly used in high power industrial installations. Pulsed operation of DBDs may lead to higher discharge efficiencies.

Driving circuits

Drivers for this type of electric load are power HF-generators that in many cases contain a transformer for high voltage generation. They resemble the control gear used to operate compact fluorescent lamps or cold cathode fluorescent lamps. The operation mode and the topologies of circuits to operate [DBD] lamps with continuous sine or square waves are similar to those standard drivers. In these cases, the energy that is stored in the DBD's capacitance does not have to be recovered to the intermediate supply after each ignition. Instead, it stays within the circuit (oscillates between the [DBD]'s capacitance and at least one inductive component of the circuit) and only the real power, that is consumed by the lamp, has to be provided by the power supply. Differently, drivers for pulsed operation suffer from rather low power factor and in many cases must fully recover the DBD's energy. Since pulsed operation of [DBD] lamps can lead to increased lamp efficiency, international research led to suiting circuit concepts. Basic topologies are resonant flyback and resonant half bridge. A flexible circuit, that combines the two topologies is given in and and may be used to adaptively drive DBDs with varying capacitance.

An overview of different circuit concepts for the pulsed operation of DBD optical radiation sources is given in "Resonant Behaviour of Pulse Generators for the Efficient Drive of Optical Radiation Sources Based on Dielectric Barrier Discharges".

References

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