Patent ID: 12245352

DETAILED DESCRIPTION

Embodiments of the invention will be now described with reference to the attached Figures. It is to be noted that the following description is merely used for enabling the skilled person to understand the invention, without any intention to limit the applicability of the invention to other embodiments which could be readily understood and/or envisaged by the reader.FIG.1illustrates a generator100for forming a plasma discharge in a fluid.FIG.1shows a body of fluid102within vessel104. Vessel104may be any suitable structure capable of containing fluid102. A cathode108and an anode110are installed within the vessel104, and are in contact with the body of fluid102, which may be a liquid. Optionally, fluid102may be water.FIG.1also illustrates the release and migration of cations from anode110towards cathode108, signified by arrows103. In the specific example of the electrolytic decomposition of water, the cations are H+ions.

An electric potential of negative polarity is supplied to the cathode108, and an electric potential of positive polarity is applied to the anode110. For electrical safety, the anode110is grounded. Since plasma discharges can have a high heating temperature, the cathode108may be made of a refractory material. The anode110can be produced from various materials, in particular materials which exhibit resistance to damage and destruction in electrolytic reactions in a liquid medium, such as nickel or titanium for example.

FIG.2illustrates the formation of a gas bubble205formed at a cathode108, and the propagation of the gas bubble205in a fluid102. A non-uniform high-voltage electric field is created at the end of cathode108to initiate the plasma discharge in fluid102. The cathode108may be in the form of a rod or a needle. As the voltage across the cathode108and the anode110increases an electric conduction current flow from the cathode108(electrons and ions), and a gas vapor bubble205forms in the liquid around the cathode as the fluid102is heated. The heating of the fluid may be to a temperature above boiling. The heating of the fluid102is caused by both the presence of conduction currents in the fluid102and electrical currents of plasma discharge formed at the cathode108. As a result of electrolytic decomposition of water, atomic hydrogen is released at anode110, and hydroxyl anions are released at the cathode108, which then react to form hydrogen (H2) and oxygen (O2). The propagation of electric field lines and electric ion currents from the anode to the cathode (for example of H+ ions) are signified by arrows inFIG.1.

During the plasma discharge, a two-phase substance consisting of a gas vapor phase in the form of a gas vapor bubble205and a liquid phase is formed in the fluid. In particular, the gas-vapor area (phase) is formed around the cathode108inside the fluid102in which the cathode108is located. The surface of the gas vapor bubble205is the boundary between the phases, as shown byFIG.2. The electrical properties of conductivity inside the gas-vapor bubble205and the liquid phase102are very different. The electrical conductivity of the gas vapor bubble205is determined by the ionization of, and mobility of ions in, the gas vapor mixture inside the bubble205, while the electrical conductivity of the liquid phase102is determined by the ionization of molecules, chemical composition and physical properties of the liquid phase. The plasma discharge occurs inside the gas vapor bubble205. The plasma discharge emits strong visible and infrared radiation, causing luminescence including luminescence of the fluid102. As mentioned, inside the liquid phase currents flow, and these currents cause thermal heating of the liquid phase.

There is no clear phase boundary between the gas vapor area of the bubble205and the surrounding liquid phase102. Instead, the phase boundary is blurred and has strong thermal and electrical fluctuations, which lead to instability of the plasma discharge around the cathode108in the liquid phase, and cause periodic breakdown of the plasma discharge. The plasma discharge is dramatically weakened, then amplified, which is characterized by sharp jumps in the electrical current across the cathode108and anode110.

Similar to what is observed in a corona discharge in a gas, plasma discharge occurs inside the gas vapor bubble205only at high conduction currents. The gas vapor bubble205, under the action of the plasma discharge, rapidly heats up and subsequently increases in volume, as shown by the expanding concentric ellipses inFIG.2. The electrical resistance inside the gas vapor bubble increases, reducing current in the plasma discharge to its extinction, and the gas vapor bubble205subsequently cools and bursts. This process is repeated, leading to instability of plasma discharge, which initiates and extinguishes periodically and rapidly. At the same time, the electric current in the plasma discharge also has a pulsating character, causing instability of the discharge of the pulsating plasma. The instability of the plasma discharge adversely affects the efficiency of the treatment of the fluid102.

The stability of the plasma discharge can be increased by increasing the voltage across the electrodes108,110in order to increase the number of charge carriers inside the gas-vapor bubble205, thus reducing the electrical resistance of the bubble205. However,

FIG.3shows that increasing the voltage across the cathode108and anode110leads to electrical breakdown of the fluid102, and shorting between the anode108and cathode110due to the formation of an arc discharge309. Arc309can cause burnout of, and irreparable damage to, cathode108, requiring repair or replacement of cathode108.

To overcome the deficiencies outlined above in existing methods of igniting plasma discharges in liquids between a pair of electrodes108,110, the claimed invention proposes to confine the interface between the gas-vapor area and liquid by installing an additional stabilizing electrode416.FIG.4illustrates an electrode configuration400showing the installation of an additional stabilizing electrode416between the cathode108and the anode110. In the example shown inFIG.4, the stabilizing electrode416is shown interposed across the full width of the vessel104, and positioned closer to the cathode108than the anode110. However, the position of the stabilizing electrode416shown byFIG.4is purely illustrative, and the stabilizing electrode may be interposed in any suitable position between cathode108and anode110. Similarly, the stabilizing electrode416may only extend partially across the width of the vessel104if required. As used herein, the term “between” is intended to be given its normal meaning in the art, referring specifically to locations where the stabilizing electrode416will intercept and interact with the plasma discharge424, thus allowing it to perform its stabilizing function.

A plasma discharge424is produced within gas bubble422and between the cathode108and the additional stabilizing electrode416. In this case, the additional stabilizing electrode416stabilizes the plasma discharge424by confining it, i.e. by locally fixing the volume of the plasma discharge424and gas bubble422. Confining the volume of the plasma discharge424and gas bubble422using the stabilizing electrode416overcomes the previously discussed gas bubble volume instabilities that lead to bursting of the gas-vapor bubble and extinguishment of the plasma discharge.

As mentioned above in connection withFIG.2, the heating of the liquid is caused in part by electrical currents within the plasma discharge424formed at the cathode108. In a single-cathode arrangement, such as that shown byFIG.4, the amount of current that can be allowed to flow through plasma discharge424in gas bubble422is somewhat limited in order to prevent thermal damage to the cathode108. This defines a maximum fluid treatment efficiency that is achievable using a single cathode configuration.

FIG.5illustrates a system500involving an array of cathodes108(such as cathode108shown inFIG.4) coupled to a common stabilizing electrode416. A plasma discharge424is initiated in a gas bubble422between the common stabilizing electrode416and each respective cathode108. The scheme shown byFIG.5is designed to increase the level of fluid treatment efficiency by overcoming the aforementioned issues which may be experienced with single cathode arrangements. InFIG.5, the cathodes108are installed in such a way as to form a continuous area of the plasma discharge424on the surface of the stabilizing electrode416, as the boundaries of the gas bubbles422formed between the common stabilizing electrode416and each respective cathode108merge to form a quasi-continuous gas bubble and sheet-like plasma discharge. This increases the volume of the fluid102that can be treated in a single application. WhilstFIG.5illustrates an example involving five individual cathodes108, in reality any number of cathodes108could be implemented together with a common stabilizing electrode416.

FIG.6is an illustrative block diagram600that depicts electrical components that may be coupled to the electrodes108,110,416, shown inFIG.4or5.FIG.6shows a constant high voltage HV direct-current (DC) power supply614coupled to the cathode108and anode110. Power supply614is operated at voltages on the order of, for example, >1 kV (often in the range 1-20 kV or 5-10 kV), and, for example, at currents of >1 A (often in the range 1 A-5 A). Additionally, a high-frequency high-voltage alternating current (AC) power supply620is coupled to the cathode108and the stabilizing electrode416. AC power supply620may be operated, for example, at voltages on the order of 5-10 kV, at currents on the order of 0.02-0.10 A, and at frequencies on the order of 5-30 kHz. Optionally, depending upon plasma conditions, the stabilizing electrode416may be unpowered, and in such cases, the high-frequency high-voltage AC power supply620may be inactive or absent. Alternatively, in some plasma conditions, the coupling between the high frequency AC power supply620and the stabilizing electrode416may be inactive, such that the power supply may be switched on and off when needed. In the event the high-frequency high-voltage AC power supply620is inactive or absent, the stabilizing electrode becomes insulated from the rest of the circuit, and is only capacitively connected to the circuit. As such, the stabilizing electrode can float passively.

When igniting the plasma discharge424in a saline solution or other electrolyte (for example, an alkali or acid), DC power supply614can be operated at voltages on the order of, for example, 0.1-0.5 kV, and at currents on the order of, for example, 15-25 A. The voltage provided by DC power supply614can be adjusted by pulse-width modulation with a pulsed supply voltage.

The stabilizing electrode416may be a plate, a rod, a sphere, or combinations thereof. In the example ofFIG.6, the stabilizing electrode416is shown having a curved semi-elliptical shape, which is convex with respect to the cathode108. Equally, stabilizing electrode416may be configured to be substantially flat, square, elliptical, or parabolic. The stabilizing electrode416may be curved in a concave or convex manner, for example with respect to cathode108.

The stabilizing electrode416may be porous. In the example shown byFIG.6, the stabilizing electrode416has perforations along its surface. In a preferred example, these perforations may extend completely through the surface of the stabilizing electrode416, however the perforations take the form of surface indentations that extend only partially into the surface of the stabilizing electrode416. The stabilizing electrode may be made from a conductive material, for example a conductive metal, or may be made from a ceramic material. For example, the stabilizing electrode may be a sintered ceramic material. Suitable stabilizing electrode materials include, for example, tungsten, tungsten-ceramic composites, silicon carbide, and combinations thereof.

A decoupling inductor624is optionally interposed between cathode108and DC power supply614. Decoupling inductor624protects the DC power supply614, by blocking alternating currents and high frequency signals associated with AC power supply620from reaching DC power supply614. Alternatively, the decoupling inductor624may be interposed between the DC power supply614and the anode110. In principle, the decoupling inductor624may be interposed at any suitable position within the circuit provided the decoupling inductor624is in a series arrangement with the cathode108and anode110.

A decoupling capacitor626is optionally interposed between cathode108and AC power supply620. Decoupling capacitor626protects the AC power supply620, by blocking direct currents associated with DC power supply614from reaching AC power supply620. Alternatively, the decoupling capacitor626may be interposed between the DC power supply614and the anode110. In principle, the decoupling capacitor626may be interposed at any suitable position within the circuit provided the decoupling capacitor626is in a series arrangement with the cathode108and anode110.

With reference toFIG.6, a proposed method of initiation and stabilization of a plasma discharge in a liquid is given as follows. When power is supplied by DC power supply614and AC power supply620to cathode108, a gas-vapor bubble forms at the cathode108. The high-frequency AC power supply620initiates an electric spark breakdown between the cathode108and the stabilizing electrode416, leading to the propagation of a plasma streamer through the gas bubble422, in which a narrow channel conductive spark or streamer is formed. It is through this streamer that the plasma discharge itself424occurs. The narrow channel conductive spark may have a diameter of, for example, 0.1-0.3 mm, and the plasma discharge may have a diameter of, for example, 10-30 mm or more. In the event that the plasma discharge424becomes extinguished, another high-frequency spark discharges automatically between the cathode408and the stabilizing electrode416, allowing the plasma discharge to be restored in the fluid102. The plasma discharge424between the cathode108and the stabilizing electrode416is initiated by a spark discharge current, which acts as a precursor for the plasma discharge current (which is provided by the DC power supply). The spark discharge current is lower than the plasma discharge current. Consequently, the electric potential of the high-frequency high-voltage spark discharge is set higher than the electric potential of the plasma discharge at the cathode108. Thus, the process of initiation and stabilization of the electrical breakdown of the plasma discharge424in the liquid is sustained automatically, ensuring operability of the proposed method.

The operation of the device shown inFIG.6recalls the work of a thyratron, which is a type of gas-discharge lamp. A thyratron is controlled via a controlling electrode, similar to plasma control achieved in the proposed method and device using stabilizing electrode416. The difference is that the plasma discharge424of the claimed invention is controlled by an additional stabilizing electrode416by high voltage and low current from high-frequency AC power supply620. Here, a small high-frequency discharge current controls a high plasma initiation current and maintains its stable electrical breakdown.

A more specific implementation of the proposed method of initiation and stabilization of the electrical breakdown of the plasma discharge in a liquid is provided by two non-limiting examples of device designs for plasma processing of a liquid that follow.

Exemplary Device1

FIG.7is a diagram of an exemplary first device700for plasma treatment of a fluid. The first device700comprises a cathode708and anode710immersed in a fluid702. Fluid702is confined within vessel704, and the vessel704comprises a layer of insulative material706. The vessel704is made of high-strength materials, such as steel. The insulative material706may be made from ceramic, glass or high-temperature plastic.

In the example ofFIG.7, cathode708is clad with bushing insulator712and adopts a rod-like shape, however other shapes may be used. Cathode708is shown oriented perpendicular to anode710. Stabilizing electrode716is interposed between cathode708and anode710, and is clad with bushing insulator718. In the example ofFIG.7, the stabilizing electrode416is shown having a linear, rod-like shape.

A high-voltage (HV) direct-current (DC) power supply714is coupled to the cathode708and anode710. DC Power supply714is operated at voltages on the order of, for example, >1 kV (often in the range 1-20 kV), and, for example, at currents of >1 A (often in the range of 1-5 A). Additionally, a high-frequency high-voltage alternating current (AC) power supply720is coupled to the cathode708and the stabilizing electrode716. AC power supply716may be operated, for example, at voltages on the order of 5-10 kV, at currents on the order of 0.02-0.10 A, and at frequencies on the order of 5-30 kHz. Optionally, as outlined above and depending upon plasma conditions, the stabilizing electrode716may not be powered by the high-frequency high-voltage AC power supply720, and so the high-frequency high-voltage AC power supply720may be absent. Alternatively, in some plasma conditions, the coupling between the high frequency AC power supply720and the stabilizing electrode716may be inactive.

As with decoupling inductor624, decoupling inductor724is interposed between cathode708and DC power supply714. As discussed in connection withFIG.6, decoupling inductor724protects the DC power supply714, by blocking alternating currents and high frequency signals associated with AC power supply720from reaching DC power supply714. Alternatively, the decoupling inductor724may be interposed between the DC power supply714and the anode710. In principle, the decoupling inductor724may be interposed at any suitable position within the circuit provided the decoupling inductor724is in a series arrangement with the cathode708and the anode710.

As with decoupling capacitor626, decoupling capacitor726is interposed between cathode708and AC power supply720. Decoupling capacitor726protects the AC power supply720, by blocking direct currents associated with DC power supply714from reaching AC power supply720. Alternatively, the decoupling capacitor726may be interposed between the DC power supply and the anode710. In principle, the decoupling capacitor726may be interposed at any suitable position within the circuit provided the decoupling capacitor726is in a series arrangement with the cathode708and the anode710.

Operation of the first device700shown in theFIG.7is similar to that of the device shown in theFIG.6. When the DC power supply714and AC power supply720are switched on, a gas-vapor bubble722is formed at the cathode708, the spark breakdown of which between the cathode708and the additional controlling electrode716is produced by a high-frequency AC power supply720.

Inside the gas-vapor bubble722, a narrow channel conductive spark discharge is formed that provides seed electrons through which a plasma discharge723is initiated. The spark discharge occurs inside the plasma discharge. In case of extinction of the plasma discharge723, a subsequent spark discharge is triggered immediately and automatically under the action of a high-strength electric field between the cathode708and the stabilizing electrode716produced by high-frequency AC power supply720(coupled to the cathode708and the stabilizing electrode716), restoring the plasma discharge723in the fluid702.

When igniting plasma discharge723in a saline solution or other electrolyte (for example, an alkali or acid), DC power supply714can be operated at voltages on the order of, for example, 0.1-0.5 kV, and at currents on the order of, for example, 15-25 A. The voltage provided by DC power supply714can be adjusted by pulse-width modulation with a pulsed supply voltage.

FIG.7shows an optional catalyst tank728connected to the vessel704. Catalyst tank728holds catalyst729, which may be in liquid or gaseous form. Catalyst729may be delivered into fluid702through inlet730as fluid702circulates around vessel704. The circulation of fluid702around vessel704is illustrated by clockwise arrows. Inlet730comprises a valve731to control the flow of catalyst729into vessel704. Catalyst729may facilitate chemical reactions with the plasma discharge723, in order to improve the efficiency of the treatment of fluid702. Optionally, a liquid or gaseous catalyst may be delivered into the fluid702through tube732. In the example ofFIG.7, tube732is shown interposed immediately beneath stabilizing electrode716, however tube732may be positioned at any suitable point through a sidewall of vessel704.

An optional fluid extender tank734may be connected to vessel704and catalyst tank728. Fluid extender tank734serves to prevent rupture of the vessel704during any thermal expansion of fluid702, by providing an overspill tank for fluid702as fluid702circulates around vessel704.

The device700may further comprise a sump738. Sump738comprises a filter and serves to collect dirt from fluid702as fluid702circulates around vessel704. Sump738is connected to outlet740via valve741, which allows opening and closing of outlet740. The contents of the sump738may be drained away from device700through outlet740.

Exemplary Device2

FIG.8is a diagram of an exemplary second device800for plasma treatment of a fluid. The second device800comprises a cathode808and anode810immersed in a fluid702. Fluid802may the same fluid as fluid702shown in connection withFIG.7, or may be a different fluid. Fluid802is confined within vessel804, and the vessel804comprises a layer of insulative material806. The vessel804is made of high-strength materials, such as steel. The insulative material806may be made from ceramic, glass or high-temperature plastic.

In the example ofFIG.8, cathode808is installed into the vessel804through bushing insulator812and adopts a rod-like shape, however other shapes may be used.FIG.8shows cathode808mounted through a sidewall of vessel804, and, in contrast toFIG.7, cathode808is oriented parallel to anode810. Anode810is mounted into the vessel804through bushing insulator811. Stabilizing electrode816is mounted through an opposite sidewall of vessel804to cathode808, and is interposed between cathode808and anode810. Stabilizing electrode816is installed into the vessel804through bushing insulator818, which may be made from heat-resistant ceramic, for example.

A high voltage (HV) direct-current (DC) power supply814is coupled to the cathode808and anode810. In a similar manner to the electrical circuit arrangement shown in connection withFIG.7, DC Power supply814is operated at voltages on the order of, for example, >1 kV (often in the range 1-20 kV), and, for example, at currents of >1 A (often in the range 1-5 A). Additionally, a high-frequency high-voltage alternating current (AC) power supply820is coupled to the cathode808and the stabilizing electrode816. AC power supply816may be operated, for example, at voltages on the order of 5-10 kV, at currents on the order of 0.02-0.10 A, and at frequencies on the order of 5-30 kHz. In the example ofFIG.8, the stabilizing electrode816is shown having a linear, rod-like shape. Optionally, as outlined above and depending upon plasma conditions, the stabilizing electrode816may not be powered by the high-frequency high-voltage AC power supply820, and so the high-frequency high-voltage AC power supply820may be absent. Alternatively, in some plasma conditions, the coupling between the high frequency AC power supply820and the stabilizing electrode816may be inactive.

In a similar manner toFIG.7,FIG.8shows a decoupling inductor824optionally interposed between cathode808and DC power supply814. As discussed in connection withFIGS.6and7, decoupling inductor824protects the DC power supply814, by blocking alternating currents and high frequency signals associated with AC power supply820from reaching DC power supply814. Alternatively, the decoupling inductor824may be interposed between the DC power supply814and the anode810. In principle, the decoupling inductor824may be interposed at any suitable position within the circuit provided the decoupling inductor824is in a series arrangement with the cathode808and the anode810.

In a similar manner toFIG.7,FIG.8shows a decoupling capacitor826optionally interposed between cathode808and AC power supply820. Decoupling capacitor826protects the AC power supply820, by blocking direct currents associated with DC power supply814from reaching AC power supply820. Alternatively, the decoupling capacitor826may be interposed between the DC power supply814and the anode810. In principle, the decoupling capacitor826may be interposed at any suitable position within the circuit provided the decoupling capacitor826is in a series arrangement with the cathode808and the anode810.

When switching on the power of the DC power supply814and AC power supply820, a gas-vapor bubble822is formed at the cathode708, the spark breakdown of which between the cathode808and the additional controlling electrode816is produced by AC power supply820. Stabilizing electrode816is shown horizontally aligned with cathode808, and gas bubble822propagates from cathode808towards stabilizing electrode816. The distance of propagation and dynamics of gas bubble822can be controlled by modifying an amount of separation between cathode808and stabilizing electrode816.

Inside the gas-vapor bubble822, a narrow channel conductive spark discharge is formed, which provides seed electrons through which a plasma discharge823is initiated. The spark discharge occurs inside the plasma discharge. In case of extinction of the plasma discharge823, a subsequent spark discharge is triggered immediately and automatically under the action of a high-strength electric field between the cathode808and the stabilizing electrode816produced by high-frequency AC power supply820(coupled to the cathode808and the stabilizing electrode816), restoring the plasma discharge823in the fluid802.

When igniting plasma discharge823in a saline solution or other electrolyte (for example, an alkali or acid), DC power supply814can be operated at voltages on the order of, for example, 0.1-0.5 kV, and at currents on the order of, for example, 15-25 A. The voltage provided by DC power supply814can be adjusted by pulse-width modulation with a pulsed supply voltage. Operation of the second device800ofFIG.8is analogous to that of the first device700shown in theFIG.7.

FIG.8shows an optional catalyst tank728connected to the vessel804. Catalyst tank728holds catalyst729, which may be in liquid or gaseous form. Catalyst729may be delivered into fluid802through inlet730as fluid802circulates around vessel804. The circulation of fluid702around vessel704is illustrated by clockwise arrows. Inlet730comprises a valve731to control the flow of catalyst729into vessel804. Catalyst729may facilitate chemical reactions with the plasma discharge823, in order to improve the efficiency of the treatment of fluid802. Optionally, a liquid or gaseous catalyst may be delivered into the fluid802via channel832which passes through stabilizing electrode816. Channel832allows the liquid or gaseous catalyst to be fed directly into the plasma discharge823, between cathode808and stabilizing electrode816.

An optional fluid extender tank734may be connected to vessel804and catalyst tank728. Fluid extender tank734serves to prevent rupture of the vessel804during any thermal expansion of fluid802, by providing an overspill tank for fluid802as fluid802circulates around vessel804.

The device800may further comprise a sump738. Sump738comprises a filter and serves to collect dirt from fluid702as fluid702circulates around vessel804. Sump738is connected to outlet740via valve741, which allows opening and closing of outlet740. The contents of the sump738may be drained away from device800through outlet740.

A distinction between the examples ofFIG.7andFIG.8is that, inFIG.8, the fluid802flow does not necessarily pass through the plasma discharge823(as shown by the clockwise arrows). This is because, in the example ofFIG.8, the fluid802is at a supercritical temperature, and allowing the fluid802to circulate through the plasma discharge823could lead to turbulent effects, causing instabilities in the plasma discharge823and potentially causing the plasma discharge823to extinguish completely. Instead, it has been found to be optimal to circulate fluid802around the vessel804in a region principally above the plasma discharge823.

FIG.9shows a module900comprising multiple devices902for plasma treatment of a fluid. Each device902may house a multi-electrode system, such as the arrangement of the anode710,810cathode708,808and stabilizing electrode716shown inFIGS.7and8. The devices902are mounted at opposing ends to manifold904, which controls the distribution of flow and pressure of the fluid702,802. The fluid702,802which may be a liquid, optionally an aqueous solution or water, enters the module900via inlet906, and exits the module900via outlet908. The example ofFIG.9depicts a module900comprising ten individual devices902, however those skilled in the art will appreciate that any number of individual devices902may form module900, depending upon the particular application.

In one example of use, the fluid702,802to be treated, as shown inFIGS.7and8, may be a liquid, and may optionally be a saline solution. Treatment of the fluid702,802by the plasma discharge may desalinate the fluid702,802to produce water. More specifically, the desalination of the fluid702may yield potable water.

In another example, the fluid702,802may be heated as a result of treatment by the plasma discharge. The fluid702,802may be heated past the boiling point of fluid702,802and any excess heat in the fluid702,802may be transferred to heat exchanger tank736through heat exchanger737.

Whilst the above disclosure is in the context of heating or desalinating a fluid using a plasma discharge, the skilled person will appreciate that the techniques and device configurations described herein are equally applicable to the treatment of fluids for alternative purposes.

While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present application as defined by the appended claims. Such variations are intended to be covered by the scope of this application. As such, the foregoing description of embodiments of the present application is not intended to be limiting. Rather, any limitations to the invention are presented in the following claims.