FR2699091A1 - Method for producing particles of a first fluid in a second fluid, the fluids being immiscible with each other, and device for its implementation. - Google Patents

Abstract

A process for producing particles of a first fluid (f1) in a second fluid (f2), the two fluids (f1 and f2) being immiscible with each other, consists in introducing the first fluid (f1) into a cavity (1 ) closed by at least one membrane (3) comprising a determined number of holes (5i) and separating the first fluid (f1) from the second fluid (f2) outside the cavity (1), to excite the membrane (3) for the vibrate at a frequency determined as a function of the mechanical resonance frequency of the membrane (3), and under the combined effect of the pressure of the first fluid (f1) on the membrane (3) and the vibrational movement of the membrane (3), in forming particles (4i) of the first fluid (f1) in the second fluid (f2) as the first fluid (f1) passes through the holes (5i) of the membrane (3), the dimensions of which are determined as a function of the amplitude of the combined effect of the pressure and the vibrational movement, and of the dimensions of the holes (5i) of the membrane (3), the particles (4i) of the first fluid (f1) being released from the membrane (3) into the second fluid (f2) when they (4i) have reached dimensions close to those imposed by the holes ( 5i). The invention applies to the field of the environment and more particularly to the oxygenation of water. The invention also applies in the medical field and more particularly in vascular tomographies etc ...

Description

Method for producing particles of a first fluid in
a second fluid, the fluids being immiscible with one another,
and device for its implementation.

 The present invention relates to a method for producing particles of a first fluid in a second fluid, the two fluids not being miscible with each other, and a device for its implementation.

 A first field of application of the invention is that of improving the quality of the environment and in particular that of the oxygenation of natural waters and urban, industrial and domestic effluents.

 For natural waters, certain bodies of water such as lakes and rivers are regularly depleted of oxygen following high summer heat adding to the surrounding pollution. This phenomenon deeply disturbs the flora and fauna by asphyxiation and promotes the development of certain highly invasive anaerobic species.

 For industrial waters, many oxidizable materials of mineral or organic type are present and when they are rejected in natural waters, these materials oxidize and pump dissolved oxygen causing serious disturbances of the environment such as those mentioned above. . Regarding domestic water, some European countries plan to recover certain domestic water, sometimes called "gray water", in order to reuse it for certain works that do not require a high quality of water.

To do this, it is necessary to be able to store this water in large tanks which will have to be oxygenated in order to avoid certain degradations and odors. Other fluids can be used for water treatment, in particular other gases than oxygen for nitrification or denitrification, etc. In this field of application, these are mainly small air bubbles or oxygen that are used.

Other gases can be used, in particular chlorine for the enrichment of drinking water with chlorine, carbon dioxide etc ...

Conversely, the creation of droplets of a liquid in a gas can be used, such as for example water droplets in the air for humidifying domestic air or in greenhouses for agriculture.

 The applications are not limited to the field of the environment or agriculture and other applications are used, in particular in the automobile industry, where a mixture of air and fine gasoline droplets is injected into the engines .

 Another field of application is that of the medical field, which requires the creation of oxygen bubbles in the blood to allow an acoustic tomography of the circulatory system.

 The large number of applications shows that it is important to have an efficient and inexpensive method of dispersing a fluid f1 in another fluid f2, the two fluids being immiscible with each other, by producing small particles of determined dimensions of the fluid f1 in the fluid f2.

 In the example of a gas, for example oxygen, to be dispersed in a liquid, for example water, it is known that oxygen is relatively poorly soluble in water. When an oxygen bubble is present in the water, Archimedes' push, which tends to cause the oxygen bubble to rise towards the surface of the water at a speed proportional to its volume, does not favor its setting in solution. Consequently, bubbles of very small sizes typically with a diameter of less than 0.2 mm having a very short lifetime, ie rapid dissolution, allow optimum efficiency to be obtained; in the optimal case of dissolution no bubble will reach the surface.

 This problem is all the more important in the medical field, where in order to avoid a risk of embolism in the case of acoustic tomography, the bubbles introduced into the blood must not exceed a diameter greater than a few tens of micrometers while having a diameter sufficient to modify the acoustic impedance of the blood.

 A first method for generating bubbles or droplets of a fluid f1 in another fluid f2, consists in blowing the fluid f1 through a small pipe, or nozzle, in the fluid f2. It is possible to generate bubbles or droplets of the fluid f1 in the fluid f2 provided that the two fluids f1 and f2 are immiscible with one another.

 It is observed experimentally that a force is necessary to increase the surface of a first fluid f1 in contact with a second fluid f2. This force, called surface tension, corresponds to work, or surface energy, necessary to create the new surface. The pressure necessary to make a bubble or a droplet come out and the size thereof are related to the surface tensions between the different interfaces: fluid interface ~ 1 / nozzle material, fluid interface ~ 1 / fluid f2, fluid interface ~ 2 / nozzle material, as well as the densities of the two fluids and the radius of the nozzle hole. Consequently there is a pressure threshold and a bubble size beyond which nothing happens. For the bubble or the droplet to detach from the nozzle, the supply of mechanical energy dE, defined by the formula dE = P.dV, where P defines the pressure exerted on the fluid and dV the increase in volume of the bubble or the droplet, is sufficient to overcome the surface energy as well as that necessary to close the bubble or the droplet.

For example, to generate air bubbles in water with a low flow rate, the radius of a bubble being close to 2.10-3 meters, through a hole with a radius close to 10-3 meters, a minimum pressure of approximately 150 Pascals is required for a normal distance traveled before dissolution greater than fifty meters. For a hole with a radius of only 104 meters you need a pressure of around 150,000
Pascals to generate bubbles with a radius close to 2.2.1 0A meters for a normal distance traveled before dissolution of 0.5 meters.

 To generate very small bubbles, it is therefore necessary to use very small holes with all the drawbacks associated with them. Among these drawbacks, the main ones must be mentioned, such as a difficult implementation, a high gas pressure necessary in addition to the static pressure of the fluid f2, and the fact that the smaller the hole and the greater the risk of it becoming blocked. is tall.

 A second known method for generating bubbles of small dimensions from f1 to f2 consists, in the particular case where the fluid f1 is a gas, using a chemical reaction involving gas evolution.

This method has several drawbacks:
- the medium to be treated is the site of a chemical reaction which can be polluting for the environment,
- the parameters of gas evolution such as the size of the bubbles depend closely on the conditions of experimentation such as the temperature, the pressure etc ...,
- the chemicals in reaction are exhausted and provision must be made for periodic renewal.

A third method consists in mechanically dispersing one of the two fluids in the other:
A surface separates the two fluids f1 and f2 which are immiscible with each other and under a mechanical action of the stirring type, part of the fluid f1 crosses the separation surface of the two fluids to disperse in the fluid f2.

 This third method is used in particular for enriching water with oxygen in certain water treatment centers. This method uses large paddle wheels which pass through and rotate the water separation surface, thereby generating water droplets in the air. During their suspension, the droplets enrich themselves with oxygen by simple dissolution at the water / air interface. However, this method is very poorly effective.

 To overcome the aforementioned drawbacks, the object of the invention is to generate very small particles of determined dimensions from a fluid f1 in another fluid f2, the two fluids being immiscible with each other, using vibration techniques and materials related to them.

 To this end, the subject of the invention is a method for producing particles of a first fluid (wire) in a second fluid (f2), the two fluids (f1 and film being immiscible with each other, characterized in that it consists in introducing the first fluid (wire) into a cavity (1) closed by at least one membrane (3) comprising a determined number of holes (5i) and separating the first fluid (wire) from the second fluid (f2) outside the cavity (1), to excite the membrane (3) to make it vibrate at a determined frequency as a function of the mechanical resonance frequency of the membrane (3), and under the combined effect of the pressure of the first fluid (wire ) on the membrane (3) and of the vibration movement of the membrane (3), to form particles (4i) of the first fluid (wire) in the second fluid (f2) when the first fluid (wire) passes through holes (5i) of the membrane (3), the dimensions of which are determined as a function of the amplitude of the co effect Combined with the pressure and the vibration movement, and the dimensions of the holes (5i) of the membrane (3), the particles (4i) of the first fluid (wire) freeing themselves from the membrane (3) in the second fluid (f2 ) when they (4i) have reached dimensions close to those imposed by the holes (5 ~).

Other characteristics and advantages of the present invention will appear more clearly on reading the description which follows, made with reference to the appended figures which represent:
FIG. 1, a block diagram of the method according to the invention,
- Figure 2, a diagram of a first embodiment of a
device for implementing the method according to the invention,
FIG. 3, a detailed view of FIG. 2,
- Figure 4, a diagram of a second embodiment of a
device for implementing the method according to the invention,
- Figure 5, a diagram of a third embodiment of a
device for implementing the method according to the invention,
FIG. 6, a detailed view of FIG. 5,
- Figure 7, a diagram of a fourth embodiment of a
device for implementing the method according to the invention,
- Figure 8, a fifth embodiment of a device for the
implementation of the method according to the invention,
FIG. 9, a detailed view of FIG. 8, and
- Figures 1 osa and 1 or, examples of holes.

 In these figures, the homologous elements are designated by the same reference and the scales are not respected.

 As described above, a contribution of mechanical energy is necessary to overcome the surface energy developed at the various interfaces involved, as well as that necessary to form a particle.

 The present invention has the advantages that it allows, thanks to the mechanical energy supplied by vibration techniques, to form particles of a first fluid f1 in a second fluid f2, and that it makes it possible to detach the particles from the first fluid f1 of the separation surface of the two fluids in the second fluid f2 before the particles reach their size limit, and that it thus makes it possible to obtain particles of the first fluid f1 whose dimensions are almost identical to those of the holes of the separation surface when they pass through this surface. In addition, the limit pressure necessary for the release of the particles from the separation surface is reduced compared to the pressure required without vibrational movement.

 FIG. 1 briefly shows a block diagram of the method according to the invention. A first fluid f1 is introduced into a cavity, or reservoir 1, via a supply pipe, or nozzle 2. A separation surface 3 for example a membrane, represented by a thick broken line closing the upper part of the reservoir 1 is brought into vibration, vibration symbolized by a vertical double arrow, and under the combined effect of the pressure of the first fluid f1 symbolized by an arrow at the inlet of the nozzle 2 and the vibration of the membrane 3, the method according to the invention produces small particles 4i represented in the figure by small circles, from the first fluid f1 in the second fluid f2 outside the reservoir 1 to the passage of the first fluid f1 through the membrane 3, by holes Si symbolized by the interruptions of the thick line representing the membrane 3.

 In the method according to the invention, the pressure of the first fluid f1 is determined so that the second fluid f2 cannot enter the reservoir 1 containing the fluid fl. In practice, an overpressure of a few millibars is applied to the first fluid fl. On the other hand, if an uninterrupted production of particles 4g, of bubbles for example, is desired, the reservoir 1 containing the fluid f1 must be large enough so as to make the variation in pressure negligible when the bubbles 4i are released from the membrane 3 in the second fluid f2. Conversely, if a sequenced generation of particles 4i is desired, it is possible to optimize the volume of the reservoir 1 containing the first fluid f1. It is however possible to intervene on the pressure of the first fluid f1 and / or on the excitation of the vibrations.

 Advantageously, the excitation frequency of the vibrations is determined to coincide with the mechanical resonance frequency of the membrane 3. Thus the amplitude of the vibrations is maximum for optimal efficiency of the method according to the invention.

 A first embodiment of a device for implementing the method according to the invention is illustrated by the diagram in FIG. 2.

 The device comprises a reservoir 6, for example cylindrical, containing the first fluid f1 introduced into the reservoir 6 via a nozzle 7 coupled to a first lateral face 8 of the reservoir 6. A membrane 9, of circular shape, the diameter is between the outside diameter and the inside diameter of the cylindrical tank 6 is deposited on a second lateral face 10, opposite the first lateral face 8, in the form of a crown corresponding to the thickness of the cylindrical wall of the tank 6 and comes close the reservoir 6 containing the first fluid fl. The membrane 9 corresponds to the separation surface between the first fluid f1 and the second fluid f2 outside the reservoir 6.

 The membrane 9 is generally perforated with small holes Ili so as to diffuse the first fluid f1 into the second fluid f2 through the membrane 9 through the holes Iii of small diameter of the order of 0.2 mm. However for certain materials such as porous ferroelectric ceramics, the porosity of the material is sufficient for the diffusion of the fluid f1 in the fluid f2. The membrane 9 has a determined number of holes Ili whose dimensions, shape and distribution over the surface of the membrane 9 are determined mainly as a function of the material used for the membrane 9, of the mode of excitation of the membrane 9 and of the fluids f1 and f2. The membrane 9 is made, for example, from a flat film of any polymer. The cutting of the membrane 9 and of the holes Ili is obtained by conventional machining techniques used for thin materials.

 The membrane 9 is fixed to the reservoir 6 by means of a fixing crown 12 of cylindrical shape whose diameters, exterior and interior, correspond to those of the reservoir 6. The seal of the reservoir 6 is ensured by a seal 13 whose diameters, exterior and interior, correspond to those of the reservoir 6. The seal 13 is crushed between the crown-membrane assembly and the reservoir 6. The membrane 6 is also mechanically coupled to a device 14 transmitting a vibration movement to the membrane 9, movement symbolized by a double arrow. The device 14 is placed in the reservoir 6 containing the fluid f1 and it is for example centered relative to the membrane 9 and rests on the first lateral face 8, or bottom, of the reservoir 6.

 The vibrating device 14 is for example a fluid-tight motor F1. By vibrating, it transmits the mechanical vibrations to the membrane 9 at a frequency coinciding with the mechanical resonance frequency of the membrane 9 for the production of particles 15i of the first fluid f1 in the second fluid f2.

 FIG. 3 represents a detail view of FIG. 2 delimited by a circle in broken lines.

 This figure represents a part of the membrane 9 pierced with a hole lii separating the first fluid f1 from the second fluid f2. The fluid f1 under the combined effect of its pressure, symbolized by a vertical arrow, on the membrane 9 and the vibration movement of the membrane 9, symbolized by a double arrow, enters the hole Here, and a particle 15g of the first fluid f1 begins to form in the second fluid f2.

 In a second embodiment of a device according to the invention, represented by FIG. 4, a membrane 16 is made of a metallic and / or magnetic material. In this case the vibrating device is, for example, an electromagnet 17 making it possible to transmit an oscillatory movement to the membrane 16, either by direct magnetic effect if the membrane 16 is an alloy with high magnetic permeability, or by secondary effect due to the currents of Eddy induced in the membrane 16 if it is made from an electrically conductive material. In this embodiment there is not necessarily a mechanical coupling between the electromagnet 17 and the membrane 16. The reservoir 6 being of the same type as for the previous embodiment it is not redescribed, as is the case for the method of fixing the membrane 16 to the tank 6.

 In a third embodiment represented by FIG. 5, a device according to the invention comprises a membrane 18 perforated with holes 19i made of a material whose main property is to deform mechanically when an electrical excitation is applied to it. This material is for example of the piezoelectric type.

Several types of piezoelectric materials are particularly suitable for this application, in particular ferroelectric polymers, ferroelectric materials of all types, porous ferroelectric ceramics, electrostrictive materials, etc.

Thus, when an alternating electric field of determined frequency is applied between electrodes deposited on the surface of a piezoelectric material, the latter undergoes deformation at the same frequency.

 The device also includes a reservoir 20, a fixing ring 21 and a seal 22 of identical shape to the previous embodiments. The reservoir 20 and the fixing ring 21 are made of an electrically conductive material and the seal 22 in an electrically insulating material.

In this embodiment, a first face 23 and a second face 24 of the membrane 18 are covered respectively over their entire surface, without obstructing the holes 19i of the membrane 18, with a metallization to respectively form a first electrode 25 and a second electrode 26. The electrode 25 and 26 sandwich the piezoelectric membrane 18 The resumption of electrical contact between the first electrode 25 of the membrane 18 and the reservoir 20 is effected by means of a metal insert 27 in the form of crown whose internal diameter corresponds to the internal diameter of the reservoir 20 and the external diameter to the diameter of the membrane 18. The insert 27 is clamped between the first electrode 25 of the membrane 18 and the reservoir 20 by means of the crown fixing 21 via the seal 22 and an excitation voltage V is applied to the membrane 18 via the insert 27 in co ntact with the first electrode 25. An electrical conductor wire 28 brings the excitation voltage V to the insert 27 passing through the bottom 29 of the tank 20 via a sealed bushing 30, at the inside the tank 20 containing the first fluid fl. A resumption of contact between the mechanical mass and a potential serving as a reference is carried out for example on the bottom 29 of the reservoir 20. The reference potential, for example the mass M, is brought back to the second electrode 26 of the membrane 18, by via the fixing ring 21, which is mechanically and electrically connected to the tank 20, for example by screws 31 ~. The excitation of the membrane 18 which will generate the formation of particles 32i is effected by means 33 of producing electrical signals, for example a generator of sinusoidal or square signals coupled to a power amplifier not shown. The frequency and level of excitation depend on parameters such as:
- the piezoelectric properties of the material used,
- the diameter and thickness of the membrane 18,
- the geometry and the distribution of the holes 19 ~,
the mechanical conditions for embedding the membrane 18 on the tank 20, etc.

 FIG. 6 represents a detail of FIG. 5 marked by a circle in broken lines. This detail represents a part of the membrane 18 perforated with a hole 19g. The first face 23 and the second face 24 of the membrane 18 are metallized and serve as electrodes 25 and 26 between which is applied the excitation voltage V delivered by the means 33 for producing electrical signals. The principle of particle formation remaining the same as that described for FIG. 3, it will therefore not be re-described.

 A fourth embodiment represented by FIG. 7 is a variant of the previous embodiment. In this embodiment, the membrane 18 is partially covered by the first electrode 25 and the second electrode 26 which form, respectively on the first face 23 and the second face 24 of the membrane 18, a crown on the perimeter of the membrane 18, of which the width must be sufficient for the amplitude of the vibrations to be optimal for the formation of the particles 32j, and to bring the excitation voltage between the two electrodes 25 and 26 respectively via the insert 27 and the crown fastening 21.

 FIG. 8 represents a fifth embodiment similar to the third embodiment illustrated by FIG. 5 but where the fluid contained in the reservoir 20 can be a conductive fluid f ′ 1. The device comprises a membrane 34 pierced with holes 35i, a first electrode 36 and a second electrode 37 are electrically insulated from each other and from the conductive fluid f '1. For this, the electrodes 36 and 37 of the membrane 34 are covered respectively with a first layer 38 and with a second layer 39 of electrical insulator, for example an insulating polymer, except in the area where an electrical contact must be maintained. that is to say in the part of the membrane 34 which is pinched between the fixing ring 21 and the metal insert 27. Similarly, the internal wall of the reservoir 20 and the part of the insert 27 in contact with the conductive fluid f '1 are covered, for example, by a layer 40 of electrically insulating polymer. The electrical conductor 28 will of course be isolated. The layers 38 and 39 also serve as protective layers for the electrodes 36 and 37.

 To avoid electrical contact between the two electrodes 36 and 37 during the passage of the conductive fluid f '1 in the holes 35 ~, the metallization forming the electrodes 36 and 37 is recessed with respect to the hole 35i and the layer of insulating polymer 38 and 39 fills this withdrawal without obstructing the holes 35 ~.

 A detail of the membrane identified by a circle in broken lines in FIG. 8 is represented by FIG. 9.

 In this figure, part of the membrane 34 pierced with a hole 35i is shown. The first electrode 36 and the second electrode 37 are deposited respectively on each of the faces of the membrane 34 leaving a space 37j not metallized around the hole 35g to allow the layers 38 and 39 of insulating polymer, deposited on the metallization, to fill this space without obstructing the hole 35g. The principle of particle formation being the same as for the previous embodiments, it is therefore not described again.

 Figures 10a and 10b respectively illustrate a front view and a section along the axis A -A of a rectangular piece 40 of a film constituting a membrane. Three holes 41, 42, 43 are drilled in the film on the same axis which is the cutting axis A -A. The shape of the holes 41, 42, 43 is optimized according to the various configurations of the device according to the invention according to the type of oscillation used by the device, its geometry, etc. Among the possible shapes, those of FIGS. 10a and 10b represent, from left to right, cylindrical 41, conical 42 and star 43 shapes.

 By way of example, a circular membrane is produced in a flat film of piezoelectric polymer of the PVDF type, metallized on its two faces, the diameter of which is of the order of 50 millimeters and the thickness of the order of 25 micrometers . The holes in the membrane have a diameter of about 0.2 millimeters. The first fluid f1 is for example air, or oxygen, blown inside the tank containing the first fluid f1 and bubbles of air or oxygen with a diameter equivalent to the diameter of the holes are produced in the second fluid f2, for example water.

 Typically, for the configuration which has just been described, the excitation frequency is a few KHz and the excitation voltage level of the membrane is between 50 V and 100 V.

 Of course, the invention is not limited to the embodiments previously described. In particular, the geometry and the dimensions of the elements constituting the device for implementing the method according to the invention must be adapted as a function of the fluids f1 and f2 used.

Claims (9)

 1. Method for producing particles of a first fluid (wire) in a second fluid (~ 2), the two fluids (f1 and f2) being immiscible with each other, characterized in that it consists in introducing the first fluid (wire) in a cavity (1) closed by at least one membrane (3) having a determined number of holes (5i) and separating the first fluid (wire) from the second fluid (f2) outside the cavity (1), excite the membrane (3) to make it vibrate at a determined frequency as a function of the mechanical resonance frequency of the membrane (3), and under the combined effect of the pressure of the first fluid (wire) on the membrane (3) and from the vibrating movement of the membrane (3), to form particles (4i) of the first fluid (wire) in the second fluid (f2) as the first fluid (wire) passes through the holes (5i) of the membrane (3), the dimensions of which are determined as a function of the amplitude of the combined effect of pressure and movement d e vibration, and the dimensions of the holes (5i) of the membrane (3), the particles (4i) of the first fluid (wire) freeing themselves from the membrane (3) in the second fluid (f2) when they (4i) have reaches dimensions close to those imposed by the holes (5i).  2. Device for implementing the method of claim 1, characterized in that it comprises a cavity (6; 20) containing the first fluid (wire) pierced with at least one hole allowing the introduction of the first fluid (wire) in the cavity (6; 20) and of which at least one end (10) is closed by a membrane (9 16; 18; 34) comprising a determined number of holes (they; 19i; 35i) of determined dimensions, forming a separation between the first fluid (wire) contained in the cavity (6; 20) and the second fluid (f2) outside the cavity (6; 20), and further comprises means for transmitting a vibration movement to the membrane (9; 16; 18; 34).  3. Device according to claim 2, characterized in that the means for transmitting a vibration movement to the membrane (9) comprises a vibrating mechanical device (14) in the cavity (6), impermeable to the first fluid (wire) and coupled to the membrane (9) to transmit the vibration movement to it.  4. Device according to claim 2, characterized in that the membrane (16) consists of a material sensitive to magnetic excitation and in that the means for transmitting to it a vibration movement comprises a device (17) producing a field magnetic.  5. Device according to claim 4, characterized in that the material constituting the membrane (16) is an electrically conductive material sensitive to a secondary magnetic effect due to the currents of Foucault.  6. Device according to claim 4, characterized in that the material constituting the membrane (16) is a magnetic material sensitive to a direct magnetic effect.  7. Device according to claim 2, characterized in that the cavity is a reservoir (20) conducting electricity, in that the membrane (18; 34) consists of a piezoelectric material sensitive to an electrical excitation (V) , in that the means for transmitting the vibration movement to the membrane (18; 34) comprise a first means (33) generating the electrical excitation (V), a second means (25; 36, 27, 28) transmits the electrical excitation (V) on the membrane (18; 34), and a third means (21, 26; 37, 31i) for sealingly fixing the membrane (18; 34) to the reservoir (20) and for transmitting a potential (M) serving as a reference potential for the electrical excitation (V).  8. Device according to claim 7, characterized in that the first means (33) comprises at least one generator of electrical signals delivering a voltage (V) for exciting the membrane (18; 34), in that the second means comprises an electrical connection (28) bringing the excitation voltage (V) to a first electrode (25; 36) deposited on a first face (23) of the membrane (18; 34) facing the first fluid (wire) and in that the third means comprises a fixing ring (21) conducting the electricity and fixing the membrane (18; 34) on the tank (20) in a leaktight manner by means of a seal (22) electrical insulator pinched between the membrane (18; 34) and the reservoir (20), the crown (21) also making it possible to transmit the reference potential (M) on a second electrode (26; 37) deposited on a second face ( 24) of the membrane (18; 34) opposite the second fluid (f2), the two electrodes being is electrically removed from each other.  9. Device according to any one of claims 7 and 8, characterized in that the electrodes (25; 36, 26; 37) and the interior of the reservoir (20) are covered with a layer of electrical insulator (36 , 39, 40) to electrically isolate them from a conductive fluid (f '1) contained in the reservoir (20).