US2826544A - Hydraulic distribution means for electrodialysis systems - Google Patents

Description

March 11, 1958 D. R. DEWEY n HYDRAULIC DISTRIBUTION MEANS FOR ELECTRODIALYSIS SYSTEMS Filed April 26, 1954 3 Sheets-Sheet 1 Ill March 1953 D. R. DEWEY ll 2,826,544

HYDRAULIC DISTRIBUTION MEANS FOR ELECTRODIALYSIS SYSTEMS Filed' April 26, 1954 3 Shets-Sheet 2 March 11, 1958 D. R. DEWEY ll 2,

HYDRAULIC DISTRIBUTION MEANS FOR ELECTRODIALYSIS SYSTEMS Filed April 26, 1954 s Sheets-Sheet 5 //0 use 1 80982303 Daazais lz-flewe yl;

United States Patent Davis R. Dewey ill, Lincoln, Mass, assignor to Ionics, Incorporated, Cambridge, Mass., a corporation of Massachusetts Application April 26, 1954, Serial No. 425,481;

2 Claims. (Cl. Mi l-45M) This invention relates to modifying the concentration of electrolytes in solutions thereof in electrodialysis sys tems and more particularly to apparatus for hydraulic flow distribution of solutions in membrane chambers of electrodialysis systems.

in the co-pending application to Norman W. Rosenberg, Serial No. 299,592, filed luly 18, 1952, now Patent No. 2,708,658, there is disclosed apparatus comprising in its simplest form essentially a central chamber and two end chambers. Zhe end chambers contain an electrolyte solution and electrodes. When a direct current voltage is impressed u on the electrodes, one of them becomes a cathode and the other an anode, thereby making one end chamber, the cathodic end chamber and the other chamber the anodic end. chamber. The central chamber is scuarated from the two end chambers by electrolytically conducting ionexchange membranes, and contains, preferably, a flowing electrolyte solution. When it is desired to remove electrolyte continuously from the solution flowing through the central chamber, the membrane separating the central chamber from the cathodic and chamber is selectively permeable to cations an: the membrane separating it from the anodic end chamber is selectively permeable to anions. Thus, on passage or" direct current through this assembly, and on flowing solution through the central chamber, cations and anions are respectively carried by the current into the cathodic and anodic end chambers through the selective membranes, and, consequently, the solution in the central chamber is dernineralized, at least in part. Electro-neutrality is preserved in the end chambers by electrode reactions.

Due to the formation of polarized solution films formed at adjacent inner surfaces of both membranes when the solution in the central chamber is subjected to demineralization, the solution undergoing treatment is forced to follow a narrow confined tortuous path while it is in contact with the membranes. This may be obtained by separating two membranes by a thin spacer having portions cut away to provide a continuous narrow tortuous channel therein. in apparatus wherein demineralization (i. e. removal of electrolyte) is effected, the two membranes have different polarity in the sense that the transport number of any cation (or anion) differs in the two membranes; preferably, for high eificiency in such apparatus one membrane is selectively permeable to cations (cation 1 iembrane) and the other membrane is selectively permeable to anions (anion membrane).

In the commercial application of this principle of solution demineraiization a large number of such membranes and tortuous path chambers thercbelween (called concentrating and dilutingchambers) are employed with in the bounds of a single pair of electrodes pa sing a direct current therethrough.

In cells of elcctrodialysis systems designed centration and dilution it is "e con tfcsii d to dis- 2,826,544 Patented Mar. 11, 1958 tribute one stream of solution to alternate add-numbered chambers and to feed another stream of solution to the even-numbered chambers and simultaneously keeping the two streams of solutions separate from each other. Furthermore, these cells require a third stream of solution to be separately fed through the electrode compartments. Such systems and processes for removing salts and electrolytes from solutions thereof often called demineralization are shown in the Juda and McRae application, Serial No. 207,289, filed January 23, 1951, now Patent No. 2,767,135. y

in the copending application to Dewey and Gilliland, Serial No. 213,514, filed March 2, 1951, now Patent No. 2,741,591, of which this case is a continuation-inpart, there is disclosed another multiple chamber system to which the present invention of feed distribution is applicable. This parent case is based upon the partial separation of different species of ions of like charge which is ellected when those species are caused to pass, by means of an applied potential, from one electrolytic solution chamber into a second electrolytic solution chamber through ion-permeable partitions or membranes. To efiect such result efficiently a series of such chambers are employed having membranes with spacers defining said chambers between them and as sembled between headers containing electrodes chambers. Such a system may or may not have a mid-chamber feed as Well as at the end headers.

This invention is accordingly directed to systems of introducing one or more separate hydraulicstreams and removing one or more separate hydraulic streams to or from closely spaced chambers separated by membranes, such as those preferred in systems of liquid dcmineralization, ion fractionation systems, and other multiple chamber electrodialysis systems wherein one or more feed streams are caused to flow from chamber to chamber in a predetermined manner for the purpose of modifying the concentration of electrolytes in solutionsthereof.

The invention will be best understood by reference to the accompanying drawings of the representative embodiments thereof in which:

Figure 1 is a perspective view of a battery of chambers in electrical series.

Figure 2 is an oblique view showing in exploded relation typical units comprising one cell of a battery of chambers connected hydraulically in series.

Figure 3 is a schematic flow diagram showing the flow of solutions through a battery of chambers connected hydraulically in series.

Figure 4 is an oblique view showing in exploded relation typical units comprising one chamber of a battery of chambers connected hydraulically in parallel.

Figure 5 is a schematic flow diagram showing the flow of solutions through a battery of chambers connected hydraulically in parallel.

Figure 6 is an oblique bottom view of the header and feed spacer of a multiple stage separating apparatus showing the structural elements in exploded relation.

Figure 7 is an oblique bottom view showing in exploded relation, the membranes and spacer comprising one chamber of the apparatus of Figure 6.

Figure 8 is an exploded view of two membranes and a spacer showing a narrowly confined tortuous path.

lreferred apparatus for carrying out the process of this invention is shown in Figures 1 through 8 hereinabove. Referring particularly to Figure 1, a battery of chambers 17 in electrical series is held between a pair of header- end plates 10 and 10a of insulating fabricating material, the assembly being held in tight compressional unison by means of the bolts 15 which engage the headerend plates. Each headeris provided with four ducts 11,

12, 13 and 14 extending through said headers and terminating on the outer side in four tubes to which hydraulic coupling can be made to carry the solutions to and from the cells. Through the center region of each header extends a terminal bus 16 through which electrical contact may be made with the end electrodes of the battery of chambers 17.

The battery of chambers 17 comprises an array of barriers of alternating hydraulically impermeable anion permeable and cation permeable membranes between which insulating thin spacers are situated. Each barrier is provided with appropriate ports through which the various solutions may flow. Electrodes are situated at each end and make contact, when the battery is assembled between the header-end plates and 10a, with the terminal busses 16. The barriers are separated by spacers of insulating material with cut-out sections defining the chambers situated between the barriers. Channels are provided in each spacer to allow one of the solutions to enter and leave the chamber defined by that spacer. Appropriate channels are also defined to provide for the by-passing of the other solution around that chamber located in the spacer. The particular arrangement of the various ports and channels is determined by the location of the ducts 11, 12, 13 and 14 on the header-end plates 10 and/or 10a, and the particular order of hydraulic flow desired, whether series or parallel.

Figure 2 shows the arrangement and configuration of the membranes or barriers and spacers when series flow of both solutions is desired. The barriers (membranes) 18 and 19 are each provided with a pair of ports, 23-24 and 27-43, one of each pair of which is situated so as to overlie one of the ducts 11, 12, 13 or 14 of the headerend plate 10. As shown in Figure 2, ports 23 and 27 are situated to overlie duct 11, and ports 24 and 2% are situated to overlie duct 14. In this case ducts 12 and 13 are not used and may be plugged by appropriate means. The barrier similarly is provided with a pair of ports 25 and 26 each situated to allow for the passage of one of the solutions as it passes from the channels provided by the preceding spacer 21. The spacer 21 is cut out at the center region to define the chamber 31, a baffie 31a being provided to distribute the liquid through the chamber as it flows and to support the center regions of the spacers. the entry and exit channels and 32 which respectively align with port 23 of barrier 18 and port 25 of barrier 20. It will be noted that these entry and exit channels are relatively narrow passages defined by surrounding spacer material, the latter presenting supporting means for the adjacent membrane thus preventing any pressure deflection of the membrane into the entry or exit channels. With wide entry and exit channels, serious leakage may occur from the treating chamber due to pressure defiection of the unsupported membranewith resulting loss of solution being treated and in efiiciency of operation. Passage of the other solution is provided by the deflecting path 29 which extends between the port 24 of the barrier 18 and the port 26 of the barrier 20. The spacer 22 is similar to the spacer 21 but placed in the opposite position. It is similarly cut out at the center to define the other chamber 35 of the cell, and has a similar baflie 35a. Entry and exit to the chamber 35 are provided by the channels 34 and 36 respectively, which respectively align with the port 26 of the barrier 20 and the port 28 of the barrier 19. Passage of the solution from the first described chamber 31 is provided by the deflector path 33 which extends between the port 25 of the barrier 20 and the port 27 of the barrier 1.9. From the barrier 19 the two solutions pass through subsequent chambers in the same manner they flowed from the ports in the barrier 18. Any desired number of chambers may be assembled from barrier units, similar to those shown, each separated from the adjacent barrier by one of the spacers,

Entry and exit to chamber 31 are provided by and it will be seen that each solution will flow in series through its respective anode or cathode chamber, as shown diagrammatically in Figure 3 where one series of chambers 37 is connected in hydraulic series, represented by the arrows showing the flow, and separated from the other series of chambers 38, also connected in hydraulic series. In the series cell arrangement shown in Figure 2 the two solutions would enter through the ducts 11 and 14 of one header-end plate 10 and leave by corresponding ducts on the other header-end plate 100;.

Figure 4 shows the arrangement and configuration of the barriers (membranes) and spacers when parallel flow of both solutions is desired. In this case the barriers 4t) and 62 and the barrier 51 are each provided with two pairs of ports 41-42; 43-44; 52-53; 54-55; 6364-; and 65-456; one of each pair of which is situated to overlie one of the ducts 11, 12, 13 or 14 of the header-end plate 19, and to align with the corresponding ports in the other barriers. The spacer 45 is cut out at the center region to define the chamber 47, a baffle 47a being provided to distribute the liquid as it flows through the chamber 47. Entry and exit to chamber 47 are provided by the entry and exit channels 46 and 48 which respectively align with the ports 41 and d2 of the barrier 40 and with the ports 52 and 53 of the barrier $1. Passage of the other solution around chamber 47 is provided by the ports 49 and 5b which align with the ports 53 and 44 of barrier ill and with the ports 54 and 5 of the barrier 51. The spacer 56 is similar to the spacer 45, but placed in the opposite position. It is cut out at the center to define the other chamber 66 of the cell, and is similarly provided with a bafiie 613a. Entry and exit to the chamber 60 are provided by the entry and exit channels 59 and 61, respectively which align with the ports 54 and 55 of the barrier 51 and with the ports and 66 of the barrier 62. Passage of the solution feeding the first-described chamber 47 is provided by the ports 57 and 53 which align with the ports 52 and 53 of the barrier 51 and with ports 63 and 64 of the barrier e2. From the barrier 62 the two solutions pass into and out of the next subsequent chamber in the same manner as they entered the described chamber from the barrier 4-11. As with the chambers arranged for hydraulic series flow, any desired number of chambers may be assembled in electrical series from barrier units similar to those shown, each separated from the adjacent barriers by one of the spacers. It will be seen that the solutions flow through the respective anode and cathode chambers in parallel, entering each of one group of chambers by the ports and channels aligning with port 41; and entering each of the alternate group of chambers by the ports and channels aligning with port 43 and leaving by the ports and channels aligning with the port 44. The parallel flow is shown diagrammatically in Figure 5 where one group of chambers 67 is connected in hydraulic parallelism separately from the other group of chambers 68, also connected in hydraulic parallelism. In the parallel cell arrangement shown in Figure 4 the solutions would enter the cells through the ducts 12 and 14 of the header-end plate 10 and be withdrawn by ducts 11 and 13 of the same header-end plate 10 the ducts in the opposite header-end plate 10a being plugged. Or alternatively ducts 11 and 13 may be plugged and the solution withdrawn through corresponding ducts on the opposite header-end plate 10a.

With the barriers and spacers of the type shown in Figures 1 through 5 other orders of flow than those explained above are also possible. For instance one solution may be conducted in series flow through its respec tive chambers while the other is conducted in parallel flow, the particular order being determined by the configuration of the barriers and spacers as explained above. Another alternative is to provide for countercurrent flow of the two solutions by feeding one in through the headerend plate opposing the one through which the other solutron enters.

Still another alternative is batchwise operation which involves merely filling and emptying either or all the chambers.

Preferably the width of chambers defined by the spacers is kept as low as is practical to decrease the re sistance of the electrolytic path and to maintain a minimum volume of solution in the cell in order to facilitate reversal of the cells without causing an appreciable amount of intermixing of the two solutions. To avoid electrical losses due to short circuiting of the cell by the electrolytic streams flowing through them the ports and channels should be as small as possible consistent with hydraulic pressure drop limitations. In preferred cells the spacers are made of rubber sheeting 0.08 cm. thick and expose elfective areas of barrier surfaces of 25 square centimeters. It will be understood, however, that nothing regarding the spacing of barriers and areas of chambers is critical and spacers several centimeters thick may be used successfully.

Another system for supplying feed streams through multiple stage separation of ionic species as disclosed in the parent copending case noted above is shown in Figures 6 and 7 wherein the headers A and B consist of fiat blocks of insulating fabricating material, each provided with a central chamber 1th) and 101, conveniently a circular recess bored into a face of each header A and B. Each chamber 100 and till contains an electrode 90 and 91 of appropriate material held therein by busses 92 and 93 to which the electrodes 90 and 91 are fastened. The busses 92 and 93 extend through the end walls of the headers A and B in order that electrical connection can be made to them. A pair of ducts 69--70 and 7172 which terminate at their outer ends in tubular extensions to which hydraulic coupling may be made, are provided in each header A and B and communicate with the electrode chamber 100 and 101. Outward from each chamber extends a short narrow channel 73 whose function will appear presently.

The feed spacer C consists of a flat block of insulating fabricating material having an internal opening extending through it thereby defining the feed chamber 74. Flat bafiies 75 extend into the feed chamber 74 to distribute liquid flowing through it and to support the membranes placed on each side of it. A pair of channels 76 and 77 extend outwardly from the feed chamber 74 and also extend through the width of the feed spacer C. A duct 78 terminating at its outer end in a tubular extension to which hydraulic coupling can be made extends laterally into the feed spacer C and communicates with the feed chamber 74 defined therein. Gaskets 79, 80, and spacers 81 and 82 having the appropriate configuration (determined by the shape of the member they fit against) are provided to prevent leakage from the electrode and feed chambers. They are conveniently made from rubber sheet material. The gaskets 79 and 80 situated adjacent each header A and B each contains a port 83 and 84 which overlies the channels 73 provided in the headers A and B.

The desired number of membranes with spacers separating them are held between each header and the feed spaced as indicated at D and E to form the enriching and stripping section. The spacers are conveniently formed from rubber sheet material. A pair of membranes 9t? and 91 separated by a spacer 92 defining a single chamber 5 5 are shown in Figure 7. The membranes 9th and 91 each have a port 93 and 94 extending through them near their edges. The ports 93 .and 9d are situated so that when the membranes as and 91 are assembled as at D between the gaskets i9 and spacer 81, the port 3 of membrane 90 overlies the port 83 of gasket 79 and the port 94 of the membrane 91 overlies one of the channels 85 of the spacer 81 corresponding to one of the channels 76 and 77 of the feed spacer C. The spacer 92 has a cut-out central region which defines the chamber 95 between the membranes. Channels 97 and 98 extend outwardly from the chamber and are situated so that one of them communicates with the port 93 of the membrane 90 and the other communicates with the port 94 of the membrane 91. Baffles 96 extend into the chamber 595 and distribute the flow of liquid therethrough and also support the mid-regions of the membranes. It will thus be seen that when the membranes 90 and 91 and spacer d2 shown in Figure 7 are assembled at D in Figure 6 there is provided a series hydraulic circuit from the electrode chamber 100 of the header A to the feed chamber 7 1-, the itinerary being channel 73, port 83, port 1 3, channel 97, chamber 95, channel 98, port 94 and channel 76. A similar arrangement of membranes and spacer assembled between spacer 82 and the gasket 80, as indicated at B will be seen to provide a similar series circuit between feed chamber 74 and the electrode chamber of the bottom header B. It will be understood that the above description is of a unit having but one enriching chamber and one stripping chamber and that more of either may be provided simply by adding additional membranes and spacers at D and/or E, making whatever obvious modifications are necessary to provide a series hydraulic circuit throughout. The entire assembly is conveniently held together in tight compressional relationship by means of the four bolts (57 which extend through the headers and feed spacers exterior of the chambers.

Various characteristic alternative flow paths of tortuous designs in the spacers situated between the two membranes for internal hydraulic distributions are possible, one of which is shown in Figure 8. As shown in Figure 8 the spacer lid, situated between two membranes and H2 and in face-to-face contact with the surfaces thereof, is in the form of a tlat plate or sheet; this spacer is made of an electrical y insulating material such as rubber or a plastic and is provided with a continuous cut-out portion forming tortuous path or chamber 116, the path or chamber being spanned at a few 10- cations by patches 118 of very thin tough pellicle, such as Scotch tape or the like serving to hold the spacer together. The chamber lilo communicates with a solution inlet 129 and with a discharge outlet 12.2. As is apparent from Figure 8, solution entering the inlet 12% is caused to cross back and forth across the surfaces of the membranes 1m and 112, the solution being confined in its travel to the chamber 116. An advantage resulting from the use of parallel chambers is the fact that the unit is not put out of operation in the event one of the chambers becomes clogged. It should be understood, however, that feed streams for the diluting and concentrating chambers could also be in countercurrent flow.

A number of possible variations in channel flow of feed streams through the spacers are shown, for example, in application Serial No. 299,592 referred to above.

Selectively permeable barriers having utility in this invention may, for example, be prepared in accordance with the specification of the patent to luda and McRae, Ser. No. 2,636,851, issued April 28, 1953.

Having described and illustrated preferred embodiments of the invention What is claimed as new and patentable is:

1. Apparatus for transferring ions of one solution to another comprising at least two headers, at least two electrodes in juxtaposition thereto, and therebetween a plurality of perforated non-conducting spacer members alternating with and disposed in face-to-face contact with selectively ion permeable membranes, said spacer members having continuous tortuous perforations therethrough and running in parallel to the faces in contact with said membranes to form tortuous path chambers,

branes and aligning narrow entry and'exit channels in the'odd-numbered spacers defining said odd-numbered chambers, said exit ports and exit channels communicating only with said odd-numbered chambers through said exit channels, second conduit means for introducing and removing liquids from the even numbered chambers comprising entry and exit ports in said met branes and aligning narrow entry and exit channels in the even numbered spacers defining said even numbered chambers, said latter exit ports and exit channels communicating only with said even numbered chambers, said narrow entry and exit channels preventing pressure deflection of said membranes into said entry and exit chan nels, said first and second conduit means being aligned with the interior ends of header ports in said headers so as to permit liquid to flow freely through said header ports to and from said conduit means, external piping means communicating with the external ends of said header ports thereby to introduce liquids into said chambers, means for forcing liquids through said external piping means, header ports, conduit means and chambers, entry and exit passage means extending through said headers and communicating with said electrodes so as to permit liquid to flow freely by said electrodes, and means for passing a direct electric current transversely through the membranes and chambers.

2. Apparatus for modifying the concentration of electrolytes in solutions comprising'two headers, tWo electrodes in juxtaposition thereto, and therebetween a plurality of perforated non-conducting spacer members each alternating with and disposed in face-to-face contact on one side with a conductive selectively cation permeable membrane and on the other side With a conducting selectively anion permeable membrane, said spacer members having continuous tortuous perforations therethrough and running in parallel to the faces in contact with said membranes to form tortuous path chambers, said alternating spacer members and membranes being disposed between said headers, first conduit means for introducing and removing liquids from odd-numbered chambers comprising entry and exit ports in said membranes and aligning narrow entry and exit channels in 8 the odd-numbered spacers defining said odd-numbered chambers, said exit ports and exit channels communicating only With said odd-numbered chambers through said exit channels, said first conduit means entering and leaving said odd numbered chambers at opposite ends of said tortuous path, second conduit means for introducing and removing liquids from the even numbered chambers comprising entry and exit ports in said membranes and aligning narrow entry and exit channels in the even numbered spacers defining said even numbered chambers, said narrow entry and exit channels preventing pressure deflection of said membranes into said entry and exit channels, said latter exit ports and exit channels cornmunicating only with said even numbered chambers, said second conduit means entering and leaving said even numbered chambers at opposite ends of said tortuous path, said first and second conduit means being aligned with the interior ends of header ports in said headers, so as to permit liquid to flow freely through said header ports to and from said conduit means, external piping means communicating with the external ends of said header ports thereby to introduce liquids into said chambers, means for forcing liquids through said external piping means, header ports, conduit means and chambers, entry and exit passage means extending through said headers and communicating with said electrodes so as to permit liquid to flow freely by said electrodes and means for passing a direct electric current transversely through the membranes and chambers.

References Cited in the file of this patent UNITED STATES PATENTS OTHER REFERENCES Meyer et al.: I-lelvetica Chimica Acta, vol. (1940), pages 795-800.

Claims (1)

1. APPARATUS FOR TRANSFERRING IONS OF ONE SOLUTION TO ANOTHER COMPRISING AT LEAST TWO HEADERS, AT LEAST TWO ELECTRIDES IN JUXTAPOSITION THERETO, AND THEREBETWEEN A PLURALITY OF PERFORATED NON-CONDUCTING SPACER MEMBERS ALTERNATING WITH AND DISPOSED IN FACE-TO-FACE CONTACT WITH SELECTIVELY ION PERMEABLE MEMBRANES, SAID SPACER MEMBERS HAVING CONTINUOUS TORTUOUS PERFORATIONS THERETHROUGH AND RUNNING IN PARALLEL TO THE FACES IN CONTACT WITH SAID MEMBRANES TO FORM TORTUOUS PATH CHAMBERS, SAID ALTERNATING SPACER MEMBERS AND MEMBRANES BEING DISPOSED BETWEEN SAID HEADERS, FIRST CONDUIT MEANS FOR INTRODUCING AND REMOVING LIQUIDS FROM ODD-NUMBERED CHAMBERS COMPRISING ENTRY AND EXIT PORTS IN SAID MEMBRANES AND ALIGNING NARROW ENTRY AND EXIT CHANNELS IN THE ODD-NUMBERED SPACRES DEFINING SAID ODD-NUMBERED CHAMBERS, SAID EXIT PORTS AND EXIT CHANNELS COMMUNICATING ONLY WITH SAID ODD-NUMBERED CHAMBERS THROUGH SAID EXIT CHANNELS, SECOND CONDUIT MEANS FOR INTRODUCING AND REMOVING LIQUIDS FROM THE EVEN NUMBERED CHAMBERS COMPRISING ENTRY AND EXIT PORTS IN SAID MEMBRANES AND ALIGNING NARROW ENTRY AND EXIT CHANNELS IN THE EVEN NUMBERED SPACERS DEFINING SAID EVEN NUMBERED CHAMBERS, SAID LATTER EXIT PORTS AND EXIT CHANNELS COMMUNICATING ONLY WITH SAID EVEN NUMBERED CHAMBERS, SAID NARROW ENTRY AND EXIT CHANNELS PREVENTING PRESSURE DEFLECTION OF SAID MEMBRANES INTO SAID ENTRY AND EXIT CHANNELS, SAID FIRST AND SECOND CONDUID MEANS BEING ALIGNED WITH THE INTERIOR ENDS OF HEADER PORTS IN SAID HEADERS SO AS TO PERMIT LIQUID TO FLOW FREELY THROUGH SAID HEADER PORTS TO AND FROM SAID CONDUIT MEANS, EXTERNAL PIPING MEANS COMMUNICATING WITH THE EXTERNAL ENDS OF SAID HEADER PORTS THEREBY TO INTRODUCE LIQUIDS INTO SAID CHAMBERS, MEANS FOR FORCING LIQUIDS THROUGH SAID EXTERNAL PIPING MEANS, HEADER PORTS, CONDUIT MEANS AND CHAMBERS, ENTRY AND EXIT PASSAGE MEANS EXTENDING THROUGH SAID HEADERS AND COMMUNICATING WITH SAID ELECTRODES SO AS TO PERMIT LIQUID TO FLOW FREELY BY SAID ELECTRODES, AND MEANS FOR PASSING A DIRECT ELECTRIC CURRENT TRANSVERSELY THROUGH THE MEMBRANES AND CHAMBERS.

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