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Title:
GAS SPARGING FOR TRANSPORT OF DISSOLVED SPECIES THROUGH A BARRIER
Document Type and Number:
WIPO Patent Application WO/2014/035919
Kind Code:
A2
Abstract:
Provided are systems and methods for using gas bubbles to promote mass transport within a reactor system. Such systems may be catalytic - including photocatalytic - systems that are adapted to produce products such as hydrogen, oxygen, hydrocarbons, ammonia, and others.

Inventors:
REECE STEVEN Y (US)
FULLER THOMAS F (US)
BURCHELL DOREEN (US)
Application Number:
PCT/US2013/056714
Publication Date:
March 06, 2014
Filing Date:
August 27, 2013
Export Citation:
Click for automatic bibliography generation   Help
Assignee:
SUN CATALYTIX CORP (US)
International Classes:
B01J10/00
Foreign References:
US20050161342A12005-07-28
US20100043877A12010-02-25
US20110272273A12011-11-10
US20020155948A12002-10-24
US20100000874A12010-01-07
US20050227071A12005-10-13
US20090148359A12009-06-11
US20100294726A12010-11-25
US7192562B12007-03-20
GB2108402A1983-05-18
US20120145532A12012-06-14
US20060144700A12006-07-06
US20070119706A12007-05-31
US6024935A2000-02-15
Attorney, Agent or Firm:
ROSEDALE, Jeffrey, H. et al. (Cira Centre 12th Floor,2929 Arch Stree, Philadelphia PA, US)
Download PDF:
Claims:
What is Claimed:

1. A system, comprising: a first chamber and a second chamber; a semipermeable barrier disposed so as to separate the first and second chambers; each of the first and second chambers containing an aqueous electrolyte having a photocatalyst dispersed therein, and an inlet that places the interior of at least one of the first and second chambers into fluid communication with a first pressurized gas.

2. The system of claim 1, wherein at least a portion of the first chamber, a portion of the second chamber, or both, is characterized as being essentially transparent to visible light.

3. The system of claim 1, wherein the interior of the first chamber is essentially free from electrical communication with the interior of the second chamber.

4. The system of claim 1, wherein the first gas comprises air, hydrogen, oxygen, nitrogen, argon, carbon dioxide, or any combination thereof.

5. The system of claim 1, wherein the first gas is at a pressure greater than ambient pressure.

6. The system of claim 1, further comprising at least one second inlet in fluid

communication with the environment exterior to the second chamber.

7. The system of claim 6, further comprising a supply of a second pressurized gas in fluid communication with the at least one second inlet.

8. The system of claim 7, wherein the second pressurized gas comprises air, oxygen, nitrogen, argon, carbon dioxide, or any combination thereof.

9. The system of claim 9, wherein the second pressurized gas is at a pressure greater than ambient pressure.

10. The system of claim 1, wherein the photocatalyst disposed within the first chamber is capable of evolving hydrogen from water.

1 1. The system of claim 1, wherein the fluid is present in the first chamber at a depth of between from about 1 mm to about 50 cm.

12. The system of claim 1, wherein the system comprises a plurality of first inlets.

13. The system of claim 1, wherein the photocatalyst disposed within the second chamber is capable of evolving oxygen from water.

14. The system of claim 1, wherein the second fluid is present in the second chamber at a depth of between from about 1 mm to about 50 cm.

15. The system of claim 6, wherein the system comprises a plurality of second inlets.

16. The system of claim 1, wherein the first chamber, the second chamber, or both, comprises a redox mediator disposed within.

17. The system of claim 16, wherein the redox mediator is soluble in a fluid disposed within the first chamber, within a fluid disposed within the second chamber, or both.

18. The system of claim 16, wherein the redox mediator is capable of accepting or donating an electron, or both and exhibits a potential (E) between the potential for the evolution hydrogen gas (EHER) and the potential for evolution of oxygen gas (EOER) ·

19. The system of any of claims 16, 17, or 18, wherein the redox mediator comprises a couple having a reduction potential that is more positive than the conduction band edge of the photocatalytic material

20. The system of claim 1, wherein the first chamber is essentially impermeable to hydrogen gas, the second chamber is impermeable to oxygen gas, or both.

21. The system of claim 1, wherein the semipermeable barrier comprises a material that restricts passage of one or more of hydrogen gas, oxygen gas, the first catalytic material, the second catalytic material, or any combination thereof.

22. The system of claim 1, wherein the semipermeable barrier comprises a porous separator, a glass frit, an ionomer, or any combination thereof.

23. The system of claim 1, wherein the semipermeable barrier permits passage of redox mediators, ions, or both, between the first and second chambers.

24. The system of claim 1 , further comprising a recovery module capable of fluid communication with the first chamber and adapted to recover at least a portion of hydrogen gas evolved at the first chamber.

25. The system of claim 1, wherein the system comprises a plurality of first and second chambers, the first and second chambers being arranged in an alternating fashion.

26. The system of claim 1, wherein the first and second chambers are disposed next to one another.

27. The system of claim 1, wherein the first and second chambers are disposed atop one another.

28. The system of claim 1, further comprising a distributor configured so as to distribute into the first chamber gas delivered to the first inlet.

29. The system of claim 6, further comprising a distributor configured so as to distribute into the second chamber gas delivered to the second inlet.

30. A method, comprising: contacting a first gas through a first fluid that comprises a first catalytic material capable of evolving hydrogen gas from the first fluid under set conditions; contacting a second gas through a second fluid that comprises a second catalytic material capable of evolving oxygen gas from the second fluid under set conditions, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material evolves hydrogen gas from the first fluid, the second catalytic material evolves oxygen gas from the second fluid, or both.

31. The method of claim 30, wherein the first gas comprises hydrogen.

32. The method of claim 31, wherein the first gas comprises hydrogen recovered from the first fluid.

33. The method of claim 30, further comprising recovering at least some of the hydrogen gas evolved from the first fluid.

34. The method of claim 30, further comprising recovering at least some of the oxygen gas evolved from the second fluid.

35. The method of claim 30, wherein the barrier comprises a material that restricts passage of one or more of hydrogen gas, oxygen gas, the first catalytic material, the second catalytic material, or any combination thereof.

36. The method of claim 30, wherein the barrier is adapted to permit passage of a dissolved species.

37. The method of claim 30, wherein the first gas is contacted to the first fluid by way of sparging.

38. The method of claim 30, wherein the second gas is contacted to the second fluid by way of sparging.

39. The method of claim 30, wherein the first catalytic material, the second catalytic material, or both, are characterized as being photocatalytic.

40. The method of claim 30, wherein the conditions comprise exposure to illumination.

41. A method, comprising: contacting a first gas to a first fluid that comprises a first catalytic material capable of effecting a reduction reaction; contacting a second gas to a second fluid that comprises a second catalytic material capable of effecting an oxidation reaction, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material produces a first product from the first fluid, the second catalytic material produces a second product from the second fluid, or both.

42. The method of claim 41, wherein the first fluid, the second fluid, or both, comprises water.

43. The method of claim 41, wherein the first product comprises hydrogen, a hydrocarbon, ammonia, or any combination thereof.

44. The method of claim 43, wherein the first product comprises hydrogen.

45. The method of claim 41, wherein the second product comprises oxygen, ferric ion, sulfur, carbon dioxide, or any combination thereof.

46. The method of claim 45, wherein the second product comprises oxygen.

47. The method of claim 41, wherein the first catalytic material, the second catalytic material, or both, is characterized as being photocatalytic.

48. The method of claim 41, wherein contacting the first gas to the first fluid comprises bubbling the first gas into the first fluid.

49. The method of claim 41, wherein contacting the second gas to the second fluid comprises bubbling the second gas into the second fluid.

50. The method of claim 41, wherein the first gas effects mass transport of the first catalytic material within the first fluid, wherein the second gas effects mass transport of the second catalytic material within the second fluid, or both.

51. A method of transporting dissolved species, comprising: contacting a first gas to a first fluid that comprises a dissolved species; the first fluid being separated by a semipermeable barrier from a second fluid; and the contacting being performed under conditions such that the dissolved species is transported through the barrier.

52. The method of claim 51, wherein the dissolved species comprises an ion.

53. The method of claim 51, wherein the dissolved species comprises at least a portion of a redox couple.

54. The method of claim 51, wherein the first fluid comprises a first catalytic material disposed within.

55. The method of claim 51, wherein the second fluid comprises a second catalytic material disposed within.

56. The method of claim 51, further comprising contacting a second gas to the second fluid.

57. The method of claim 51, wherein the second fluid comprises a dissolved species.

58. The method of claim 51, wherein the dissolved species comprises one or more of protons, hydronium, hydroxide, an alkali metal ion, alkaline an earth metal ion, a halide ion, an oxyanion of nitrogen, an oxyanion of sulfur, an oxyanion of a halogen, an oxyanion of boron, an oxyanion of phosphorus, or any combination thereof.

Description:
GAS SPARGING FOR TRANSPORT OF

DISSOLVED SPECIES THROUGH A BARRIER

RELATED APPLICATION

[0001] This application claims priority to United States Patent Application 61/693,452, "Gas Sparging for Transport of Dissolved Species Through a Barrier," filed August 27, 2012, the entirety of which application is incorporated herein by reference for any and all purposes.

TECHNICAL FIELD

[0002] The present application relates to the fields of mass transport, catalytic gas production, and photocatalysis.

BACKGROUND

[0003] One limitation of existing reactor systems, as typically encountered, occurs when mass transport of dissolved species through solution is required by a means other than pure diffusion. Such mass transport is most suitably accomplished with minimal work or

consumption of energy, as any energy consumed in effecting mass transport necessarily reduces the overall energy efficiency of the system..

[0004] Existing art describes gas sparging as a means of 1) aerating liquid suspensions and 2) removing electrolytically depleted plate boundary layers in metal purification. No previous technology has been able to communicate a method by which sparging is used as an efficient means of mass transport of dissolved species through a barrier.

[0005] Existing technology does not provide methods that provide adequate mass transport of ions in reactors that demand the separation of suspended components while permitting the transport of dissolved species. Existing technology also does not address transport through a barrier. Accordingly, there is a long-felt need in the art for a low-energy method to enhance mass transport of dissolved species.

SUMMARY

[0006] The present invention describes a source of bubbles to create rapid mass transport of dissolved species through a porous separator and/or membrane. While the separator/membrane allows for the diffusion of dissolved species, the transport of any solid or suspended components is prevented. In one embodiment, the present disclosure provides systems that comprise: 1) One or more dissolved species

2) A separator that divides the system into at least two compartments

3) A source of bubbles.

[0007] Without being bound to any particular theory, the bubbles cause the transport of the dissolved species from at least one compartment to at least one other compartment.

[0008] In one aspect, the present disclosure provides systems, the systems comprising a first chamber having an interior, at least one first inlet configured to place the interior of the first chamber into fluid communication with the environment exterior to the first chamber; a second chamber having an interior, at least one second inlet configured to place the interior of the second chamber into fluid communication with the environment exterior to the second chamber; and a barrier disposed so as to separate the first and second chambers.

[0009] In another aspect, the present disclosure provides systems. These systems suitably include a first chamber and a second chamber; semipermeable barrier is disposed so as to separate the first and second chambers; each of the first and second chambers containing an aqueous electrolyte having a photocatalyst dispersed therein, and an inlet that places the interior of at least one of the first and second chambers into fluid communication with a first pressurized gas. These systems are particularly suitable for photocatalytic processes, e.g., the photocatalytic production of hydrogen and/or oxygen from water under illumination.

[0010] Also provided are methods, the methods comprising contacting a first gas through a first fluid that comprises a first catalytic material capable of evolving hydrogen gas from the first fluid under set conditions; contacting a second gas through a second fluid that comprises a second catalytic material capable of evolving oxygen gas from the second fluid under set conditions, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material evolves hydrogen gas from the first fluid, the second catalytic material evolves oxygen gas from the second fluid, or both.

[0011] Further provided are methods, the methods including contacting a first gas to a first fluid that comprises a first catalytic material capable of effecting a reduction reaction on the first fluid under set conditions; contacting a second gas to a second fluid that comprises a second catalytic material capable of effecting an oxidation reaction on the second fluid under set conditions, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material produces a first product from the first fluid, the second catalytic material produces a second product from the second fluid, or both.

[0012] Additionally provided are methods of transporting dissolved species. These methods suitably include contacting a first gas to a first fluid that comprises a dissolved species; the first fluid being separated by a semipermeable barrier from a second fluid; and the contacting being performed under conditions such that the dissolved species is transported through the barrier.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The summary, as well as the following detailed description, is further understood when read in conjunction with the appended drawings. For the purpose of illustrating the invention, there are shown in the drawings exemplary embodiments of the invention; however, the invention is not limited to the specific methods, compositions, and devices disclosed. In addition, the drawings are not necessarily drawn to scale or proportion. In the drawings:

[0014] Figure 1 provides an exemplary photocatalytic reactor. H 2 and O 2 bubbles are evolved on the left and right sides of the barrier, respectively. The redox mediator (A/B) facilitates transport of electrons from the O 2 side of the reactor to the H 2 side. The porous barrier is permeable to species A and B, but rejects solid photocatalysts (suspended materials 1 and 2). Gas bubbles evolved by the photocatalyst promote mixing and mass transport of the redox mediator (A and B) through the barrier;

[0015] Figure 2 provides a provides a schematic depiction of flow controlled gas delivery through sparging. Mass flow controllers deliver gasses to spargers, shown here as perforated tubes. Immersed in a liquid on either side of a porous barrier, spargers create bubbles to facilitate mass transport of dissolved species. Pumps, impellers, valves, and the like may all be used to modulate gas flow into a chamber;

[0016] Figure 3 provides a schematic depiction of flow controlled gas delivery through sparging. Pumps deliver gases to spargers, shown here as perforated tubes. Immersed in a liquid on either side of a porous barrier, spargers create bubbles to facilitate mass transport of dissolved species. Pumps, impellers, valves, and the like may all be used to modulate gas flow into a chamber;

[0017] Figure 4 provides a schematic of an exemplary dual bed colloidal suspension reactor;

[0018] Figure 5 illustrates a gas sparging system in which product gas is recirculated through a pump into the channels;

[0019] Figure 6 provides various experimental and cell parameters;.

[0020] Figure 7 illustrates Sherwood number plotted versus channel air flow rate for combinations of orifice diameters and cells (error bars omitted for clarity); [0021] Figure 8 illustrates channel mass-transfer coefficient for potassium chloride plotted against the total system volumetric flow rate for an orifice diameter of 0.26 mm (error omitted for clarity)

[0022] Figure 9 illustrates channel mass-transfer coefficient for potassium chloride plotted against the total system volumetric flow rate for an orifice diameter of 2.38 mm (error bars omitted for clarity);

[0023] Figure 10 illustrates the effect of sparger position on channel mass-transfer coefficient for exemplary cell 1 ; and

[0024] Figure 1 1 further illustrates the effect of sparger position on channel mass- transfer coefficient for exemplary cell 2.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0025] The present invention may be understood more readily by reference to the following detailed description taken in connection with the accompanying figures and examples, which form a part of this disclosure. It is to be understood that this invention is not limited to the specific devices, methods, applications, conditions or parameters described and/or shown herein, and that the terminology used herein is for the purpose of describing particular embodiments by way of example only and is not intended to be limiting of the claimed invention. Also, as used in the specification including the appended claims, the singular forms "a," "an," and "the" include the plural, and reference to a particular numerical value includes at least that particular value, unless the context clearly dictates otherwise. The term "plurality," as used herein, means more than one. When a range of values is expressed, another embodiment includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent "approximately" or "about," it will be understood that the particular value forms another embodiment. All ranges are inclusive and combinable, and all documents cited herein are incorporated by reference in their entireties for any and all purposes.

[0026] It is to be appreciated that certain features of the invention which are, for clarity, described herein in the context of separate embodiments, may also be provided in combination in a single embodiment. Conversely, various features of the invention that are, for brevity, described in the context of a single embodiment, may also be provided separately or in any subcombination. Further, reference to values stated in ranges include each and every value within that range.

[0027] In a first aspect, the present disclosure provides systems. The systems suitably include a first chamber having an interior, at least one first inlet configured to place the interior of the first chamber into fluid communication with the environment exterior to the first chamber. The systems also suitably include a second chamber. The systems may also include at least one second inlet configured to place the interior of the second chamber into fluid communication with the environment exterior to the second chamber; and a barrier disposed so as to separate the first and second chambers.

[0028] As described elsewhere herein, the presently disclosed and methods are particularly suitable for photocatalytic processes, e.g., photocatalytic production of hydrogen and/or oxygen under illumination, such as solar illumination. One embodiment of the disclosed systems that is suitable for this particular application is shown in Figure 4, which figure depicts a dual chamber reactor system having colloidal photocatalyst suspensions in each of the two chambers. The chambers are separated by a porous membrane. The depth of the reactor chambers is given by d c h, the width by w ce ii, and the length by L c h. As shown, sunlight or other illumination impinges on the reactor and its contents.

[0029] A reactor may, as shown, include two channels, two types of colloidal photocatalysts, an electrolyte solution capable of carrying charge, a membrane separator, and a thin plastic film designed to capture product gases. The two channels may be separated by a porous membrane that allows conduction of ions and neutral molecules. The two channels suitably contain distinct colloidal photocatalysts suspended in liquid water. In each of the channels, separate oxidation and reduction reactions occur that allow for the generation of hydrogen gas in one channel and oxygen gas in the other channel. At one photocatalyst, the oxidation reaction is:

4A+2H 2 0 >4H + ^tB ' +0 2 . and at the other photocatalyst, the reduction reaction is:

4H + +4B " hv > 2H 2 +4A .

[0030] A and B are species that transport charge from one channel to the other channel. These charge carrying species are present in the solution in the channels. These species serve as the electronic charge carriers that transport between the two channels to keep an overall charge balance in the reactor. Species that serve as electron carriers are commonly referred to as redox shuttles or redox mediators; one example of a redox mediator is the iodide/ triiodide couple. [0031] The reactor channels are suitably separated by a porous membrane. The porous membrane acts as a separator, separating the hydrogen and oxygen products, separating the colloidal catalysts, but allowing the transport of the redox mediator between both channels. A thin plastic film or other barrier may be used to cover the tops of each of the channels so as to collect the produced gases. The film may be transparent and suitably allows the passage of photons. Additionally, because the channels are contained, the hydrogen and oxygen gases produced upon reaction are captured by the plastic film, which is able to expand or contract based on the amount of gas produced. Further, because of the transparent plastic film that covers the channels, light passes and allows the reaction to proceed but evaporation of water into the air is mitigated. After the water splitting proceeds in one channel, charged species are transported through the membrane to the adjacent channel. The membrane is suitably placed at least at the height of the solution in the channels. The membrane is suitably selected so that the resistance to transport is low. Dissolved gases are expected to diffuse from one channel to another. The efficiency loss from this crossover of dissolved gases can be estimated, assuming knowledge of the separator area.

[0032] There are several reasons to enhance mass transfer in a dual-bed suspension reactor. First, reactor channel width is mass-transfer limited, and mass-transfer rates must be increased in order to mitigate the mass-transfer limitation. For example, if the reactor width was infinitely long, infinitely fast mass transfer would be needed to satisfy reactions occurring in the channels. Therefore, any increase in the reactor width must be accompanied with an increase in mass-transfer rates. Second, an increase in the reactor width requires that the reactor must be fully utilized. If the reaction occurs only near the membrane, then increasing reactor width provides little benefit, as any photocatalyst far from the membrane would not be utilized. In order to address both of these issues, one may apply gas sparging to the solution in the channels to enhance mass-transfer and promote channel uniformity. Gas sparging increases the rate of mass-transfer, so as to allow the channels to be sized considerably wider than the mass-transfer limited reaction diffusion model suggests. Additionally, by introducing gas into the solution, a well-mixed bulk phase is expected to form, promoting the uniformity in the solution and increasing reactor utilization.

[0033] One exemplary system is shown in Figure 2, which figure is described in further detail elsewhere herein. It should be understood that in some embodiments, only one of two chambers features an inlet; in other embodiments, both chambers feature gas inlets. In other words, in some embodiments, only one of the two chambers is connected to a gas source; in others, two or more chambers are connected to a gas source. It should be understood that separate chambers need not be connected to the same gas source.

[0034] In some embodiments, the system includes a first chamber and a second chamber; a semipermeable barrier is disposed so as to separate the first and second chambers; each of the first and second chambers containing an aqueous electrolyte having a photocatalyst dispersed therein, and an inlet that places the interior of at least one of the first and second chambers into fluid communication with a first pressurized gas. Suitable electrolytes, photocatalysts, and gases are described elsewhere herein. Systems according to the foregoing arrangement are particularly well-suited to photocatalytic processes, e.g., photocatalytic production of hydrogen and/or oxygen from water. These systems suitably include a sparging section that bubbles one (or more) gases into the first, second, or both chambers to as to enhance mass transport (e.g., ion transport) across the barrier that separates the first and second chambers. The sparging gas may be, e.g., air, oxygen, hydrogen, a noble gas, a non-reactive gas (e.g., nitrogen), or similar.

[0035] In some embodiments, at least a portion of the first chamber, a portion of the second chamber, or both, may be characterized as being essentially transparent to visible light. This may be accomplished by constructing the chamber from, e.g., glass or plastic. This is especially suitable in embodiments when the system operates in a photocatalytic fashion, such that illumination (natural, artificial, or both) aids in effecting a catalytic reaction between a catalytic material and a substrate (e.g., water) to produce a product. Systems may include their own illumination sources, and may also include mirrors, lenses, and other optical components. Such optical components may be configured to direct, redirect, intensify, diffuse, or otherwise manipulate illumination to the system and the contents of the system's chambers.

[0036] The systems may be configured such that the interior of the first chamber is essentially free (though this is not a requirement) from electrical communication with the interior of the second chamber. This may be accomplished by electrically insulating their two chamber interiors from one another.

[0037] Systems according to the present disclosure may also include a supply of a first gas in fluid communication with at least one first inlet. The gas may or may not be in a compressed form (e.g., compressed to above ambient pressure), and may be, for example, air, hydrogen, oxygen, nitrogen, argon, carbon dioxide, or any combination thereof. Noble gases may also be used. The gas may be suitably in a tank or other vessel from which the gas may be controllably released. The gas may also be in the headspace of the first and/or second chamber.

The disclosed systems may also include a device (e.g., a compressor, a pump, a fan, and the like) configured to forcibly introduce air (e.g., ambient air from the environment exterior to the system) or other gas into the chamber. In this way, the systems may be constructed so as not to require a tank or other vessel of compressed gas. It should be understood that the systems may include an inlet to the second chamber, which inlet permits passage of a second gas (which may or may not be the same gas as the sparging gas of the first chamber) into the second chamber, as described below

[0038] Likewise, the disclosed systems may include a supply of a second gas in fluid communication with at least one second inlet. Suitable gases are described above in connection with the description of the first gases. In some particularly suitable embodiments, the first gas comprises hydrogen and the second gas (particularly in embodiments where the second chamber produces oxygen) comprises a gas that is inert to combustion (e.g. air, oxygen, nitrogen, argon, carbon dioxide, or any combination thereof). The systems may include a distributor (e.g., a manifold, perforated pipe, and the like) that effects distribution of gas into the chamber to which the distributor is associated. A distributor may include one or more apertures through which gas is exerted into the chamber; such apertures may be termed "inlets" in some cases. For example, an inlet may feed gas to a distributor, and that gas may in turn be distributed into a chamber through one or more inlets of the distributor.

[0039] The first chamber may have disposed within a first catalytic material capable of evolving hydrogen from water under set conditions. Such catalytic materials may be characterized as being photocatalytic. A non-exhaustive listing of such materials is found in United States patent application 12/486,694 (filed June 17, 2009), United States patent application 12/576,066 (filed October 8, 2009), United States patent application 13/452,258 (filed April 20, 2012), and international application PCT/US2009/005521, the entireties of which are incorporated herein by reference in their entireties for any and all purposes. Some such materials include metal oxides (e.g. Ti02 and other suboxides of titatium, Fe203 and other iron oxides, SrTi03, CuO, Cu20, BiV04, W03) III-V semiconductor materials (e.g. GaAs, GaP, AlGaAs, InGaAs, InGaP, GaAsP, AlInAs) , II-VI semiconductor materials (e.g., CdS, CdSe, CdTe, ZnTe, CdZnTe), and silicon, as well as doped versions thereof. It should be understood that a photocatalytic material may be a semiconductor, a molecule, a polymer, a composite material, a protein or other biomolecule, or a biological organism (e.g. bacteria or algae).

Photocatalysts may be of various shapes and sizes (e.g. rods, spheres, cubes, tetrapods, or irregular shapes, and a photocatalyst particle may be, e.g., from 0.1 nm - 1 cm or larger in size, [0040] The first catalytic material is suitably disposed within a first fluid. The first fluid (e.g., water, acid, base, electrolyte) may serve as a substrate for a catalytic reaction effected by the first catalytic material.

[0041] The first chamber may define a volume of, e.g., about 1 mL to 5 L, 10 L, 20 L, or more, depending on the needs of the user. The first fluid may be present in the first chamber at a depth in the range of from between about 1 mm to about 50 cm. It should be understood that a chamber may be round, elongate, spherical, hemispherical, or essentially any shape. Elongate - e.g., tubular - chambers are considered especially suitable, but other shapes may be used. It is not a requirement that any two chambers be of the same shape, size, or material. For example, the ratio of the volumes of two chambers separated by a membrane could be 1 : 1, 1 : 10, 1 : 100, 1 : 1000, or even 1 : 10,000. Likewise, a system could comprise a cylindrical central chamber bordered by one, two, three, or more other chambers.

[0042] In some embodiments, the system includes a plurality of first inlets. One such embodiment is shown in Figure 2, which illustrates multiple inlets that supply gas to the first (left-hand, in Figure 2) chamber. The inlets may be pinholes in configuration, but may also be slits. There is no requirement that all inlets be of the same configuration, and the disclosed systems may feature first inlets that differ from one another in size, shape, or both. The inlets may, for example, be formed in the material of the chamber, but may also be present in a pipe, manifold, or other structure that is positioned to deliver gas to the chamber. Gas inlets may be placed against or nearly against the separator but may also be placed at a distance from the separator. The size and shape of the inlets may affect the size of the bubbles, which in turn may be used to affect the rate of mass transport. Inlet may define a cross-sectional dimension in the range of from 0.01 mm to 100 mm, in some embodiments. A chamber may include only a single aperture through which gas is introduced into the chamber, but may also include two, three, five, ten or more such apertures. The amount of gas flowed per unit of reactor volume may also be varied to affect the rate of mass transport. In some embodiments, one may consider the unit of space-time, or reactor fluid volume divided by the volumetric flow rate entering the reactor, is relevant. Space-time values for gas-sparged photoreactors may range, for example, from about 10, 50, or 100 s to 500, 1000, or even about 2000 s. Reactor fluid volume may be in the range of

3 3 3 3 3 3

from about 0.01 m to about 0.1 m , about 0.1 m to 1 m , 1 m to 10 m , or even greater than 10 m 3 .

[0043] The second chamber may have disposed within a second catalytic material capable of evolving oxygen from water under set conditions. The second catalytic material may be one that is characterized as being photocatalytic; suitable such materials are described elsewhere herein. The second material may also be disposed within a second fluid; suitable fluids (e.g. water) are described elsewhere herein. The second chamber may be of the same size, shape, or both as the first chamber, but this is not a requirement. The second fluid may be present in the second chamber at a depth of between from about 1 mm to about 50 cm.

[0044] The disclosed systems may include a plurality of second inlets, to which the discussion of the first inlets above may be applied.

[0045] The systems may also include one or more redox mediators. Redox mediators may be disposed within the first chamber, the second chamber, or both. Figure 1 presents one exemplary depiction of a redox mediator disposed within a system according to the present disclosure.

[0046] A redox mediator is suitably soluble in a fluid disposed within the first chamber, within a fluid disposed within the second chamber, or both. In some embodiments, the redox mediator is capable of accepting or donating an electron, or both and exhibits a potential (E) between the potential for the evolution of hydrogen gas (EHER) and the potential for evolution of oxygen gas (E 0 ER). These potentials may be described by a modified form of the Nernst equation:

J¾ER - 0 V - 0.059 V x pH

[0047] These potentials are referenced versus the normal hydrogen electrode potential (NHE, 0 V). The redox mediator may comprise a couple having a potential that is more positive than the conduction band edge of the first photocatalytic material present in the system and more negative than the valence band edge of the second photocatalytic material present in the system. Suitable first catalytic materials include, e.g., silicon, oxides of copper, nitrides and oxynitrides of tantalum, cadmium chalcogenides (e.g. CdS, CdSe, CdTe), strontium titanate, titanium dioxide, gallium nitride, and zinc oxide, as well as doped and undoped mixtures thereof.

Suitable second catalytic materials include strontium titanate, titanium dioxide, nitrides and oxynitrides of tantalum, gallium nitride, zinc oxide, bismuth vanadate, oxides of iron, and doped and undoped mixtures thereof.

[0048] A non-exhaustive listing of redox mediators includes sulfur/sulfides, a halogen/halides (fluoride/fluorine, chloride/chlorine, bromide/bromine, iodide/iodine), transition metal ions (e.g., iron, vanadium, manganese, cobalt, chromium, copper, nickel, palladium, platinum, ruthenium, osmium, rhodium, iridium, rhenium, silver, zinc), and/or coordination complexes (e.g. ferrocene/ferrocinium, Fe(CN)6 7Fe(CN)6 " , Co(phen) 3 /Co(phen) 3 , tin (e.g. stannous/stannic ions), uranium (e.g. U 5+ /U 6+ ions), a molecule, a dye, biomolecules (e.g., ferrodoxin, azurin, plastocyanine, cytochrome c, NADP+/NADPH, NAD+/NADH), and the like. Other suitable redox mediators will be found by those of ordinary skill in the art with little difficulty.

[0049] The first chamber may be formed of a material (or include a layer) that is essentially impermeable to hydrogen gas. Exemplary such materials include glass, plastics, metals, and combinations thereof. The chamber may be formed of a rigid material or of a flexible material, or even both. Chambers may be formed from a hydrogen-permeable material but may be lined with a hydrogen-impermeable barrier layer or coating. The second chamber may, in some embodiments, comprise a material that is essentially impermeable to oxygen gas. Materials that are essentially impermeable to gas will have diffusivity constants (units of cm 2 •Pa ^sec "1 ) less than 10 "16 , between 10 "16 and 10 ~12 , between 10 "15 and 10 "13 , about 10 "14 , or greater than 10 ~12 . The chambers may also be impermeable to gases other than hydrogen, oxygen, or both, depending on the needs of the user.

[0050] A variety of materials may be used as barriers (also termed separators). The barrier may comprise a material that restricts passage of one or more of hydrogen gas, oxygen gas, the first catalytic material, the second catalytic material, or any combination thereof.

Barriers may be formed from a porous material, a glass frit, and the like. Ionomers and other materials that permit transport of ions are considered especially suitable. A barrier may be configured (e.g., Figure 1) to permit the passage of redox mediators, ions, or both, between the first and second chambers. Common barriers include membranes comprised of Nafion and other commercially available ionomer-containing polymers (some exemplary manufacturers include Gore, DuPont, Tokyama, and GE), as well as porous separators (some exemplary manufacturers of such matterials include, for example, Celgard, Waters, Enteck, Teijin, and Mitsubishi) Gas inlets (including the first and second inlets) may be disposed in or on the barrier. The barrier may be oriented essentially vertically (e.g., Figure 1, Figure 2). Alternatively, the barrier may be inclined at an angle of between 0 and 90 degrees relative to the vertical. The barrier need not be straight or flat, as it may contain one or more curves, bumps, hollows, or other such features. It should be understood that gas may be introduced into a chamber at multiple locations. For example, gas might be introduced by way of a perforated tube at the bottom of the chamber and also by a perforated tube along the side of the chamber. The gas need not necessarily be stored in a tank; gas may also be evolved by way of a chemical reaction (e.g., acid and base), with the gas then being introduced into the chamber. The barrier may be stiff or flexible, and may also be configured so that it is moveable. A system may also be configured such that a barrier may be moved between two or more positions so as to allow a used to adjust the relative volumes of two or more chambers.

[0051] The disclosed systems may also include a recovery module capable of fluid communication with the first chamber and adapted to recover at least a portion of hydrogen or other gas evolved at the first chamber. The recovery module may be a tank, a condenser, a pipe, or some combination of these. The hydrogen or other product gas may then be stored, transported, or otherwise held over for later use. For example, hydrogen may be held over for later use in combustion, a fuel cell, or other processes. The systems may also include one or more units or components adapted to recover other products formed in the system, including oxygen, hydrocarbons, and the like; it should be understood that the present disclosure is not limited to systems and methods that produce only hydrogen and oxygen. Likewise, the disclosed systems may include a recovery module capable of fluid communication with the second chamber and adapted to recover at least a portion of hydrogen or other gas evolved at the second chamber

[0052] In other alternative embodiments (not shown), the disclosed systems include a plurality of first and second chambers. The first and second chambers may be arranged in an alternating fashion. In some embodiments, the first and second chambers are disposed next to one another. The chambers may be arranged in an A-B-A-B-A-B fashion. The chamber may also be arranged such that several first chambers encircle a second chamber, or vice versa. Essentially any chamber configuration may be used, including embodiments wherein the first and second chambers are disposed atop one another. Such an embodiment may be used to reduce the physical "footprint" of the system. Another exemplary embodiment is shown in Figure 5. In that figure, product gas is recirculated through a pump into the channels at a pressure adequate to effect sparging. Although other gases aside from product gas can be used, product gas is a convenient, readily-available gas source.

[0053] The present disclosure also provides methods. These methods suitably include contacting a first gas (e.g., via sparging) through a first fluid that comprises a first catalytic material capable of evolving hydrogen gas from the first fluid under set conditions; contacting a second gas through a second fluid that comprises a second catalytic material capable of evolving oxygen gas from the second fluid under set conditions, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material evolves hydrogen gas from the first fluid, the second catalytic material evolves oxygen gas from the second fluid, or both. [0054] In some embodiments, the first gas comprises hydrogen. The hydrogen may be hydrogen recovered from the first fluid. The user may recover at least some of the hydrogen gas evolved from the first fluid, although this gas need not be recirculated back to the first fluid.

[0055] The methods may also include recovering at least some of the oxygen gas evolved from the second fluid. Gas recovery (of any gas) may be effected by condensation, extraction, and other techniques known to those of ordinary skill in the art, including absorption..

[0056] The barrier may comprise (as described elsewhere herein) a material that restricts passage of one or more of hydrogen gas, oxygen gas, the first catalytic material, the second catalytic material, or any combination thereof. The barrier may be adapted to permit passage of a dissolved species.

[0057] The first and second gases may be contacted to the first and second fluids by sparging (e.g., bubbling) and other methods known to those of ordinary skill in the art. As described elsewhere herein, the first catalytic material, the second catalytic material, or both, may be materials that are characterized as being photocatalytic.

[0058] The present disclosure provides additional methods. These methods suitably include contacting a first gas to a first fluid that comprises a first catalytic material capable of effecting a reduction reaction to produce a product of interest; contacting a second gas to a second fluid that comprises a second catalytic material capable of effecting an oxidation reaction to produce a product of interest, a barrier separating the first and second fluids, and the contacting being performed under conditions such that the first catalytic material produces a first product from the first fluid, the second catalytic material produces a second product from the second fluid, or both. Examples of reduction reactions and products of interest include conversion of water and/or protons (hydronium) to hydrogen gas, conversion of nitrogen gas to ammonia, conversion of carbon dioxide to hydrocarbon species (e.g. methane, ethane, ethylene, pentane, hexane, gasoline, diesel, etc), and the like. Examples of oxidation reactions and products of interest include conversion of water and/or hydroxide to oxygen, conversion of ferrous ion to ferric ion, conversion of sulfide and/or polysulfide to sulfur, conversion of contaminated waste water to carbon dioxide or another form of oxidized carbon-containing species.

[0059] In some embodiments, the first fluid, the second fluid, or both, comprises water. Other suitable fluids include organic solvents including acetonitrile, chlorohydrocarbons (e.g. carbon tetrachloride, chloroform, dichloromethane, etc), formamides (e.g. diethylformamide, dimethylformamide, etc), alkyl carbonates (e.g. ethylene carbonate, propylene carbonate, etc), alcohols (e.g. methanol, ethanol, butanol, etc), hydrocarbons (e.g. pentane, hexane, heptane, octane, etc)

[0060] The first product may be a variety of species. The first product may comprise hydrogen, a hydrocarbon, ammonia, or any combination thereof. Hydrogen is considered an especially suitable first product.

[0061] Similarly, a variety of species may be suitable second products. Oxygen, sulfur, ferric ion, or any combination thereof are all considered suitable second products. Oxygen is considered an especially suitable second product.

[0062] Suitable catalytic materials are described elsewhere herein. The first catalytic material, the second catalytic material, or both, may be photocatalytic.

[0063] In some embodiments, contacting the first gas to the first fluid comprises bubbling the first gas into the first fluid. Likewise, contacting the second gas to the second fluid may be effected by bubbling the second gas into the second fluid. As described elsewhere herein (and without being bound to any particular theory), the gas effects mass transport of the first catalytic material within the first fluid, wherein the second gas effects mass transport of the second catalytic material within the second fluid, or both.

[0064] In another embodiment, the present disclosure provides methods. The methods include contacting a first gas to a first fluid that comprises a dissolved species; the first fluid being separated by a barrier from a second fluid; and the contacting being performed under conditions such that the dissolved species is transported through the barrier.

[0065] The dissolved species may comprise, for example, at least a portion of a redox couple. Suitable redox couples are described elsewhere herein. The first fluid may comprise within a first catalytic material disposed within (suitable such materials are described elsewhere herein). The second fluid may likewise comprises a second catalytic material disposed within, such materials also being described elsewhere herein. The user may also contact a second gas to the second fluid. The second fluid may include a dissolved species.

[0066] The contacting may give rise to pockets (e.g., bubbles) of the gas being introduced to the fluid. In one non-limiting embodiment, the gas pockets percolate upward through the fluid. The movement of the gas gives rise to enhanced mass transport within the fluid, which mass transport may enhance the movement of one or more dissolved species (e.g., parts of redox couples, ions, and the like) across a barrier that separates the first and second chambers. It should be understood that the barrier may be configured such that at least a portion of the barrier lies above one or more inlets through which gas is introduced. In other embodiments, the barrier may be angled or otherwise shaped to "catch" or otherwise contact gas introduced into a fluid. The user may also include baffles, planes, filters, pipes, and the like so as to modulate fluid and gas movement within a given system. These components may be fixed or movable, so as to allow the user to alter fluid flow, gas flow, or both.

[0067] In one non-limiting embodiment, the invention may be used in a water-splitting photocatalytic reactor (Figure 1). In this reactor, sunlight is absorbed by photocatalyst particles that are dispersed in solution. The particles are divided into two compartments or beds, an H 2 - evolving bed and an (Revolving bed. Upon illumination, electrons are shuttled from the (¾ bed to the ¾ bed by means of a soluble redox mediator. The two beds are separated by a barrier, the purpose of which is to prevent mixing of the H 2 , (¾, and IVCVevolving photocatalysts but allow for transport of the redox mediator and other ions between the two beds.

[0068] Diffusion of the redox couple between the two beds may, in some case, be too slow to achieve desirable conversion efficiencies, thus mass transport must be augmented by some form of mixing. The mixing is suitably done with low-energy requirements, to maximize the overall efficiency of the solar conversion. The problem may be solved in a relatively low cost and energy efficient manner by bubbling gas through the liquid (Figure 2). Buoyant bubbles disturb the liquid through which they rise, creating the necessary convective movement of the medium and facilitating mass transport of the dissolved species. The rate of ion transport may thus be controlled by the size of the bubbles, rate of bubble production, and distance between the sparging lines and between the line and the reactor barrier. Examples of various components of this invention are listed below.

[0069] Non-limiting component examples

[0070] Dissolved Species: Ions or molecules are suitably mobile through the separator. These may include redox couples, such as those listed above, that have reduction potentials more positive than the conduction band edge of a photocatalyst. Specific examples include couples comprising vanadium (e.g. V(ffl)/V(TI)), copper (e.g. Cu(II)/Cu(0))s, iron (e.g. Fe(III)/Fe(II)), iodine (e.g. I3-/T). Other ions that may be dissolved in one fluid and are transported across a separator include the various ions described in international patent application

PCT/US2012/034442 (incorporated herein by reference in its entirety for any and all purposes), e.g., protons, hydronium, hydroxide, alkali metal ions, alkaline earth metal ions, halide ions, oxyanions of nitrogen, oxyanions of sulfur, oxyanions of halogens, oxyanions of boron, oxyanions of phosphorus, combinations thereof, and the like.

[0071] Separator: As described elsewhere herein, a separator may include selective membranes (e.g., Nafion™) or simple mechanical barriers (e.g., porous separators and/or glass frits), including those listed elsewhere herein. The barrier may permit the mass transport of dissolved species but limit the mixing of gases and any solids or suspended materials. A separator may, in some cases, be one that permits passage of ions but does not permit the passage of photocatalytic material that is dispersed in fluid on either side of the separator.

[0072] Gas Sources: May include a flow controlled gas delivery system (sparger) with tubes with perforations of a size that maximizes agitation and ion mass transport. Photocatalysts may also be a source of gas bubbles and may include semiconducting, photocatalytic particles of various size and composition. Specific examples include cadmium sulfide and iron oxide. Other chemical sources may be gas sources, including combining ammonia borane with protons so as to evolve hydrogen. In some embodiments, a user might use a pump to draw gas evolved at the first chamber (e.g., hydrogen gas); such gas might be drawn from the headspace of the chamber. A pump might also be used to introduce air or other gas into the second chamber, particularly in embodiments when the second chamber forms oxygen.

[0073] The present disclosure also provides methods of transporting dissolved species. These methods comprises contacting a first gas to a first fluid that comprises a dissolved species; the first fluid being separated by a semipermeable barrier from a second fluid; and the contacting being performed under conditions such that the dissolved species is transported through the barrier. As described elsewhere herein, the dissolved species may comprises an ion, e.g., a proton, a halide ion, or one or more of the various ions described elsewhere herein. The dissolved species may, in some cases, comprise at least a portion of a redox couple. The first fluid (e.g., water, an aqueous electrolyte, and the like) may include a first catalytic material disposed within. The first catalytic material is suitably a photocatalytic material, a variety of which are described elsewhere herein. The second fluid may also be water or an aqueous electrolyte, and the second fluid may also comprise a second catalytic material disposed within. Suitable catalytic materials are described elsewhere herein.

[0074] The methods may also include contacting a second gas to the second fluid. The second fluid may also comprise a dissolved species; dissolved species may include one or more of protons, hydronium, hydroxide, alkali metal ions, alkaline earth metal ions, halide ions, oxyanions of nitrogen, oxyanions of sulfur, oxyanions of halogens, oxyanions of boron, oxyanions of phosphorus, or any combination thereof. It should be understood that the disclosed methods include application (e.g., sparging) of gases to the first, second, or both fluids so as to enhance mass (e.g., ion) transport across a separator that divides the first and second chambers.

The sparging may be effected in a continuous or non-continuous (e.g., intermittent) manner. The sparging is also suitably effected during performance of the methods or during system operation, e.g., while the photocatalyst of the system is under illumination. [0075] Additional Disclosure

[0076] To illustrate the disclosed invention, various experiments were performed on exemplary reactors, e.g., a system according to non-limiting Figure 6. That figure summarizes various reactor parameters, including channel width, volumetric flow rate of air, and orifice diameter parameters relative to the design of the cell. The figure shows walls and a base as the body. The walls and base of the cell were made from commercially-available clear polycarbonate (McMaster Carr). Gas sparging tubes were fixed in place on the base of the cell; tubes were made from clear acrylic plastics and flow entered the tubes from both ends. A thin metal frame holds a filter paper separator and slides into grooves in both the walls and the base. The metal frame was fabricated from 316 stainless steel sheets and the separator was Grade 1, 11 μιη pore size paper (Whatman).

[0077] Illustrative Experimental Procedures

[0078] Channels were cleaned using type 1 deionized and distilled water to remove residual ions and impurities. Sparging tubes were then put in place. Generally, the sparging tubes were located in the center of the channel along the length of the channel. Channels were then filled with deionized water up to a liquid level line that completely submerged the cross sectional area available for transport through the filter paper separator. The liquid was allowed to sit for several minutes to allow any residual electrolyte to reach equilibrium in the cell. After ensuring that the separator was secure, thin polycarbonate rectangular bars were placed adjacent to the separator frame. These bars helped reduce splashing over the frame that could influence the concentration in the channels.

[0079] After ensuring that the flow rates are set to the correct values, known masses of lithium chloride and potassium chloride were added separately to the channels. The contents of each channel were stirred to ensure a uniform concentration cell from as early on as possible; channels may be referred to as donor or receiver channels. The lithium chloride donor channel was used in the early stages of the experimental process to determine the mass-transfer coefficient; accordingly, the measurements in this work are based on the measureable concentrations of potassium chloride; the liquid diffusivity of potassium chloride was assumed to be 1.99 x lO^ mV 1 , and the mass-transfer coefficient for each experiment is determined by fitting experimental data.

[0080] Potassium chloride then leaves its donor channel, and the electrolyte enters the lithium chloride donor channel, and the concentration is measured over time. To prevent any mechanical gradients, fluid removed from a channel was replaced with deionized water of the same volume. This ensured that convection through the filter paper was from random pressure changes and not due to some sort of systematic error. The concentrations were measured using an ion chromatograph.

[0081] Lithium chloride and potassium chloride were chosen as the transporting species because their concentrations are easily measured by ion chromatography. A Thermo Scientific Dionex™ ICS-2100 Ion Chromatography System was used to measure the lithium and potassium chloride concentrations; the system has a real-time liquid eluent generation system, a sampling port, a pumping mechanism, a liquid guard and column combination, a suppressor cell to enhance the eluting species conductivity, a conductivity cell, and Chromeleon™ software that serves as a data collection point. A calibration curve was typically made before running any samples. After running a sample, the type of species and its concentration were identified based on the standards set by the calibration curve. For a sample, a plot showing the peak area versus time was produced, which is referred to as a chromatogram of the sample. From the

chromatogram, Chromeleon™ software calculated the concentration of the peak.

[0082] Two exemplary cells (cells 1 and 2) were analyzed as part of these experiments. Various characteristics of cells 1 and 2 are set forth below:

C fice Size (sita

dkaass! e½sisel *

Q.2§ 0.32, 0.31, 0.61, 1.22, l.M

2 38 0 2, 0.31, 0.6L 1.53

— 0

0.07.9.17, 0.52, 6.80, 1.22

2.31 0.07, &ί?, 0.52, SIS, 1.53

— 0

[0083] Some exemplary results are shown in Figure 7, which shows calculated

Sherwood numbers for the variety of cells described in the figure legend. Without being bound to any particular theory, these data suggest the mass transfer is higher for a 20 cm channel width cell as compared to a 10 cm channel width cell. Figure 8 provides additional data that show the channel mass-transfer coefficient for potassium chloride plotted as a function of the total flow rate in the cell for an orifice diameter of 0.26 mm. The mass-transfer coefficient appears to be nearly the same for both channel widths.

[0084] Figure 9 provides additional analysis of an exemplary system. In that figure, the channel-mass-transfer coefficient for potassium chloride is plotted as a function of the total flow rate in the cell for an orifice diameter of 2.38 mm. Without being bound to any particular theory, the differences in the transport coefficient are not especially significant with respect to the channel width. Again without being bound to any particular theory, comparing Figure 8 and 9 suggests that the transport coefficient appears to be independent of the orifice diameter. Also, despite containing twice the volume of solution, the transport coefficient appears to be the same for different channel widths in both figures. This result implies that the mass-transfer coefficient may not depend strongly on channel width. Therefore, a similar measured mass-transfer coefficient is to be expected with a larger or smaller reactor size, at least for the two widths studied here.

[0085] Further experiments examined the effect of sparging tube proximity to the filter paper. Figure 10 shows the results for cell 1. The behavior at lower and higher channel gas flow rates, 0.12 L/min and 1.53 L/min, respectively, are shown. Each data point represents the position of the sparger relative to the separator. In both cases, the mass-transfer coefficient increases by moving the sparger further from the separator. Without being bound to any particular theory, this result can be seen as surprising, as one might expect the concentration boundary layer thickness to be reduced by bringing the sparger closer to the separator.

[0086] The effect of sparging tube proximity to the filter paper is also examined for cell 2. The results are shown in Figure 1 1. The slope of the line trends down, which is opposite to what Figure 10 shows. Again without being bound to any particular theory, Figures 10 and 11 are consistent with the idea that the convection that occurs in each cell is unique to that cell. Therefore, one may represent cells 1 and 2 with individual mass-transfer correlations. The results from the use of these correlations can be used to predict the behavior of different channel width cells.