Dialysis (chemistry)

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Small-molecule dialysis using dialysis tubing Dialysis Figure.png
Small-molecule dialysis using dialysis tubing

In chemistry, dialysis is the process of separating molecules in solution by the difference in their rates of diffusion through a semipermeable membrane, such as dialysis tubing. [1]

Contents

Dialysis is a common laboratory technique that operates on the same principle as medical dialysis. In the context of life science research, the most common application of dialysis is for the removal of unwanted small molecules such as salts, reducing agents, or dyes from larger macromolecules such as proteins, DNA, or polysaccharides. [2] Dialysis is also commonly used for buffer exchange and drug binding studies.

The concept of dialysis was introduced in 1861 by the Scottish chemist Thomas Graham. [3] He used this technique to separate sucrose (small molecule) and gum Arabic solutes (large molecule) in aqueous solution. He called the diffusible solutes crystalloids and those that would not pass the membrane colloids. [4]

From this concept dialysis can be defined as a spontaneous separation process of suspended colloidal particles from dissolved ions or molecules of small dimensions through a semi permeable membrane. Most common dialysis membrane are made of cellulose, modified cellulose or synthetic polymer (cellulose acetate or nitrocellulose). [5]

Etymology

Dialysis derives from the Greek διά, 'through', and λύειν, 'to loosen'. [3]

Principles

Dialysis is the process used to change the matrix of molecules in a sample by differentiating molecules by the classification of size. [6] [7] It relies on diffusion, which is the random, thermal movement of molecules in solution (Brownian motion) that leads to the net movement of molecules from an area of higher concentration to a lower concentration until equilibrium is reached. Due to the pore size of the membrane, large molecules in the sample cannot pass through the membrane, thereby restricting their diffusion from the sample chamber. By contrast, small molecules will freely diffuse across the membrane and obtain equilibrium across the entire solution volume, thereby changing the overall concentration of these molecules in the sample and dialysate (see dialysis figure at right).

Osmosis is another principle that makes dialysis work. During osmosis, fluid moves from areas of high water concentration to lower water concentration across a semi-permeable membrane until equilibrium. In dialysis, excess fluid moves from sample to the dialysate through a membrane until the fluid level is the same between sample and dialysate.

Finally, ultrafiltration is the convective flow of water and dissolved solute down a pressure gradient caused by hydrostatic forces or osmotic forces. In dialysis, ultrafiltration removes molecules of waste and excess fluids from sample. [6] [7]

For example, dialysis occurs when a sample contained in a cellulose bag and is immersed into a dialysate solution. During dialysis, equilibrium is achieved between the sample and dialysate since only small molecules can pass the cellulose membrane, leaving only larger particles behind.

Once equilibrium is reached, the final concentration of molecules is dependent on the volumes of the solutions involved, and if the equilibrated dialysate is replaced (or exchanged) with fresh dialysate (see procedure below), diffusion will further reduce the concentration of the small molecules in the sample.

Dialysis can be used to either introduce or remove small molecules from a sample, because small molecules move freely across the membrane in both directions. Dialysis can also be used to remove salts. This makes dialysis a useful technique for a variety of applications. See dialysis tubing for additional information on the history, properties, and manufacturing of semipermeable membranes used for dialysis.

Types

Diffusion dialysis

Diffusion dialysis is a spontaneous separation process where the driving force which produces the separation is the concentration gradient. It has an increase in entropy and decrease in Gibbs free energy which means that it is thermodynamically favorable. Diffusion dialysis uses anion exchange membranes (AEM) or cation exchange membranes (CEM) depending on the compounds to separate. AEM allows the passage of anions while it obstructs the passage of cations due to the co-ion rejection and preservation of electrical neutrality. The opposite happens with cation exchange membranes. [8]

Electrodialysis

Electrodialysis is a process of separation which uses ion-exchange membranes and an electrical potential as a driving force. It is mainly used to remove ions from aqueous solutions. There are three electrodialysis processes which are commonly used - Donnan dialysis, reverse electrodialysis, and electro-electrodialysis. These processes are explained below. [9]

Donnan dialysis

Donnan dialysis is a separation process which is used to exchange ions between two aqueous solutions which are separated by a CEM or an AEM membrane. In the case of a cation exchange membrane separating two solutions with different acidity, protons (H+) go through the membrane to the less acidic side. This induces an electrical potential that will instigate a flux of the cations present in the less acidic side to the more acidic side. The process will finish when the variation of concentration of H+ is the same order of magnitude as the difference of concentration of the separated cation. [10]

Reverse electrodialysis

Reverse electrodialysis is a technology based on membranes which gets electricity from a mixing of two water streams with different salinities. It commonly uses anion exchange membranes (AEM) and cation exchange membranes (CEM). AEMs are used to allow the pass of anions and obstruct the pass of cations and CEMs are used to do the opposite. The cations and anions in the high salinity water moves to the low salinity water, cations passing through the CEMs and anions through the AEMs. This phenomenon can be converted to electricity. [11]

Electro-electrodialysis

Electro-electrodialysis is an electromembrane process utilizing three compartments, which combines electrodialysis and electrolysis. It is commonly used to recover acid from a solution using AEM, CEM and electrolysis. The three compartments are separated by two barriers, which are the ion exchange membranes. The compartment in the middle has the water to be treated. The compartments located on the sides contain clean water. The anions pass through the AEM, while the cations pass through the CEM. The electricity creates H+ in the anions' side and OH− in the cations' side, which react with the respective ions. [9]

Procedure

Equipment

Separating molecules in a solution by dialysis is a relatively straightforward process. Other than the sample and dialysate buffer, all that is typically needed is:

General protocol

A typical dialysis procedure for protein samples is as follows:

  1. Prepare the membrane according to instructions
  2. Load the sample into dialysis tubing, cassette or device
  3. Place sample into an external chamber of dialysis buffer (with gentle stirring of the buffer)
  4. Dialyze for 2 hours (at room temperature or 4 °C)
  5. Change the dialysis buffer and dialyze for another 2 hours
  6. Change the dialysis buffer and dialyze for 2 hours or overnight

The total volume of sample and dialysate determine the final equilibrium concentration of the small molecules on both sides of the membrane. By using the appropriate volume of dialysate and multiple exchanges of the buffer, the concentration of small contaminants within the sample can be decreased to acceptable or negligible levels. For example, when dialyzing 1mL of sample against 200mL of dialysate, the concentration of unwanted dialyzable substances will be decreased 200-fold when equilibrium is attained. Following two additional buffer changes of 200mL each, the contaminant level in the sample will be reduced by a factor of 8 x 106 (200 x 200 x 200).

Variables and protocol optimization

Although dialyzing a sample is relatively simple, a universal dialysis procedure for all applications cannot be provided due to the following variables:

Additionally, the dialysis endpoint is somewhat subjective and application specific. Therefore, the general procedure might require optimization.

Dialysis membranes and MWCO

Dialysis membranes are produced and characterized according to molecular-weight cutoff (MWCO) limits. While membranes with MWCOs ranging from 1-1,000,000 kDa are commercially available, membranes with MWCOs near 10 kDa are most commonly used. The MWCO of a membrane is the result of the number and average size of the pores created during production of the dialysis membrane. The MWCO typically refers to the smallest average molecular mass of a standard molecule that will not effectively diffuse across the membrane during extended dialysis. Thus, a dialysis membrane with a 10K MWCO will generally retain greater than 90% of a protein having a molecular mass of at least 10kDa. [12] [13]

It is important to note that the MWCO of a membrane is not a sharply defined value. Molecules with mass near the MWCO limit of the membrane will diffuse across the membrane more slowly than molecules significantly smaller than the MWCO. In order for a molecule to rapidly diffuse across a membrane, it typically needs to be at least 20- to 50-times smaller than the MWCO rating of a membrane. Therefore, it is not practical to separate a 30kDa protein from a 10kDa protein using dialysis across a 20K rated dialysis membrane.

Dialysis membranes for laboratory use are typically made of a film of regenerated cellulose or cellulose esters. See reference for a review of cellulose membranes and manufacturing. [14]

Laboratory dialysis formats

Dialysis is generally performed in clipped bags of dialysis tubing or in a variety of formatted dialyzers. The choice of the dialysis set up used is largely dependent on the size of the sample and the preference of the user. Dialysis tubing is the oldest and generally the least expensive format used for dialysis in the lab. Tubing is cut and sealed with a clip at one end, then filled and sealed with a clip on the other end. Tubing provides flexibility but has increased concerns regarding handling, sealing and sample recovery. Dialysis tubing is typically supplied either wet or dry in rolls or pleated telescoped tubes.

A wide variety of dialysis devices (or dialyzers) are available from several vendors. Dialyzers are designed for specific sample volume ranges and provide greater sample security and improved ease of use and performance for dialysis experiments over tubing. The most common preformatted dialyzers are Slide-A-Lyzer, Float-A-Lyzer, and the Pur-A-lyzer/D-Tube/GeBAflex Dialyzers product lines.

Applications

Dialysis has a wide range of applications. These can be divided into two categories depending on the type of dialysis used.

Diffusion dialysis

Some applications of the diffusion dialysis are explained below.

Electrodialysis

Some applications of the electrodialysis are explained below.

Advantages and disadvantages

Dialysis has both advantages and disadvantages. Following the structure of the previous section, the pros and cons are discussed based on the type of dialysis used. Advantages and drawbacks of both, diffusion dialysis and electrodialysis, are outlined below.

Diffusion dialysis

The main advantage of diffusion dialysis is the low energy consumption of the unit. This membrane technique operates under normal pressure and does not have a state change. Consequently, the energy required is significantly reduced, which reduces the operating cost. There is also the low installation cost, easy operation and the stability and reliability of the process. Another advantage is that diffusion dialysis does not pollute the environment. [8]

A disadvantage is that a diffusion dialyser has a low processing capability and low processing efficiency. There are other methods such as electrodialysis and reverse osmosis that can achieve better efficiencies than diffusion dialysis. [8]

Electrodialysis

The main benefit of electrodialysis is the high recovery, especially in the water recovery. Another advantage is the fact that not high pressure is applied which implies that the effect fouling is not significant and consequently no chemicals are required to fight against them. Moreover, the fouling layer is not compact which leads to a higher recovery and to a long membrane life. It is also important that the treatments are for concentrations higher than 70,000 ppm eliminating the concentration limit. Finally, the energy required to operate is low due to the non-phase change. In fact, it is lower in comparison with the needed in the multi effect distillation (MED) and mechanical vapour compression (MVC) processes. [20]

The main drawback of electrodialysis is the current density limit, the process must be operated at a lower current density than the maximum allowed. The fact is that at certain voltage applied the diffusion of ions through the membrane are not linear leading to water dissociation, which would reduce the efficiency of the operation. Another aspect to take into account is that although low energy is required to operate, the higher the salt feed concentration is, the higher the energy needed will be. Finally, in the case of some products, it must be considered that electrodialysis does not remove microorganisms and organic contaminants, therefore a post-treatment is necessary. [20]

See also

Related Research Articles

<span class="mw-page-title-main">Kidney dialysis</span> Removal of nitrogenous waste and toxins from the body in place of or to augment the kidney

Kidney dialysis is the process of removing excess water, solutes, and toxins from the blood in people whose kidneys can no longer perform these functions naturally. This is referred to as renal replacement therapy. The first successful dialysis was performed in 1943.

<span class="mw-page-title-main">Semipermeable membrane</span> Membrane which will allow certain molecules or ions to pass through it by diffusion

Semipermeable membrane is a type of biological or synthetic, polymeric membrane that will allow certain molecules or ions to pass through it by osmosis. The rate of passage depends on the pressure, concentration, and temperature of the molecules or solutes on either side, as well as the permeability of the membrane to each solute. Depending on the membrane and the solute, permeability may depend on solute size, solubility, properties, or chemistry. How the membrane is constructed to be selective in its permeability will determine the rate and the permeability. Many natural and synthetic materials which are rather thick are also semipermeable. One example of this is the thin film on the inside of the egg.

A hydrogen ion is created when a hydrogen atom loses or gains an electron. A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle-free space. Due to its extremely high charge density of approximately 2×1010 times that of a sodium ion, the bare hydrogen ion cannot exist freely in solution as it readily hydrates, i.e., bonds quickly. The hydrogen ion is recommended by IUPAC as a general term for all ions of hydrogen and its isotopes. Depending on the charge of the ion, two different classes can be distinguished: positively charged ions and negatively charged ions.

<span class="mw-page-title-main">Hemodialysis</span> Medical procedure for purifying blood

Hemodialysis, also spelled haemodialysis, or simply dialysis, is a process of purifying the blood of a person whose kidneys are not working normally. This type of dialysis achieves the extracorporeal removal of waste products such as creatinine and urea and free water from the blood when the kidneys are in a state of kidney failure. Hemodialysis is one of three renal replacement therapies. An alternative method for extracorporeal separation of blood components such as plasma or cells is apheresis.

An artificial membrane, or synthetic membrane, is a synthetically created membrane which is usually intended for separation purposes in laboratory or in industry. Synthetic membranes have been successfully used for small and large-scale industrial processes since the middle of twentieth century. A wide variety of synthetic membranes is known. They can be produced from organic materials such as polymers and liquids, as well as inorganic materials. The most of commercially utilized synthetic membranes in separation industry are made of polymeric structures. They can be classified based on their surface chemistry, bulk structure, morphology, and production method. The chemical and physical properties of synthetic membranes and separated particles as well as a choice of driving force define a particular membrane separation process. The most commonly used driving forces of a membrane process in industry are pressure and concentration gradients. The respective membrane process is therefore known as filtration. Synthetic membranes utilized in a separation process can be of different geometry and of respective flow configuration. They can also be categorized based on their application and separation regime. The best known synthetic membrane separation processes include water purification, reverse osmosis, dehydrogenation of natural gas, removal of cell particles by microfiltration and ultrafiltration, removal of microorganisms from dairy products, and Dialysis.

<span class="mw-page-title-main">Ion exchange</span> Exchange of ions between an electrolyte solution and a solid

Ion exchange is a reversible interchange of one kind of ion present in an insoluble solid with another of like charge present in a solution surrounding the solid with the reaction being used especially for softening or making water demineralised, the purification of chemicals and separation of substances.

<span class="mw-page-title-main">Dialysis tubing</span>

Dialysis tubing, also known as Visking tubing, is an artificial semi-permeable membrane tubing used in separation techniques, that facilitates the flow of tiny molecules in solution based on differential diffusion. In the context of life science research, dialysis tubing is typically used in the sample clean-up and processing of proteins and DNA samples or complex biological samples such as blood or serums. Dialysis tubing is also frequently used as a teaching aid to demonstrate the principles of diffusion, osmosis, Brownian motion and the movement of molecules across a restrictive membrane. For the principles and usage of dialysis in a research setting, see Dialysis (biochemistry).

<span class="mw-page-title-main">Ion chromatography</span> Separation of ions and polar molecules

Ion chromatography separates ions and polar molecules based on their affinity to the ion exchanger. It works on almost any kind of charged molecule—including large proteins, small nucleotides, and amino acids. However, ion chromatography must be done in conditions that are one unit away from the isoelectric point of a protein.

<span class="mw-page-title-main">Microdialysis</span> Biological fluid sampling technique

Microdialysis is a minimally-invasive sampling technique that is used for continuous measurement of free, unbound analyte concentrations in the extracellular fluid of virtually any tissue. Analytes may include endogenous molecules to assess their biochemical functions in the body, or exogenous compounds to determine their distribution within the body. The microdialysis technique requires the insertion of a small microdialysis catheter into the tissue of interest. The microdialysis probe is designed to mimic a blood capillary and consists of a shaft with a semipermeable hollow fiber membrane at its tip, which is connected to inlet and outlet tubing. The probe is continuously perfused with an aqueous solution (perfusate) that closely resembles the (ionic) composition of the surrounding tissue fluid at a low flow rate of approximately 0.1-5μL/min. Once inserted into the tissue or (body)fluid of interest, small solutes can cross the semipermeable membrane by passive diffusion. The direction of the analyte flow is determined by the respective concentration gradient and allows the usage of microdialysis probes as sampling as well as delivery tools. The solution leaving the probe (dialysate) is collected at certain time intervals for analysis.

<span class="mw-page-title-main">Electrodialysis</span> Applied electric potential transport of salt ions.

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<span class="mw-page-title-main">Osmotic power</span> Energy available from the difference in the salt concentration between seawater and river water

Osmotic power, salinity gradient power or blue energy is the energy available from the difference in the salt concentration between seawater and river water. Two practical methods for this are reverse electrodialysis (RED) and pressure retarded osmosis (PRO). Both processes rely on osmosis with membranes. The key waste product is brackish water. This byproduct is the result of natural forces that are being harnessed: the flow of fresh water into seas that are made up of salt water.

<span class="mw-page-title-main">Gibbs–Donnan effect</span> Behaviour of charged particles near a semi-permeable membrane

The Gibbs–Donnan effect is a name for the behaviour of charged particles near a semi-permeable membrane that sometimes fail to distribute evenly across the two sides of the membrane. The usual cause is the presence of a different charged substance that is unable to pass through the membrane and thus creates an uneven electrical charge. For example, the large anionic proteins in blood plasma are not permeable to capillary walls. Because small cations are attracted, but are not bound to the proteins, small anions will cross capillary walls away from the anionic proteins more readily than small cations.

<span class="mw-page-title-main">Osmosis</span> Chemical process

Osmosis is the spontaneous net movement or diffusion of solvent molecules through a selectively-permeable membrane from a region of high water potential to a region of low water potential, in the direction that tends to equalize the solute concentrations on the two sides. It may also be used to describe a physical process in which any solvent moves across a selectively permeable membrane separating two solutions of different concentrations. Osmosis can be made to do work. Osmotic pressure is defined as the external pressure required to be applied so that there is no net movement of solvent across the membrane. Osmotic pressure is a colligative property, meaning that the osmotic pressure depends on the molar concentration of the solute but not on its identity.

Electrodeionization (EDI) is a water treatment technology that uses DC power, ion exchange membranes, and ion exchange resin to deionize water. EDI is usually a polishing treatment to reverse osmosis (RO). EDI differs from other RO polishing technologies such as chemically regenerated mixed beds, in that it is continuous and requires no chemical regeneration. EDI is sometimes referred to as continuous electrodeionization (CEDI) since the electric current regenerates the ion exchange resin mass continuously. The CEDI technique can achieve high purity, with product conductivity on the order of 0.1 μS/cm and sometimes with resistivity as high as 18.2 MΩ-cm. Electrodeionization (EDI) is a combination of three different processes: Electrolysis, where with a continuously applied electric DC current, both positive and negative ions are directed to the electrode that has opposing electrical charge; the electrical potential pulls anions and cations from diluting chambers, though cation or anion exchange membranes, into concentrating chambers. Ion exchange, where ion exchange resin makes up the diluting chambers, and the cations and anions are affixed to resin sites as water passes through the resin bed; and chemical regeneration, which occurs by water splitting. In a chemically regenerated mixed bed, the hydrogen (H+) of acid regenerates cation resin. The hydroxide (OH-) of sodium hydroxide (caustic soda) regenerates anion resin. In EDI, the electrical current causes water to split from H2O → H+ + OH-, regenerating the resin without the need for addition of external chemicals.

<span class="mw-page-title-main">Diafiltration</span> Dilution process

Diafiltration is a dilution process that involves removal or separation of components of a solution based on their molecular size by using micro-molecule permeable filters in order to obtain pure solution.

Concentration polarization is a term used in the scientific fields of electrochemistry and membrane science.

<span class="mw-page-title-main">Desalting and buffer exchange</span>

Desalting and buffer exchange are methods to separate soluble macromolecules from smaller molecules (desalting) or replace the buffer system used for another one suitable for a downstream application. These methods are based on gel filtration chromatography, also called molecular sieve chromatography, which is a form of size-exclusion chromatography. Desalting and buffer exchange are two of the most common gel filtration chromatography applications, and they can be performed using the same resin.

Anion-exchange chromatography is a process that separates substances based on their charges using an ion-exchange resin containing positively charged groups, such as diethyl-aminoethyl groups (DEAE). In solution, the resin is coated with positively charged counter-ions (cations). Anion exchange resins will bind to negatively charged molecules, displacing the counter-ion. Anion exchange chromatography is commonly used to purify proteins, amino acids, sugars/carbohydrates and other acidic substances with a negative charge at higher pH levels. The tightness of the binding between the substance and the resin is based on the strength of the negative charge of the substance.

An ion-exchange membrane is a semi-permeable membrane that transports certain dissolved ions, while blocking other ions or neutral molecules.

A microbial desalination cell (MDC) is a biological electrochemical system that implements the use of electro-active bacteria to power desalination of water in situ, resourcing the natural anode and cathode gradient of the electro-active bacteria and thus creating an internal supercapacitor. Available water supply has become a worldwide endemic as only .3% of the earth's water supply is usable for human consumption, while over 99% is sequestered by oceans, glaciers, brackish waters, and biomass. Current applications in electrocoagulation, such as microbial desalination cells, are able to desalinate and sterilize formerly unavailable water to render it suitable for safe water supply. Microbial desalination cells stem from microbial fuel cells, deviating by no longer requiring the use of a mediator and instead relying on the charged components of the internal sludge to power the desalination process. Microbial desalination cells therefore do not require additional bacteria to mediate the catabolism of the substrate during biofilm oxidation on the anodic side of the capacitor. MDCs and other bio-electrical systems are favored over reverse osmosis, nanofiltration and other desalination systems due to lower costs, energy and environmental impacts associated with bio-electrical systems.

References

  1. ↑ Reed, R (2007). Practical Skills in Biomolecular Sciences (3rd ed.). Essex: Pearson Education Limited. p. 379. ISBN   978-0-13-239115-3.
  2. ↑ Berg, JM (2007). Biochemistry (6th ed.). New York: W.H. Freeman and Company. p.  69. ISBN   978-0-7167-8724-2.
  3. 1 2 Chisholm, Hugh, ed. (1911). "Dialysis"  . Encyclopædia Britannica . Vol. 8 (11th ed.). Cambridge University Press. p. 157.
  4. 1 2 Stancheva, K.A. (2008). "Applications of dialysis". Oxidation Communications 31. 4: 758–775.
  5. ↑ Ninfa, A.J.; Ballou, D. P.; Benore, M. (2009). Fundamental Laboratory Approaches for Biochemistry and Biotechnology. p. 45. ISBN   978-0-470-08766-4.
  6. 1 2 "What is dialysis?".
  7. 1 2 "What is dialysis and how does dialysis work?".
  8. 1 2 3 4 Luo, J.; Wu, C.; Xu, T.; Wu, Y. (2011). "Diffusion dialysis-concept, principle and applications". Journal of Membrane Science. 366 (1–2): 1–16. doi:10.1016/j.memsci.2010.10.028.
  9. 1 2 Luis, P. (2018). Fundamental Modeling of Membrane Systems: Membrane and Process Performance. Elsevier. pp. 275–292. ISBN   978-0-12-813483-2.
  10. ↑ Scott, K. (1995). Handbook of Industrial Membranes . Kidlington: Elsevier Advanced Technology. pp.  704-706. ISBN   978-1-85617-233-2.
  11. ↑ Mei, Y.; Tang, C.Y. (2018). "Recent developments and future perspectives of reverse electrodialysis technology: A review". Desalination. 425: 156–174. doi:10.1016/j.desal.2017.10.021.
  12. ↑ "Separation characteristics of dialysis membranes" . Retrieved 13 November 2013.
  13. ↑ "Fundamentals of membrane dialysis" . Retrieved 13 November 2013.
  14. ↑ Klemm, Dieter; Heublein, Brigitte; Fink, Hans-Peter; Bohn, Andreas (2005). "Cellulose: Fascinating Biopolymer and Sustainable Raw Material". Angewandte Chemie International Edition. 44 (22): 3358–3393. doi:10.1002/anie.200460587. PMID   15861454.
  15. ↑ Lovett, Louis E. (1938). "The Application of Osmosis to the Recovery of Caustic Soda Solutions Containing Hemicellulose in the Rayon Industry". Trans. Electrochem. Soc. 73 (1): 163–172. doi:10.1149/1.3493960.
  16. ↑ Marshall, R. D.; Storrow, J. Anderson (1 December 1951). "Dialysis of Caustic Soda Solutions". Ind. Eng. Chem. 43 (12): 2934–2942. doi:10.1021/ie50504a074.
  17. ↑ Lee, Eric K.; Koros, W. J. (2003). "Membranes, Synthetic, Applications: Industrial Dialysis". ScienceDirect . From Encyclopedia of Physical Science and Technology (3rd edition). Retrieved 29 September 2020.
  18. ↑ Jackowski, M.; Trusek, A. (2018). "Non-alcoholic beer production - an overview". Polish Journal of Chemical Technology. 20 (4): 32–38. doi: 10.2478/pjct-2018-0051 . S2CID   104447271.
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  20. 1 2 Charisiadis, C. "Electrodialysis/ED Reversal" (PDF).

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