Principle of Separation of Mechanism and Policy Mean Three Easy Pieces

Arsenic Removal by Membrane Filtration

Parimal Pal , in Groundwater Arsenic Remediation, 2015

4.6.1 Oxidation–nanofiltration principle

Separation mechanisms in nanofiltration involve both steric (sieving) effects and electrical (Donnan) effects. This combination allows NF membranes to be effective for removal of more than 98% of arsenic from contaminated groundwater [ 7]. Lower pumping cost and membrane cost compared to RO makes nanofiltration an economically attractive option. Separation of ionic species by a nanofiltration membrane strongly depends on the membrane properties (membrane charge and membrane pore radius). A membrane with smaller pores is better able to retain ionic species, where a highly charged membrane is better able to exclude co-ions (ions of like charge as the membrane). When charge repulsion dominates separation, it is desirable that all the target species are converted into charged forms. As discussed in Chapter 1, arsenic may be present in groundwater both in trivalent and pentavalent forms. Under normal pH conditions, trivalent arsenic largely remains in neutral form, which cannot be separated by a Donnan exclusion using a nanofiltration membrane. However, conversion of trivalent arsenic into pentavalent form facilitates its separation by nanofiltration, as corresponding ions of arsenic being negatively charged get rejected by the membrane because of charge repulsion. Soluble arsenic can be effectively removed from groundwater by a NF membrane with prior oxidation of trivalent arsenic to pentavalent state using some oxidizing agent.

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Engineering Fundamentals of Biotechnology

B. Schuur , ... M. Leeman , in Comprehensive Biotechnology (Second Edition), 2011

2.52.6.2 Principles

Two separation mechanisms are recognized in membrane science [14]. When a transport barrier limits the transport of one enantiomer, that enantiomer interacts with the membrane material, reducing the diffusivity. The other enantiomer travels easier through the membrane as it interacts less strongly. In facilitated transport on the other hand, it is the interaction with the membrane that facilitates the transport; thus a stronger interaction leads to a higher flux. Both mechanisms are displayed schematically in Figure 12 . The material remaining in the feed liquid phase is called the residue, while the transported material is the permeate.

Figure 12. Transmembrane transport of enantiomers A and B: (a) transport facilitated through interaction with the membrane and (b) transport retarded through interaction with the membrane.

Reproduced with permission from Ulbricht M (2004) Membrane separations using molecularly imprinted membranes. Journal of Chromatography B 804: 113–125, © Elsevier.

In both mechanisms, the fundamental mechanism is a difference in fluxes of the enantiomers. The flux is defined in eqn 4, where c_i is a coefficient of proportionality of enantiomer i (i  = R, S) that links the gradient in the chemical potential to the actual flux.

[4] $J_i=-c_i\frac{\text{d}{\mu }_i}{\text{d}x}$

Usually, the performance of a membrane is expressed in terms of permeability:

[5] $P_i=\frac{J_{i}x}{{[i]}_{\text{feed}}-{[i]}_{\text{permeate}}}$

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Nanotechnology in Water Treatment

Parimal Pal , in Industrial Water Treatment Process Technology, 2017

7.2.6.2 Separation Mechanisms in Adsorption by CNTs

The separation mechanism of CNTs is mainly based on electrostatic interaction as well as availability of adsorption sites. The fast adsorption kinetics in the context of adsorption of heavy metals such as Pb ²⁺, Cd²⁺, Cu²⁺, and Zn²⁺ on CNTs results in accessible adsorption sites and short intraparticle diffusion distance. Oxidized CNTs can provide better adsorption capacity due to the presence of functional groups like carboxyl, hydroxyl, and phenol groups, which act as extended adsorption sites for metal ions.

The extent of adsorption largely depends on the presence of functional groups on the surface and the nature of the sorbate. Functionalized CNTs with phenolic, carboxylic, and lactonic acid groups adsorb polar compounds efficiently where chemical interaction plays the main role in adsorption. Nonfunctionalzed CNTs, on the other hand, can adsorb nonpolar compounds like polycyclic aromatic compounds where physical interaction plays the dominant role.

The high adsorption of polar organic compounds on CNTs depends uon hydrophobic effect, π–π interactions, hydrogen bonding, covalent bonding, and electrostatic interactions between contaminants and CNTs. The π-e⁻rich CNT surface provides good electrostatic attraction, which facilitates the adsorption of positively charged organic chemicals at suitable pH. Organic compounds containing –COOH, –OH, and –NH₂ groups can also form hydrogen bonding with CNT surface during separation via electronic interaction. The cost of fabricating CNTs is much higher than that of activated carbon powder, although the removal efficiency of CNTs is higher.

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Dual-liquid phase systems

S. Wang , Z. Xu , in Absorption-Based Post-combustion Capture of Carbon Dioxide, 2016

9.2.1.1 Distribution of amine and CO₂

The separation mechanism is analyzed using 17 samples taken at nine different loadings during the absorption process. Among them, the first sample is taken before the two phases appeared, and the remaining 16 samples are taken after the two phases appeared, so there are both upper and lower samples for each loading.

The total amine concentrations (the alkalinity) and CO₂ concentrations, and, consequently, the CO₂ loadings, of all the samples can be directly titrated. The total loadings of the two phases are calculated according to the concentrations of amine and CO₂ and the weights of the upper and lower phases. The BDA and DEEA concentrations are measured using cation chromatography.

Table 9.2 lists the amine concentrations, CO₂ concentrations, and alkalinities of all the samples. The total amine amounts shown in Fig. 9.2 are calculated based on the amine concentrations and weight percentage of each phase. Table 9.2 shows that the alkalinity concentrations in the two phases are around 8   mol/kg. The weight percentage in the upper phase increased gradually with increased total loading, whereas that in the lower phase decreased. The maximum difference of alkalinity concentration measured by titration and ion chromatography (IC) was 8.84%, and most of the differences were less than 5%. Fig. 9.2 shows that the total amine amounts in the solution calculated from the IC results during absorption were almost constant, indicating the accuracy of the IC results.

Table 9.2. Amine, CO₂, and mole distributions in the two phases during absorption

Total loading mol/mol amine	Phase	Loading mol/mol	BDA mol/kg	DEEA mol/kg	CO2 mol/kg	Alkalinity a mol/kg	Weight percentage b %	Difference of alkalinity c %
0.133	/ d	/	2.103	4.200	0.845	8.486	/	0.94
0.187	Upper	0.066	1.060	5.990	0.286	8.027	58.57	1.01
	Lower	0.431	3.585	1.373	2.299	8.886	41.43	3.85
0.193	Upper	0.041	1.086	5.266	0.422	7.961	56.94	6.58
	Lower	0.464	3.175	1.614	2.064	8.412	43.06	5.32
0.244	Upper	0.024	0.367	6.680	0.170	7.427	49.17	0.16
	Lower	0.572	3.577	0.983	2.609	8.385	50.83	2.94
0.313	Upper	0.018	0.181	7.339	0.137	7.580	45.20	1.60
	Lower	0.706	3.569	1.095	3.294	8.705	54.80	5.41
0.346	Upper	0.031	0.082	6.885	0.229	7.506	41.46	6.10
	Lower	0.755	3.153	1.282	3.316	7.973	58.54	4.84
0.371	Upper	0.033	0.212	7.456	0.239	7.707	44.03	2.24
	Lower	0.748	3.361	1.276	3.501	8.475	55.97	5.63
0.402	Upper	0.035	0.128	7.855	0.279	7.745	33.56	4.72
	Lower	0.727	2.845	1.719	3.316	7.867	66.44	5.82
0.505	Upper	0.043	0.115	7.265	0.315	7.794	21.79	3.83
	Lower	0.710	2.233	2.400	3.291	7.533	78.21	8.84

a

The alkalinity by titration.

b

Weight percent of upper and lower phase at the time of sampling.

c

The alkalinity differences between IC and titration results.

d

There is no upper and lower phase at this loading.

Figure 9.2. The change of total amine amounts of the two phases during absorption.

The individual and total amine concentrations in the upper and lower phases shown in Fig. 9.3 shows that the total alkalinity concentration in each phase is almost constant during the absorption process, with that in the lower phase a little higher than that in the upper phase. The DEEA and BDA distributions, however, are quite different in the two phases. In the upper phase, the DEEA concentration increases and the BDA concentration decreases up to a total CO₂ loading of 0.37   mol/mol amine. In the lower phase, the BDA concentration first increases to 3.58   mol/kg at a loading of 0.24   mol/mol amine and then decreases to 2.2   mol/kg when approaching equilibrium. The DEEA concentration in the lower phase has the opposite tendency, first decreasing to 0.9   mol/kg, and then increasing to 2.4   mol/kg.

Figure 9.3. The relationship of the amine concentrations with total loadings of the 17 samples during absorption. (a) Upper phase, (b) lower phase.

The total amine mole distribution in the two phases during the absorption is shown in Fig. 9.4. For the convenience of analysis, volume ratios of each phase for the first point, which is homogeneous, are assumed the same as for the second point. This illustrates the amine-transition tendency more clearly. In the upper phase, with the same way as with amine concentration, the total amount of BDA decreases to a very low value, less than 0.01   mol. The DEEA amount first increases to about 0.32   mol and then decreases to 0.16   mol. In the lower phase, the DEEA amount drops quickly at first and then increases finally to about 0.2   mol, whereas the BDA amount first increases and then remains almost constant at loadings higher than 0.31   mol/mol amine.

Figure 9.4. The relationship of the amine amounts with total CO₂ loadings of the 17 samples during absorption. (a) Upper phase, (b) Lower phase.

Fig. 9.5 describes the CO₂ concentrations in terms of mole per kilogram and CO₂ loading, indicating that the CO₂ concentration in the upper phase was very low. The weight ratio of the lower phase increases with CO₂ loading, which indicates that most of the CO₂ is in the lower phase. Fig. 9.5 also tells that the CO₂ concentration in the lower phase is constant at loadings higher than 0.313, whereas the total amount in the lower phase increases as the weight of the lower phase increases.

Figure 9.5. The relationship of the CO₂ concentrations with total loadings of the 17 samples. (a) Upper phase, (b) Lower phase.

After absorption, the ratio of the number of moles of BDA in the upper and lower phase is 1/70, and the DEEA mole ratio is 1/1.18, indicating that, after absorption, most of the BDA is in the lower phase, whereas the DEEA is almost uniformly distributed. The amount of CO₂ in the lower phase after absorption is 97.4% of the total absorbed amount. The total CO₂ loading is 0.505   mol CO₂/mol amine.

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Micellar and Microemulsion Electrokinetic Chromatography

Ute Pyell , in Capillary Electromigration Separation Methods, 2018

5.4.1 Thermodynamic Models

The separation mechanism of charged compounds in ME(E)KC can be based on both chromatographic and electrophoretic principles. According to Otsuka et al. [94], the observed velocity v _ob of a (partially) ionized solute (e.g., a phenol) in a micellar medium or in a microemulsion is the weighted sum of the observed effective electrophoretic velocity v _ep of the solute (the velocity that would be observed if we were able to remove selectively the PSP from the separation electrolyte) and the observed velocity v _PSP of the PSP:

(5.11) $v_{\mathrm{ob}}=\frac{1}{k+1}{v}_{\mathrm{ep}}+\frac{k}{k+1}{v}_{\mathrm{PSP}}$

The true retention factor k (in contrast to the apparent retention factor k _app calculated with Eq. (5.4), (5.6), or (5.7), respectively) can only be calculated if the effective electrophoretic velocity v _ep of the solute zone in the separation electrolyte without PSP is known. This quantity is mainly determined by CE experiments. However, it should be noted that several assumptions are made in this case: the influence of the PSP on ionic strength, dielectric constant, and viscosity is assumed to be negligible and likewise also interactions of the solute with surfactant monomers (electrostatic and/or hydrophobic interactions) [95]. In that case, k can be calculated from:

(5.12a) $k=\frac{v_{\mathrm{ob}}-v_{\mathrm{ep}}}{v_{\mathrm{PSP}}-v_{\mathrm{ob}}}$

(5.12b) $k=\frac{{\mu }_{\mathrm{ob}}-{\mu }_{\mathrm{ep}}}{{\mu }_{\mathrm{PSP}}-{\mu }_{\mathrm{ob}}}$

With this equation, k can be calculated even for a fully ionized solute. Otsuka et al. [94] determined v _ep for phenolic compounds with a buffer containing 5   mmol   L^{−   1} SDS, while assuming that this concentration is below the CMC of SDS (this is true for pure water). However, generally, when using this approach, it has to be taken into account that the CMC of a surfactant in an aqueous separation electrolyte can be substantially lower than that in pure water [96]. In spite of this problem, Otsuka et al. [94] succeeded in explaining satisfactorily the dependence of the retention factor k on the pH of the separation buffer. Interestingly, the retention factors of the negatively charged species (deprotonated chlorinated phenols) were different from zero (pointing to hydrophobic interaction of the anionic species with the anionic micelles). In 1991, Khaledi et al. [54] investigated in detail the migration behavior of acidic solutes in MEKC dependent on the pH and concentration of an anionic surfactant. Their phenomenological approach fully confirms the considerations made before by Otsuka et al. [94].

According to the approach of Khaledi et al. [54], the retention factor k of an acid is the weighted average of the retention factors of the protonated (HA) and deprotonated (A) species:

(5.13) $k=F_{\mathrm{HA}}^{\mathrm{aq}}{k}_{\mathrm{HA}}+F_{\mathrm{A}}^{\mathrm{aq}}{k}_{\mathrm{A}}$

where F _HA ^aq = molar fraction of the protonated acid in the surrounding pseudophase, F _A ^aq = molar fraction of the deprotonated acid in the surrounding pseudophase, k _AH  =   retention factor of the protonated acid, k _A  =   retention factor of the deprotonated acid, with F _HA ^aq  + F _A ^aq  =   1. If secondary equilibria can be neglected, the molar fractions of the protonated and the deprotonated species in the surrounding pseudophase are only dependent on the pH and the acid constant K _a:

(5.14) $F_{\mathrm{HA}}^{\mathrm{aq}}=\frac{c\left({\mathrm{H}}^{+}\right)}{c\left({\mathrm{H}}^{+}\right)+K_{\mathrm{a}}}$

(5.15) $F_{\mathrm{A}}^{\mathrm{aq}}=\frac{K_{\mathrm{a}}}{c\left({\mathrm{H}}^{+}\right)+K_{\mathrm{a}}}$

(5.16) $k=\frac{k_{\mathrm{HA}}+k_{\mathrm{A}}\left(K_{\mathrm{a}}/c\left({\mathrm{H}}^{+}\right)\right)}{1+\left(K_{\mathrm{a}}/c\left({\mathrm{H}}^{+}\right)\right)}$

From Eq. (5.16), it follows for acidic solutes that the function k  =   ƒ(pH) is a sigmoidal curve with inflection point (maximum slope) at pH   =   pK _a. This also holds true for the distribution constant Κ (refer to Eq. 5.5). In EKC not only the retention factor k but also the observed (apparent) effective mobility μ describes quantitatively the migration of acidic solutes:

(5.17) $\mu =F_{\mathrm{H}\mathrm{A}}^{\mathrm{P}\mathrm{S}\mathrm{P}}{\mu }_{\mathrm{P}\mathrm{S}\mathrm{P}}+F_{\mathrm{A}}^{\mathrm{P}\mathrm{S}\mathrm{P}}{\mu }_{\mathrm{P}\mathrm{S}\mathrm{P}}+F_{\mathrm{A}}^{\mathrm{a}\mathrm{q}}{\mu }_{\mathrm{A}}^{\mathrm{a}\mathrm{q}}$

where F _HA ^PSP = molar fraction of the protonated acid in the PSP, F _A ^PSP = molar fraction of the deprotonated acid in the PSP, μ _PSP  =   observed mobility of the PSP, μ _A ^aq = observed mobility of the deprotonated acid in the surrounding pseudophase, with F _HA ^PSP  + F _A ^PSP  + F _HA ^aq  + F _A ^aq  =   1. If we define the apparent acid constant K _a,app in a medium containing a PSP as,

(5.18) $K_{\mathrm{a},\mathrm{app}}=\frac{\left(c_{\mathrm{PSP}}\left({\mathrm{A}}^{-}\right)+c_{\mathrm{aq}}\left({\mathrm{A}}^{-}\right)\right)\cdot c\left({\mathrm{H}}^{+}\right)}{\left(c_{\mathrm{PSP}}\left(\mathrm{HA}\right)+c_{\mathrm{aq}}\left(\mathrm{HA}\right)\right)}$

where c _PSP(A⁻) = concentration of deprotonated acid in the PSP, c _aq(A⁻) = concentration of deprotonated acid in the surrounding pseudophase, c _PSP(AH) = concentration of protonated acid in the PSP, and c _aq(AH) = concentration of protonated acid in the surrounding pseudophase. Then the observed overall effective mobility μ of a solute in a medium containing a micellar PSP can be described as a function of μ _HA and μ _A, K _a,app and c(H⁺):

(5.19) $\mu =\frac{{\mu }_{\mathrm{HA}}+{\mu }_{\mathrm{A}}\left(K_{\mathrm{a},\mathrm{app}}/c\left({\mathrm{H}}^{+}\right)\right)}{1+\left(K_{\mathrm{a},\mathrm{app}}/c\left({\mathrm{H}}^{+}\right)\right)}$

with

(5.20) ${\mu }_{\mathrm{HA}}=\frac{K_{\mathrm{HA}}^{\mathrm{PSP}}c\left(\mathrm{PSP}\right){\mu }_{\mathrm{PSP}}}{1+K_{\mathrm{HA}}^{\mathrm{PSP}}c\left(\mathrm{PSP}\right)}$

(5.21) ${\mu }_{\mathrm{A}}=\frac{{\mu }_{\mathrm{A}}^{\mathrm{aq}}+K_{\mathrm{A}}^{\mathrm{PSP}}c\left(\mathrm{PSP}\right){\mu }_{\mathrm{PSP}}}{1+K_{\mathrm{A}}^{\mathrm{PSP}}c\left(\mathrm{PSP}\right)}$

where K _A ^PSP = binding constant of the deprotonated species, K _AH ^PSP = binding constant of the protonated species, and c(PSP)   =   molar concentration of the PSP. The parameter K ^PSP refers to the product of the distribution coefficient K and the molar volume of the micelles. For microemulsions, equations have to be derived that use the volume fraction in place of the molar concentration. Based on Eqs. (5.14)–(5.21), Smith and Khaledi [97] developed a model to predict the migration of organic acids in MEKC. Quang et al. [98] generalized this approach. They also included ion pair interactions of the charged solute species with the oppositely charged surfactant monomers in their considerations. For an acidic solute, this type of interaction would be expected, if we were using a cationic surfactant. We then additionally have to take into consideration the ion pair formation equilibrium A   +   S_mono  ⇄   [AS_mono] (S_mono  =   surfactant monomer) with the ion pair equilibrium constant K _IP. The molar concentration of S_mono corresponds to the CMC. The electrophoretic mobility of the ion pair [AS_mono] is zero and following molar fractions are given:

(5.22) $F_{\mathrm{HA}}^{\mathrm{PSP}}+F_{\mathrm{A}}^{\mathrm{PSP}}+F_{\mathrm{HA}}^{\mathrm{aq}}+F_{\mathrm{A}}^{\mathrm{aq}}+F_{{\mathrm{AS}}_{\text{mono}}}^{\mathrm{aq}}=1$

where F _A ^aq = molar fraction of the free deprotonated species in the surrounding pseudophase, and $F_{{\mathrm{AS}}_{\text{mono}}}^{\mathrm{aq}}$ = molar fraction of the ion-paired deprotonated species in the surrounding pseudophase. CE can verify the presence or absence of ion pair formation of charged solutes with oppositely charged surfactant monomers if results are compared that were obtained (1) with a separation electrolyte containing no surfactant and (2) with a separation electrolyte containing a surfactant at a concentration below the CMC. If the calculated electrophoretic mobilities are virtually identical, the absence of ion-pair formation is verified [99]. This result is expected for hydrophilic solutes, whereas for more hydrophobic solutes, ion pair formation is more likely to occur. Interestingly, Muijselaar et al. [95] observed an additional hydrophobic interaction of the protonated form of hydrophobic acidic solutes with surfactant monomers (forming a charged adduct). This phenomenon might be important in the determination of true retention factors for very hydrophobic species. In addition, Muijselaar et al. [95] experimentally verified that both the mobility model and the retention model are able to describe adequately the migration of monovalent acids in MEKC.

The same concept as that described for acidic solutes can be used to describe the migration of basic solutes [100]. If K _IP is approaching infinity, the basic solute will be present in the surrounding pseudophase either as a neutral species or as a neutral ion pair. Consequently, in this case, the effective electrophoretic mobility of the solute in the surrounding pseudophase will be zero, and the true retention factor can be calculated with a simplified equation:

(5.23) $k=\frac{{\mu }_{\mathrm{ob}}}{{\mu }_{\mathrm{PSP}}-{\mu }_{\mathrm{ob}}}$

With this equation, Quang et al. [98] succeeded in correctly modeling the migration behavior of 17 selected aromatic amines that were separated by MEKC with SDS as PSP over a very wide parameter range as a function of pH and SDS concentration (pH   7.0–12.0, c(SDS)   =   20–80   mmol   L^{−   1}) based on only five experiments.

Approaches based on physicochemical models have to be distinguished from approaches based on empirical models. Although the use of physicochemical models has advantages, since an in-depth understanding of the underlying equilibria should be always preferred, such an approach is not always feasible, as it might be that too many experiments are required to determine all the relevant constants in the equations with sufficient accuracy. In this case, empirical (also called statistical) models are useful in minimizing the number of required experiments. Garcia-Ruiz et al. [101] name following empirical strategies for resolution optimization: the overlapping resolution mapping (ORM) scheme [102], the iterative regression strategy [103], factorial designs such as the Plackett-Burman design [104] and the orthogonal array design [105], empirical equations and artificial neural networks [106].

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Advanced Mass Spectrometry for Food Safety and Quality

Wenjie Liu , Herbert H. HillJr, in Comprehensive Analytical Chemistry, 2015

Abstract

The unique separation mechanism, speed of analysis, and portable instrumentation has made ion mobility spectrometry (IMS) the method of choice for military and homeland security applications for the detection of explosives and chemical warfare agents. Most recently, the applications of IMS, especially hyphenated with other analytical techniques such as chromatography and mass spectrometry, have grown to include a wide range of analytical applications such as metabolomics, pharmaceutical analysis, environmental monitoring, and "foodomics." This chapter critically reviews applications using IMS for the determination of different families of compounds in food composition, food flavors, food processing, and food contaminants.

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Recent Developments in Nanofiltration for Food Applications

A.W. Mohammad , ... N.A. Rosnan , in Nanomaterials for Food Applications, 2019

5.2 Theory and Mechanism of Nanofiltration Membranes

Generally, the separation mechanisms of NF membranes can be classified into three types, namely: (1) sieve mechanism or size-based exclusion (steric), (2) electrical (Donnan) exclusion, and (3) dielectric effects, which had been critically reviewed by Mohammad et al. (2015). Fig. 5.3 illustrates the combined separation mechanisms of NF membranes in separating a mixture of mono/divalent ions and water. Typically, the rejection efficiency of monovalent and divalent ions by NF membranes is around 30%–80% and 70%–95%, respectively (Hilal et al., 2004). NF membranes have much higher rejection rates toward divalents ions but partially permit the monovalent ions to pass through the membranes; hence, they can be used to fractionate electrolyte mixtures from heavy metal ions and divalent anions from wastewater (Wang et al., 2008).

Figure 5.3. Separation mechanism of nanofiltration (NF) membrane based on size exclusion, Donnan exclusion, and dielectric effect (Nicolini et al., 2016).

For uncharged solutes, the size exclusion effect is the governing factor to determine the separation performance of the NF membrane. This type of mechanism simply implies that bigger molecules will be restricted by the membrane pore size, whereas smaller molecules will pass through the membrane freely, depending solely on the molecular size. Mahlangu et al. (2017) investigated the rejection of trace organic compounds by polyethersulfone membranes with different molecular weight cut off (MWCO). Their results indicated that an increasing rejection of trace organic compounds was attained with decreasing the MWCO, implying that sieving effects play a major role for uncharged organic compounds. However, it is important to highlight that decreasing membrane's MWCO can imply considerably increased energy cost due to the relatively high operating pressures required.

An interesting feature of NF membranes is that the membrane surface will become slightly charged due to the dissociation of surface functional groups or adsorption of charge solute when in contact with aqueous solutions, which contributes to the Donnan exclusion. Theoretically, Donnan exclusion describes the equilibrium and membrane potential interactions between a charged species and the interface of the charged membrane, where charge repulsion occurs, to restrict the invasion of ions and other solutes to maintain charge balance. The rejection-based Donnan theory can be represented by Eq. (5.1) (Fornasiero et al., 2008). From this equation, the ratio of cationic and anionic species valency, $z_i/z_j$ , will determine the rejection efficiency of the different salt molecules that support the salt selectivity rejection in NF membrane.

Eq. (5.1) $R=1-{\left(\frac{\left|z_i\right|c_i}{\left|z_i\right|c_i^m+c_x^m}\right)}^{\left|\frac{z_i}{z_j}\right|}$

where $z_i$ is the charge of co-ions, $z_j$ is the charge of counterions, $c_i$ and $c_i^m$ are the concentrations of co-ions in the solution and in the membrane phase, respectively, and $c_x^m$ is the membrane charge concentration.

Furthermore, the Donnan exclusion of NF membranes can be expanded for ion selectivity separation. Hua and Chung (2017) reported a novel molecular method to tune the membrane surface charge on the polypropylene membrane support using graphene oxide (GO) as anchoring agent. They found that GO nanocomposite NF membrane modified by hyperbranched polyethyleneimine has excellent rejections toward cationic dyes at around 95%, whereas those modified by poly(styrenesulfonate) (PSS) favor the rejection toward anionic dyes up to 97% due to the Donnan effect. This study provided insights to improve the selectivity of NF membranes via surface modification.

Lastly, the phenomena of dielectric exclusion occur due to a series of concomitant effects. The primary effect is caused by the difference existing between the dielectric constant of an aqueous solution and the corresponding value of the polymeric matrix, whereas the secondary effect is due to the variations of the solvent dielectric properties inside the membrane pores with respect to the external bulk values (Bandini and Vezzani, 2003). In general, dielectric exclusion is considered as an additional mechanism of ion exclusion, appearing when the solvent is confined in nanopores. In contrast to the Donnan exclusion, dielectric exclusion is always unfavorable for any ion, independent of the ion sign. Dielectric exclusion has been critically reviewed by Oatley et al. (2012).

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Electric (Electro/Dielectro-Phoretic)—Force Field Assisted Separators

Morgane Citeau , ... Eugene Vorobiev , in Progress in Filtration and Separation, 2015

3.2.2 High-Gradient Dielectrophoretic Separation

The common dielectrophoretic separation mechanisms are based either on the sign or on the magnitude of the DEP force in a laminar flow stream. Figure 18 illustrates the basic principle of three hydrodynamic dielectrophoresis processes. Two kinds of particles are carried by the flow through the chamber, confined within a certain range in the channel. DEP force is generated in the nonuniform electric field provided by intermittent microelectrodes. Sign-based DEP separation illustrated in Figure 18(a), is achieved (1) by applying a frequency where one kind of particle is levitated by negative DEP and flushed out by the flow stream, while the other kind is immobilized on the electrodes by positive DEP. The particles levitate above the electrode surface according to their physical properties and those of the fluid. As the negative DEP force decreases with distance from electrodes and the sedimentation force acts on each particle, repelled particles are driven to an equilibrium height where the sedimentation and levitation forces are balanced. Electric field is periodically switched off (2) to release the trapped particles into a noncontaminated flow stream. Continuous separation system may be achieved using the viscous drag of feed flow.

Figure 18. Separation mechanisms based (a) on the dielectrophoretic sign, (b) on the dielectrophoretic magnitude, and (c) on the dielectrophoretic trap-and-release procedure.

Magnitude-based DEP separation illustrated in Figure 18(b), allows differentiating particles based on their effective polarizability and density. The frequency and the medium properties are selected in such a way that both kinds of particle are repelled under the nonuniform electric field. Depending on their density and dielectric properties, the particle groups are levitated to different heights. They move along the fluid flow without change of height. Combined with fluid flow with a parabolic velocity profile, those groups may achieve different velocities in the channel, improving the selective separation along the fluid path.

Figure 18(c) illustrates the trap-and-release procedure. Using first positive dielectrophoresis, two kinds of particles move towards regions of strong electric. According to their dielectrophoretic mobility in nonuniform electric field, they are trapped to different positions. Then, the voltage is switched off; particles are released and picked up by the flow stream. Release of the particles can also be accomplished by changing the A.C. frequency to a value which induces negative dielectrophoresis, bringing out further the separation. The degree of fractionation is gradually enhanced by repetition of the procedure.

As the dielectrophoresis affects particles at a small distance from the electrodes, those particle separation methods are typically used in microfluidics. Other strategies exploiting DEP force are carried out to manipulate particles in liquids by levitation, translation or orientation, and/or to discriminate them (Khoshmanesh et al., 2011; Pethig and Markx, 1997). In this chapter, the investigation subject is restricted to particle separation systems.

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Fluorinated Polyimides

Anindita Ghosh , ... Susanta Banerjee , in Handbook of Specialty Fluorinated Polymers, 2015

3.3.2.2 Mass Transport in Pervaporation Membranes

Proper understanding of the membrane separation mechanism may provide direct information about research and development for an appropriate membrane. Because of complicated penetrant membrane interactions, it is difficult to formulate a single explanation for the complex transport process. There are three principal approaches to describing mass transport in pervaporation:

1.

Solution–diffusion model

2.

Pore flow model

3.

Carrier transport model

1.

Solution–diffusion model: In the solution–diffusion model, permeates dissolve in the membrane material and then diffuse through the membrane down a concentration gradient. Separation is achieved between different permeates because of differences in the amount of material that dissolves in the membrane and the rate at which the material diffuses through the membrane. The solution–diffusion model is the most widely accepted transport mechanism for many membrane processes [209,210]. Selectivity and permeability of a pervaporation membrane mainly depend on the first two steps, that is, the solubility and diffusivity of the components in the membrane. According to this model, mass transport can be divided into the three steps; the mechanism is shown in Fig. 3.11:

a.

Sorption of liquids into the membrane at the feed side

b.

Diffusion of the sorbed components through the membrane

c.

Desorption–evaporation of the sorbed components at the permeate side

Figure 3.11. Schematic of pervaporation transport mechanism (solution–diffusion model).

2.

Pore-flow model: In pore-flow model, permeates are separated by pressure-driven convective flow through tiny pores. Separation is achieved between different permeates because one of the permeates is excluded (filtered) from some of the pores in the membrane through which other permeates move. This model was first proposed by Matsuura et al. [193,211]. In this model, mass transport involves

a.

liquid transport from the pore inlet to the liquid–vapor phase boundary,

b.

evaporation at the phase boundary, and

c.

vapor transport from the phase boundary to the pore outlet.

The main difference between the solution–diffusion model and the pore-flow model is the location of phase change in the membrane. In the pore-flow model, as shown in Fig. 3.12, the phase change occurs at a certain distance from the membrane surface in contact with the liquid feed, and accordingly the transport mechanism changes from liquid permeation to vapor permeation at the liquid–vapor boundary [193].

Figure 3.12. Schematic representation of pore-flow model.

3.

Carrier transport model: The basic idea of the carrier transport mechanism for pervaporation comes from biological membranes consisting of polypeptides, and is based on the similarity of molecular interactions between the peptides and the functional groups in synthetic polymers [212]. Membranes with carriers are classified into two categories: fixed carrier membranes and non-fixed carrier membranes [213].

Figure 3.13 represents mass transport in both fixed carrier membranes and non-fixed carrier membranes. Transport energy in the fixed carrier membranes is much higher than that in non-fixed carrier membranes because adsorption and desorption are repeated continuously when a permeating component forms a complex with a carrier in the membrane. Alternatively, once a component forms a complex with a carrier in a non-fixed carrier membrane, the other component can move only after one carrier is released from the former complex formed previously, for which high selectivity is achieved.

Figure 3.13. Schematic representation of a carrier transport model.

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Attenuation of contaminants of emerging concerns by nanofiltration membrane: rejection mechanism and application in water reuse

Minkyu Park , Shane A. Snyder , in Contaminants of Emerging Concern in Water and Wastewater, 2020

5.3 Recalcitrant contaminants of emerging concern by nanofiltration and treatment technology for such compounds

In the preceding sections, multiple separation mechanisms influence the extent of CEC rejection. With a given membrane, the charge interactions such as Donnan exclusion and dielectric exclusion and the hydrophobic interaction are membrane–compound interactions while the steric (size) exclusion is attributed to the geometry of molecules. In general, the smaller number of separation mechanisms is applied, the more recalcitrant compounds for rejection. For instance, small molecules with no charge interactions and hydrophobic interactions with membranes are recalcitrant. In other words, small molecules that are neutral in charge and hydrophilic would go through NF membranes easily. An example of a recalcitrant compound is NDMA, which is a potent carcinogen. NDMA is a type of DBP and can be formed by chlorination, chloramination, and ozonation of wastewater containing its precursors. ^58,59 NDMA has MW of 74.1   g   mol⁻¹ and is neutral in charge at a neural pH range. In addition, the presence of polar function group renders NDMA hydrophilic (Log K _ow is −0.57). ⁵⁹ Therefore, it is recalcitrant for the rejection by NF membranes. Another CEC with poor rejection rate can be 1,4-dioxane (synthetic industrial chemical). These compounds can be posttreated using UV-AOP, which is an efficient oxidative process for many classes of organic CECs. For instance, the fluence-based rate constant for monochromatic UV light (254   nm) is 2.29   ×   10⁻³ cm²mJ⁻¹, which indicates that NDMA is photolabile. ⁶⁰ The addition of H₂O₂ does not noticeably increase NDMA removal because of its high photolability. Therefore, the employment of UV or UV-AOP can complement the poor rejection of uncharged hydrophilic small molecules.

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Source: https://www.sciencedirect.com/topics/engineering/separation-mechanism

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