Why Are Cell Membranes Asymmetrical

Carbon-based membranes for membrane reactors

K. Briceño , ... K. Haraya , in Handbook of Membrane Reactors: Fundamental Materials Science, Blueprint and Optimisation, 2013

10.9.i Abbreviations

AAM	α-alumina asymmetric membrane
ASCM	adsorption selective carbon membranes
CAM	coated alumina membrane
C-MEMS	carbon microelectromechanical systems
CMR	carbon membrane reactor
CMS	carbon molecular sieves
CVD	chemical vapor deposition
FAME	fat acid methyl esters
FBR	stock-still dewdrop reactor
HAMR	hybrid adsorbent-membrane reactor
MIMIC	micro molding in capillaries
MR	membrane reactor
CMSM	carbon molecular sieves membranes
LDH	layered double hydroxides
PA	polyamic acrid
PEMFC	proton commutation membrane fuel cells
PSA	pressure swing adsorption
Pd	palladium
PDMS	polydimethylsiloxane
PFR	plug flow reactor
PTFE	polytetrafluoroethylene
SRM	steam reforming of methanol
XRD	X-ray diffraction
μTM	micro transfer molding

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Polymers for Advanced Functional Materials

L.M. Robeson , in Polymer Scientific discipline: A Comprehensive Reference, 2012

8.13.3.2.i Asymmetric membranes

Asymmetric membranes comprising a thin dumbo layer (in the range of 100  nm) are commonly employed for gas separation applications. These membranes are produced past extrusion (hollow cobweb or flat sheet) of a dope solution of polymer–solvent mixtures through an air gap (to allow for a sparse dense layer) into a coagulation bath (usually water). The polymer concentration is usually in the range of 30–35   wt.%, with solvent and other additives (such as pore formers) comprising the rest of the solution. In order to foreclose void formation and achieve optimum membrane morphology, the polymer dope solution should exist very close to the point of phase separation. This can be accomplished with the addition of a nonsolvent to approach the phase purlieus. Polysulfone is one the principal polymers employed for these membranes, with Northward-methyl pyrrolidone (NMP) being a desired solvent. Other polymers typically used for gas separation asymmetric membranes include polyimides and cellulose acetate. Cellulose acetate was an early selection for disproportionate membranes in opposite osmosis applications. ³²

Although the stage inversion process can produce very thin dense layers on a porous support membrane, the ability to produce defect-free membranes is not an inherent characteristic of the process. The resolution of this problem involves surface defect repair methods. The nigh common method involves applying a thin layer of a very permeable blanket (although generally offer poor permselectivity). Silicone condom coatings are a typical case. The defects (pinholes) can drastically reduce the separation gene of the gas mixture due to hydrodynamic flow, but applying a highly permeable coating tin eliminate the pinholes without altering the overall permeability of the membrane, thus allowing the polymer's intrinsic separation and permeability values to be achieved. This concept was demonstrated past Henis and Tripodi and predicted to be the result from serial-resistance model calculations. ^33–35

The process for making an asymmetric hollow fiber is illustrated in Figure 6 . The hollow fiber spinneret has two annular feed sections. The outer feed department delivers the polymer solution, and the inner feed department delivers a bore fluid – usually, air or an inert gas. H2o can also be employed to control the bore-side pare layer. An air gap is provided between the go out of the spinneret and the coagulation bath to control the dense layer thickness on the hollow fiber surface. The coagulation bath is commonly h2o, but tin can be whatever appropriate coagulation liquid medium. Water is preferred, equally it is nonflammable, depression cost, and environmentally benign. The fiber can be wound on spools and immersed in a water bath to remove rest solvent or tin be immune to air current back and forth in a water reservoir, a process referred to in the membrane field every bit 'piddling'.

Figure half-dozen. Illustration of asymmetric hollow cobweb spinning procedure.

The 2 virtually mutual separation modules for the gas and liquid separation processes are the hollow fiber and screw wound constructions shown in Figure seven . The hollow fiber module consists of hollow fibers placed in a cylindrical pressure chamber and encapsulated in a thermosetting polymer (east.thou., epoxy) at both ends. The feed stream is commonly on the vanquish side of the module, and the permeate stream is collected from the open ends of the hollow fibers. Optionally, the feed stream can be delivered to the bore of the hollow fibers with the permeate stream on the trounce side. The spiral wound module comprises repeating layers of a spiral wound sheets construction which contains alternating layers of the membrane, feed stream spacer, membrane, and permeate stream spacer. Proper sealing of the spiral wound layer construction allows for separation of the feed stream from the permeate stream and menstruum of the permeate stream to the permeate stream outlet.

Figure 7. Illustration of (a) hollow fiber and (b) spiral wound modules.

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Gas Sweetening1,2

Maurice Stewart , Ken Arnold , in Gas Sweetening and Processing Field Manual, 2011

Composite Membrane Structure

Disadvantages of the disproportionate membrane construction

Equanimous of a single polymer

Expensive to make out of exotic, highly customized polymers and

Produced in small quantities.

Drawback overcome by producing a composite membrane

Consists of a sparse selective layer made of one polymer mounted on an asymmetric membrane, which is made of another polymer

Composite structure allows manufacturers to use

Readily available materials for the asymmetric portion of the membrane and

Peculiarly developed polymers, which are highly optimized for the required separation, for the selective layer

Figure ane-12 is an case of a composite membrane construction.

Figure 1-12. Composite membrane structure.

Blended structures are being used in most newer advanced CO₂ removal membranes because the proprieties of the selective layer can be adapted readily without increasing membrane price significantly.

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Gas Sweetening

Maurice I. StewartJr. PhD, PE , in Surface Production Operations (Tertiary Edition), Volume 2, 2014

ix.ix.1.five Composite Membrane Structure

The disadvantages of the asymmetric membrane structure are they are composed of a unmarried polymer; they are expensive to make out of exotic, highly customized polymers; and they are produced in small-scale quantities. These drawbacks are overcome by producing a composite membrane. The composite membrane consists of a thin selective layer fabricated of 1 polymer mounted on an disproportionate membrane, which is made of another polymer.

The blended structure allows manufacturers to use readily available materials for the asymmetric portion of the membrane and specially developed polymers, which are highly optimized for the required separation and the selective layer. Figure ix.12 is an example of a composite membrane structure.

Figure nine.12. Composite membrane structure.

Composite structures are being used in well-nigh newer advanced CO_ii removal membranes because the proprieties of the selective layer tin exist adjusted readily without significantly increasing membrane cost.

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CO2-Selective Membranes

Zhi Wang , ... Vocal Zhao , in Electric current Trends and Future Developments on (Bio-) Membranes, 2018

2.one Fabrication Applied science of Disproportionate Membranes

Integral disproportionate membranes and composite membrane are the two master forms of asymmetric membranes. In integral disproportionate membranes, the same membrane materials non just serve as porous support providing mechanical strength merely also offer a dense surface layer performing separation. This limits the number of integral disproportionate membrane materials, and the separation properties are often compromised to make membranes with sufficient mechanical strength. As for composite membranes, the support and separation layers are fabricated of unlike materials and each tin can be optimized independently ( Baker and Lokhandwala, 2008).

2.1.1 Integral Asymmetric Membrane

The development of integral disproportionate membranes by Loeb and Sourirajan in the 1960s is a disquisitional breakthrough in membrane technology ( Strathmann, 1986). Integral asymmetric membranes consist of a thin skin layer and a porous support layer, which are the primeval commercialized membranes used in industrial gas separation. The training methods of integral asymmetric membranes can exist divided into ii kinds: nonsolvent-induced phase separation (NIPs) and thermally induced stage separation (TIPs). A comparison between the NIPs and TIPs is shown in Table 3.1.

Table 3.1. Comparison Between thermally induced phase separation (TIPs) and nonsolvent-induced phase separation (NIPs) Methods

Methods	Advantages	Disadvantages
NIPs	• Low need for equipment • Low energy consumption	• Big amount of solvent requirement • Poisoning the surroundings • Low porosity
TIPs	• Uniform membrane construction • Wide applicability for various material • Piece of cake to command • Superior mechanical strength	• High energy consumption

2.1.2 Blended Membrane

A tendency that has emerged in CO₂ separation membranes is a shift from integral asymmetric membranes to composite membranes, in which a highly porous back up was used to provide the required mechanical strength, and a thin layer of permselective material (typically 0.1–i.0  μm thickness) is deposited onto the support to perform the separation (Wong et al., 2016). In addition, a high-permeability gutter layer tin can be employed to prevent pore penetration.

Now, the main techniques for composite membrane preparation include coating, interfacial polymerization, coextrusion, etc. Blanket is a simple but very practical method to prepare a thin and dense selective layer. As for interfacial polymerization, two monomers or polymers with dissimilar reactive groups are dissolved in two immiscible solvents. And then an ultrathin selective layer forms at the interface betwixt the two solutions after contacting each other. Coextrusion is a common method to fabricate dual-layer hollow fiber composite membrane. This blazon of method could employ ii or more extruders to deliver different polymers to a single extrusion caput (die), which will extrude the materials in the desired form (Ullah Khan et al., 2018).

In summary, interfacial polymerization is the most common method to fabricate reverse osmosis membrane. However, information technology is restricted to laboratory-scale fabrication for CO_ii separation membrane. By using the coextrusion method, multilayer composite membranes can be obtained through one pace, which shows a college efficiency than other methods. Nonetheless, high-performance CO₂ separation materials that fit this method are very few (Suzuki et al., 1998). At nowadays, the method of blanket has been widely practical in laboratory-scale and pilot-calibration fabrication of CO_ii separation membrane (Dai et al., 2016).

Autonomously from the methods mentioned above, there are some other methods for composite membrane fabrication, such equally plasma polymerization, spray blanket, brush coating, layer-by-layer deposition, and ultrasonic deposition (Mulder, 1998). Nonetheless, CO₂ separation membrane fabricated with these methods is seldom reported, and hence these methods not discussed in this chapter.

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Molecular Diffusion

Endre Nagy , in Basic Equations of Mass Transport Through a Membrane Layer (2d Edition), 2019

4.5.1.2.1.2 Ii-Layer Composite Membrane

Considering the frequency of the asymmetric membrane or two-layer composite membrane, the time lag is given here for the solute transport through the ii-layer composite membrane. The fourth dimension lag for this organisation is published by Ash et al. (1965). Two-layer transport is illustrated in Fig. 4.v.

Figure 4.v. Schematic drawing of the two-layer blended membrane and nomenclature.

Assuming that Fick's 2nd constabulary is valid for both layers (subscripted past 1 and 2), so that:

(4.60) $\frac{\mathrm{\partial }{\mathrm{\varphi }}_1(y,t)}{\mathrm{\partial }t}=D_1\frac{{\mathrm{\partial }}^2{\mathrm{\varphi }}_1(y,t)}{\mathrm{\partial }{y}^2}0\le <y\le {\mathrm{\delta }}_1$

and:

(4.61) $\frac{\mathrm{\partial }{\mathrm{\varphi }}_2(y,t)}{\mathrm{\partial }t}=D_2\frac{{\mathrm{\partial }}^2{\mathrm{\varphi }}_2(y,t)}{\mathrm{\partial }{y}^{\mathrm{ii}}}{\mathrm{\delta }}_{\mathrm{ane}}\le y\le \mathrm{\delta }\text{.}$

Initial conditions are:

(iv.62a) $\begin{array}{ccccc}\text{at}& 0\le y\le \mathrm{\delta }\text{and}& t>0& \text{then}& {\mathrm{\varphi }}_1\left(y,0\right)={\mathrm{\varphi }}_{\mathrm{ii}}\left(y,0\right)=0\end{array}\text{.}$

The corresponding boundary weather are:

(4.62b) $\begin{array}{cccc}t>0,& y=0& \text{then}& {\mathrm{\varphi }}_{\mathrm{i}}\left(0,t\right)={\mathrm{\varphi }}_1^{\mathrm{\ast }}\end{array}$

and:

(4.62c) $D_1{\frac{d{\mathrm{\varphi }}_{\mathrm{i}}}{dy}|}_{y={\mathrm{\delta }}_{\mathrm{i}}^{-}}=D_2{\frac{d{\mathrm{\varphi }}_2}{dy}|}_{y={\mathrm{\delta }}_1^{+}}$

It is too assumed that the concentrations are in equilibrium at the interface, thus:

(4.62d) $\begin{array}{ccccc}\text{at}& t>0,& y={\mathrm{\delta }}_1& \text{then}& {\mathrm{\varphi }}_{\mathrm{i}}=H{\mathrm{\varphi }}_{\mathrm{two}}\end{array}$

and:

(4.62e) $\begin{array}{cccc}t>0,& y=\mathrm{\delta }& \text{and then}& {\mathrm{\varphi }}_{\mathrm{ii}}\left(\mathrm{\delta },t\right)=0\end{array}$

The lag time of this system, co-ordinate to Ash et al. (1965) and Zhang and Kocherginsky (2003), is:

(four.63) $\mathrm{\theta }=\frac{\mathrm{ane}}{\mathrm{half-dozen}}\left[\frac{{\mathrm{\delta }}_1^2}{D_{\mathrm{i}}}\left(\frac{{\mathrm{\delta }}_1}{D_1}+\frac{3H{\mathrm{\delta }}_2}{D_1}\right)+\frac{{\mathrm{\delta }}_{\mathrm{ii}}^2}{D\mathrm{ii}}\left(\frac{3{\mathrm{\delta }}_{\mathrm{ane}}}{D_1}+\frac{H{\mathrm{\delta }}_2}{D_1}\right)\right]\frac{J_{st}}{{\mathrm{\varphi }}^{\mathrm{\ast }}}$

where the J _st steady-state flux is:

(4.64) $J_{\mathrm{due\; south}t}=\frac{{\mathrm{\varphi }}^{\mathrm{\ast }}}{m_{ov}}$

with:

(4.65) $\frac{1}{k_{ov}}=\frac{{\mathrm{\delta }}_1}{D_{\mathrm{ane}}}+\frac{H{\mathrm{\delta }}_2}{D_{\mathrm{two}}}$

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Challenges of Membrane Engineering science in the XXI Century

H.S. Muralidhara , in Membrane Technology, 2010

2.1 History Overview

Membrane technology has a relatively curt but intense history. Asymmetric membranes (the foundation of most of today'south commercially bachelor ones) were first synthesized in 1960s. At that time, membranes were not considered good for any awarding. Later on in the 1970s and 1980s membrane engineering science blossomed and many thought they were going to solve all separation and even reaction issues ( Table 2.1).

Table two.1. Early Version of the Membrane Filtration Spectrum [i]

Exhibit A Spectrum Membrane Processes
Process	Concept	Textile Passed		Retained Material
		Type	Force	State	Type	Size
Membrane filtration		Water	Modest pressure level (x   PSI)	Suspended colloidal		>100   Å
Ultra filtration		Water	Pressue (10–600   PSI)	Collodial dissolved	Organics	>10   Å
Contrary osmosis		Water	Force per unit area (600–1500   PSI)	Dissolved	Principally inorganic	>1   Å
Electrodialysis		Ions	Voltage
Dialysis		Ions low MW organics	Concentration

During the first years the main problems to be dealt with were the product of usable membranes, the development of reasonable equipment in which the membranes could be used, and the resolving of all the practical difficulties connected with liquid pumping, cooling, high pressure tubing, gaskets, instrumentation, etc., which are as important equally the more than theoretical aspects of the process [2] .

Today, membrane engineering has a unique place in many industrial and water management applications. Some of those are well settled (i.eastward., preconcentration steps and protein fractionation in the dairy industry, municipal waste water treatment by membrane bioreactors, etc.), while others are emerging (i.e., industrial waste product water membrane bioreactors). Nevertheless, in the past 20 years, some membrane applications have not left the "promising engineering science" group (east.grand., pervaporation for aroma recovery or some enzymatic membrane reactors in a number of total-scale applications), either because of the inherent membrane limitations (low flux or selectivity) or because material or arrangement engineering drawbacks have not yet been overcome. The membrane lifetime picture has remained quite stable in the by decade, as shown in Effigy 2.1.

Figure 2.i. Membrane processes sales and life time

(adapted from Strathmann, 2001 [3]).

From a global perspective of the industrial-scale processes, membranes have succeeded in existence alternate technologies to conventional separation techniques, allowing more meaty systems (with the added advantages of a modular design) and separations, which have challenged the way process engineers think and blueprint a process. Membranes can be fitted in at various places in a production facility, and they can fifty-fifty been synergistically combined with other separation or reaction processes leading to hybrid technologies. This is 1 of the powerful features of this technology.

Membranes are currently considered among the best available technologies (BAT) in many process and waste product management applications. Even so, for some of the latter they are still more expensive than the less environmentally friendly, simply withal regulation-compliant, alternatives.

Out of the 100 quads (1 quad = 10¹⁵ BTU/yr) of energy consumed in the United states of america, the food processing industry approximately uses 2 quads. At $8/million BTU, this amounts to 8 billion dollars a year. One-half of the energy consumed in the food processing industry is toward concentration and drying. For example, corn wet milling uses 93.7 trillion BTU/year, grain milling 153.three trillion BTU/yr, and vegetable oil processing two.0 trillion BTU/year. As an example, drying and evaporation steps are used in corn milling for concentrating the steep water and farther drying it, and also to reach dryness of the germ, gluten, starch, and to concentrate dextrose solution products (Fig. 2.two). If the drying costs tin can be reduced for large-scale processing in developing countries, information technology could be an enormous reward. This is so because of the wide relation between wealth and energy consumption, as depicted in Figure 2.iii.

Figure 2.2. Drying and evaporation in corn milling.

Figure 2.3. The relationship betwixt energy consumption and Gdp (as of 2006). Countries with the lower values are in the poverty surface area.

Data source: IEA (2008) [four].

Moreover, food processing consumes large volumes of water. Therefore, the ability of membranes to produce high h2o quality streams, which tin can exist recycled, is likewise highly relevant for this industrial sector. Still, advisable agency approval such as USDA is required prior to industrial exercise.

Efficient separations are, thus, needed not but to brand industrial processes more economic, just also to accomplish the high purity and high selectivity requirements in the food processing and biotech industries. The toll of recovery or separation of a product from its raw cloth depends upon the efficiency of the separation processes involved, and they increase essentially with dilution (Fig. 2.four). In such cases, processing costs tin merely be controlled using highly efficient downstream separation/purification processes. This is especially relevant for new products (for which new processes accept to exist designed), owing to their contribution to the overall economics of the process.

Effigy 2.four. The selling price of a product is a stiff function of product concentration and, consequently, cost of separation and/or purification. Reactor cost is typically under 25% of total production cost. Three distinct categories are evident [5].

In such a scenario, membranes detect several applications in nutrient processing, owing to the different tasks they are able to perform (Tabular array 2.2).

Table 2.two. Typical Examples of Membrane Applications in Food Processing

Application	Production	Membrane Process	Industry
Cold sterilization	Beer, vino, milk	MF	Dairy, beverage
Clarification	Wine, beer, fruit juice, syrups	MF/UF	Beverage, corn milling
Drying/thicken	Whey	UF/RO	Potato, dairy
Desalting	H2o, cheese	RO/ED	Dairy, beverage
Concentration	Fruit juice, saccharide	RO	Drinkable, sugar refining
Dealcoholization	Wine	PV	Beverage
Fractionation	Egg	UF	Poultry
Product recovery	Lactic acrid, citric acid	UF/ED	Biotech

(Sources: Cuperus and Nijhuis [6]; Muralidhara [7,8])

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Membrane Bioreactor

Endre Nagy , in Basic Equations of Mass Transport Through a Membrane Layer (Second Edition), 2019

14.4.1.i Component Send Across an Asymmetric Membrane With a Single Biocatalytic Membrane Layer

The enzyme is immobilized in the spongy layer of the asymmetric membrane ( Fig. 14.eight). The substrate enters the spongy layer of the biocatalytic membrane and is transported beyond the disproportionate membrane. The skin layer is nonreactive, thus it can cause mass transport resistance of the transported components (substrate, product) only. For prediction of the inlet mass transfer rate, the resistance of both membrane layers should be taken into business relationship. The unreacted substrate can permeate into the sweeping fluid phase (if it exists) flowing in the permeate side. All assumptions given in Section 14.4 are true except the following:

Figure fourteen.8. Schematic illustration of an asymmetric enzyme membrane layers' concentration distribution without a sweeping stage (A) and with a sweeping stage (B) on the permeate side; the substrate feed solution is facing the biocatalytic support layer (Eastward, enzyme).

•

The external mass transfer resistances are negligible.

•

The transport parameters (υ, D, D _s ) are abiding.

•

The curvature, cylindrical upshot is neglected.

In this section four cases of transport are discussed. The substrate solution can enter the biocatalytic support layer and also the nonreactive peel layer. Information technology is easy to recognize that this latest feeding style is probably not advantageous, considering this layer can reduce the substrate concentration entering the biocatalytic support layer and the reaction charge per unit equally well (nada-order reaction has other behavior, considering its rate is independent of the concentration). Permit us express the mass transfer rates into the membrane layer in the case of beginning- and zip-lodge reactions every bit a limiting example of Michaelis–Menten kinetics. The inlet and outlet mass transfer rates are for four transport cases, namely first-order reaction feeding the substrate solution at the support layer without a sweeping phase and applying a sweeping stage on the permeate side (cases A and B). The same is given for zero-order reaction (cases C and D). Section 14.iv.ane.2 discusses the other four cases, namely when the substrate is feeding on the skin side of the disproportionate, biocatalytic membrane layer.

ane.

Without a sweeping phase, first-gild reaction. The differential mass balance equation is:

(xiv.59a) $\frac{d^2\mathrm{\varphi }}{dy}-Pe\frac{d\mathrm{\varphi }}{dy}-{\mathrm{\vartheta }}^2\mathrm{\varphi }=0$

with:

$Pe=\frac{\mathrm{\upsilon \delta }}{D}=\frac{\mathrm{\upsilon }}{k^o};\mathrm{\vartheta }=\sqrt{\frac{k_1{\mathrm{\delta }}^{\mathrm{two}}}{D}}\text{.}$

The inlet and outlet mass transfer rates were discussed in item in Affiliate 6 in the case of diffusive mass transport for aeroplane sheet membrane and in Chapter 8 in the case of send by diffusion plus convection. The inlet mass transfer rate is divers as (see Eq. 8.56):

(fourteen.60) $J=\mathrm{\beta }{\mathrm{\varphi }}^{\ast }$

with:

(14.61) $\mathrm{\beta }={\mathrm{grand}}^o\frac{\left(\frac{P{\mathrm{east}}^2}{\mathrm{four}}+{\Theta }^{\mathrm{two}}\right)\tanh \Theta +Pe\Theta }{\frac{Pe}{2}\tanh \Theta +\Theta }$

with:

(14.62) $\Theta =\sqrt{\frac{P{e}^2}{4}+{\mathrm{\vartheta }}^2}\text{.}$

Without a sweeping phase there is no diffusive transport in the thin, skin layer, thus concentration gradient is also zero in this layer every bit information technology is plotted in Fig. fourteen.8A.

2.

Without a sweeping phase, zero-order reaction. The differential mass balance equation for this case is:

(fourteen.63) $\frac{d^{\mathrm{two}}\Phi }{d{Y}^2}-Pe\frac{d\Phi }{dY}={\mathrm{\vartheta }}^2$

where ϑ is the dimensionless reaction modulus:

(14.64) $\mathrm{\vartheta }=\sqrt{\frac{{\mathrm{chiliad}}_0{\mathrm{\delta }}^{\mathrm{ii}}}{D{\mathrm{\varphi }}^{\ast }}}\text{.}$

The inlet mass transfer rate can be given in the classical course as (see Eqs. 8.160a and Eq. viii.160b 8.160a 8.160b ):

(14.65) $J=\mathrm{\beta }{\mathrm{\varphi }}^{\ast }$

with:

(xiv.66) $\mathrm{\beta }=k^o\left(\frac{{\mathrm{\vartheta }}^2}{Pe}\left[1-e^{-Pe}\right]+Pe\right)\text{.}$

3.

With a sweeping phase, starting time-society reaction. The significant difference in component send across the pare layer is that there is likewise diffusive ship beyond information technology. Accordingly, the result of mass transport across the skin layer should also be taken into account. Generally, at that place is not also much data on the pore construction in the skin layer. In the case of its strictly nonporous construction, convective flow inside this dense layer cannot take identify. In the case of a biocatalytic membrane reactor the skin layer should stop the macromolecular biocatalyst from leaving the membrane reactor. Accordingly, the active layer can as well accept small pores, which have relatively small resistance against the component transport, but they retain the catalyst particles. Thus component transport is considered here as transport through a porous membrane layer with diffusive plus convective fluxes. This will involve diffusive component send through a nonporous membrane layer as the limiting case, namely with Pe _south   =   0 (subscript southward denotes the peel layer). Accordingly, the mass transfer rates have to be taken into business relationship for the description of the mass transfer charge per unit in this system and are (the original expressions for the mass transfer rates are Eqs. 8.80, 8.110, and 8.111, respectively):

(fourteen.67) $J=\mathrm{\beta }\left({\mathrm{\varphi }}^{\ast }-\mathrm{\alpha }{\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }\right)$

(14.68) $J_{\mathrm{\delta }}={\mathrm{\beta }}_{\mathrm{\delta }}\left({\mathrm{\varphi }}^{\ast }-{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }\right)$

(fourteen.69) $J^o={\mathrm{\beta }}_s^o\left({\mathrm{\varphi }}_{\mathrm{southward}}^{\ast }-e^{-P{e}_{\mathrm{due\; south}}}{\mathrm{\varphi }}_{\mathrm{south},\mathrm{\delta }}^{\ast }\right)$

with:

$\mathrm{\beta }=\frac{k^o\left(\frac{Pe}{2}\tanh \Theta +\Theta \right)}{\tanh \Theta };\mathrm{\alpha }=\frac{\Theta {\mathrm{eastward}}^{-Pe/2}}{\left(\frac{Pe}{2}\right)\sinh \Theta +\Theta \cosh \Theta };$

${\mathrm{\beta }}_{\mathrm{\delta }}=\frac{D}{\mathrm{\delta }}\frac{\Theta e^{Pe/2}}{\sinh \Theta };{\mathrm{\alpha }}_{\mathrm{\delta }}=\frac{\Theta \cosh \Theta -\frac{Pe}{\mathrm{ii}}\sinh \Theta }{\Theta e^{Pe/2}};{\mathrm{\beta }}_s^o=k_s^o\frac{P{e}_{\mathrm{due\; south}}}{1-e^{-P{e}_s}};$

and:

$P{\mathrm{east}}_s=\frac{\mathrm{\upsilon }}{k_{\mathrm{due\; south}}^o};k_s^o=\frac{D_s}{{\mathrm{\delta }}_s};k^o=\frac{D}{\mathrm{\delta }}\text{.}$

It is seen that this situation is a circuitous transport process with many expressions. This is because the biochemical reactions of the inlet and outlet transfer rates are different (thus, e.g., the value of the J inlet mass transfer rate is not equal to the mass transfer rate of J _ov entering the skin layer). Thus the obtained overall mass transfer rate volition be (run into Department 8.three.iv.2):

(14.70) $J_{ov}=\mathrm{\beta }\left({\mathrm{\varphi }}^{\ast }-\mathrm{\Psi }\right)$

with (for ψ see Eq. eight.114):

(14.71) $\mathrm{\Psi }=\frac{{\mathrm{\beta }}_{\mathrm{\delta }}{\mathrm{\varphi }}^{\ast }+{\mathrm{\beta }}_{\mathrm{southward}}^o{e}^{-P{e}_{\mathrm{south}}}{\mathrm{\varphi }}_{s,\mathrm{\delta }}^{\ast }}{{\mathrm{\beta }}_{\mathrm{due\; south}}^o{H}_s+{\mathrm{\beta }}_{\mathrm{\delta }}{\mathrm{\alpha }}_{\mathrm{\delta }}}\text{.}$

It tin likewise be written in the conventional form of the mass transfer rate as $\left({\mathrm{\varphi }}_{\mathrm{south}}^{\text{∗}}=H_s{\mathrm{\varphi }}_{\mathrm{\delta }}^{\mathrm{\ast }}\right)$ :

(14.70a) $J_{ov}={\mathrm{\beta }}_{ov}\left({\mathrm{\varphi }}^{\ast }-\Psi {\mathrm{\varphi }}_{\mathrm{south},\mathrm{\delta }}^{\ast }\right)$

with:

(14.70b) ${\mathrm{\beta }}_{ov}=\mathrm{\beta }\frac{{\mathrm{\beta }}_{\mathrm{\delta }}\left({\mathrm{\alpha }}_{\mathrm{\delta }}-\mathrm{\alpha }\right)+{\mathrm{\beta }}_s^o/H_s}{{\mathrm{\beta }}_s^o{H}_s+{\mathrm{\beta }}_{\mathrm{\delta }}{\mathrm{\alpha }}_{\mathrm{\delta }}}$

and:

(14.70c) $\Psi =\frac{\mathrm{\alpha }{\mathrm{\beta }}_s{e}^{-P{\mathrm{due\; east}}_{\mathrm{due\; south}}}}{{\mathrm{\beta }}_s^o{H}_{\mathrm{south}}+{\mathrm{\beta }}_{\mathrm{\delta }}\left({\mathrm{\alpha }}_{\mathrm{\delta }}-\mathrm{\alpha }\right)}\text{.}$

iv.

With a sweeping phase, naught-lodge reaction. The adult and discussed mass transfer rates are given past Eqs. (8.167a), (8.167b), (eight.171a) and (8.171b). Thus they are:

(14.72) $J=\mathrm{\beta }\left({\mathrm{\varphi }}^{\ast }-\mathrm{\alpha }{\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }\right)$

(fourteen.72a) $\mathrm{\alpha }=\frac{P{e}^2}{{\mathrm{\vartheta }}^{\mathrm{two}}-P{e}^2{e}^{P\mathrm{eastward}}}$

(xiv.73) $J_{\mathrm{\delta }}={\mathrm{\beta }}_{\mathrm{\delta }}\left({\mathrm{\varphi }}^{\ast }-{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }\right)$

and:

(14.74) $J^o={\mathrm{\beta }}_s^o\left({\mathrm{\varphi }}_{\mathrm{south}}^{\ast }-e^{-P{\mathrm{eastward}}_s}{\mathrm{\varphi }}_{\mathrm{south},\mathrm{\delta }}^{\ast }\right)$

where:

(14.74a) $\mathrm{\beta }=k^o\left(\frac{{\mathrm{\vartheta }}^{\mathrm{two}}}{Pe}+\frac{{\mathrm{\vartheta }}^2-Pe{e}^{P\mathrm{due\; east}}}{\mathrm{i}-e^{Pe}}\right)$

(14.74b) ${\mathrm{\beta }}_{\mathrm{\delta }}=\frac{D}{\mathrm{\delta }}\left\{\left(\frac{{\mathrm{\vartheta }}^2}{Pe}\left[1-Pe\right]+\frac{{\mathrm{\vartheta }}^2-Pe{\mathrm{due\; east}}^{P\mathrm{eastward}}}{1-e^{Pe}}\right)\right\}$

and:

(fourteen.74c) ${\mathrm{\alpha }}_{\mathrm{\delta }}=\frac{Pe}{{\mathrm{\beta }}_{\mathrm{\delta }}\mathrm{\delta }\left({\mathrm{eastward}}^{Pe}-1\right)}\text{.}$

Using the equality of Eqs. (14.73) and (14.74), we tin express the value of ${\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }$ , which so involves the effect of the mass transfer resistance of the skin layer on component transport. Appropriately:

(14.75) ${\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }=\frac{{\mathrm{\varphi }}^{\ast }{\mathrm{\beta }}_{\mathrm{\delta }}+{\mathrm{\beta }}_{\mathrm{south}}^o{e}^{-P{e}_{\mathrm{due\; south}}}{\mathrm{\varphi }}_{\mathrm{due\; south},\mathrm{\delta }}^{\ast }}{{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\beta }}_{\mathrm{\delta }}+{\mathrm{\beta }}_s^o{H}_{\mathrm{south}}}\text{.}$

Replacing the value of ${\mathrm{\varphi }}_{\mathrm{\delta }}^{\ast }$ in Eq. (14.72), we get the mass transfer rate, which involves the effect of the skin layer's transfer resistance. Thus the overall mass transfer charge per unit, J _ov , is:

(14.76) $J_{ov}=\mathrm{\beta }\left({\mathrm{\Psi }}_{\mathrm{one}}{\mathrm{\varphi }}^{\ast }-{\mathrm{\Psi }}_2{\mathrm{\varphi }}_{s,\mathrm{\delta }}^{\ast }\right)$

with:

${\mathrm{\Psi }}_{\mathrm{one}}=1-\frac{\mathrm{\alpha }{\mathrm{\beta }}_{\mathrm{\delta }}}{{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\beta }}_{\mathrm{\delta }}+{\mathrm{\beta }}_s^o{H}_s};{\mathrm{\Psi }}_2=\frac{{\mathrm{\beta }}_{\mathrm{southward},\mathrm{\delta }}^o{e}^{-P{e}_s}}{{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\beta }}_{\mathrm{\delta }}+{\mathrm{\beta }}_{\mathrm{south}}^o{H}_s}\text{.}$

Or by rearranging Eq. (14.76), we get:

(xiv.77) $J_{o\mathrm{five}}={\mathrm{\beta }}_{ov}\left({\mathrm{\varphi }}^{\ast }-\mathrm{\Psi }{\mathrm{\varphi }}_{s,\mathrm{\delta }}^{\ast }\right)$

with:

(14.78) ${\mathrm{\beta }}_{ov}=\mathrm{\beta }\left(1-\frac{\alpha {\mathrm{\beta }}_{\mathrm{\delta }}}{{\mathrm{\alpha }}_{\mathrm{\delta }}{\mathrm{\beta }}_{\mathrm{\delta }}+{\mathrm{\beta }}_s^o{H}_s}\right)$

and:

(xiv.78a) $\Psi =\frac{{\mathrm{\beta }}_{s,\mathrm{\delta }}^o{\mathrm{eastward}}^{-P{\mathrm{due\; east}}_s}}{{\mathrm{\beta }}_{\mathrm{\delta }}\left({\mathrm{\alpha }}_{\mathrm{\delta }}-\mathrm{\alpha }\right)+{\mathrm{\beta }}_{\mathrm{southward}}^o{H}_s}\text{.}$

The mass transfer rates without a sweeping phase are identical to those given for one-layer mass transport. They are given hither by Eqs. (fourteen.60) and (14.65) for outset-order and nix-lodge reactions, respectively. In the absenteeism of a sweeping stage on the permeate side there is no concentration gradient in the pare layer, thus information technology does non affect the transport rate, and the convective flow should ship the component across the skin layer without noticeable resistance. (Information technology is worth noting that if transport cannot take place past convection, so the situation is wholly different; in this case, diffusive flow should ship the component[due south], which generates a big concentration gradient causing huge transport resistance.) For the clarification of mass send in the skin layer, nosotros volition suppose that this layer is also porous, though its pore size can be much less than that of the support layer. The result of the reaction in such a system was discussed in detail in Chapter 8. Thus these cases are non illustrated here. On the other mitt, mass send is a rather complex process in the presence of a sweeping phase, because the outlet mass transfer charge per unit differs from the inlet mass transfer rate, due to the biochemical reaction. Such an investigation is non establish in the literature, which is why these cases are briefly discussed in Fig. 14.9, and subsequently in Fig. 14.11. Fig. xiv.9 illustrates the relative value of the overall mass transfer coefficient ( ${\mathrm{\beta }}_{ov}/{\mathrm{\beta }}_{ov}^o$ ) equally a function of the reaction modulus, ϑ, at four different Peclet values for the case when the substrate solution is feeding on the biocatalytic support layer. Values of the Peast number were chosen to be 0, 1, 2, and 5. The value of the overall mass transfer coefficient without biochemical reaction is as well given for the sake of completeness:

Figure 14.9. The relative value of the overall mass transfer coefficient ( ${\mathrm{\beta }}_{ov}/{\mathrm{\beta }}_{ov}^o$ ) as a function of the reaction modulus predicted at different Pe numbers and applying the sweeping stage on the permeate side, feeding the substrate solution on the support layer. Eqs. (14.70b) and (xiv.78) and first-order (continuous lines) and null-order (broken lines) reactions were applied to predict the overall mass transfer coefficient, which was then related to that without a biochemical reaction (values of parameters used for prediction are: D _south   =   3   ×   x⁻¹⁰  thousandⁱⁱ/s; D  =   three   ×   ten⁻⁹  g^two/s, δ _south   =   1   μm; δ   =   500   μm; thus k _southward   =   vi   ×   10⁻⁶  m/s and k  =   3   ×   10^−four  m/s; H _south   =   ane).

$\frac{1}{{\mathrm{\beta }}_{ov}^o}=\frac{1}{{\mathrm{\beta }}_{\mathrm{southward}}^o}+\frac{H_{\mathrm{due\; south}}}{{\mathrm{\beta }}^o}$

with:

${\mathrm{\beta }}_s^o=g_{\mathrm{south}}^o\frac{P{\mathrm{east}}_s}{1-e^{-P{e}_{\mathrm{south}}}};{\mathrm{\beta }}^o=k^o\frac{Pe}{1-{\mathrm{due\; east}}^{-Pe}}\text{.}$

This figure illustrates well that the overall mass transfer coefficient can increase freely with the increase in the reaction modulus, ϑ. It is obvious that the office of the skin layer is negligible at higher reaction rates, since the substrate tin can react completely inside the biocatalytic back up layer.

On the other manus, the effect of the concentration does not be in the case of a zero-order reaction, thus its consequence on component transport can be more meaning than that of a commencement-gild reaction. Since such loftier values of the reaction modulus do non probably exist during biocatalytic reactions, the relative values of the overall mass transfer coefficients were predicted to be very loftier reaction rates as well.

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Proton exchange membranes for fuel cells

V. Arcella , ... A. Ghielmi , in Advanced Membrane Science and Technology for Sustainable Energy and Environmental Applications, 2011

15.iii.3 Membrane pattern

Although many examples can exist constitute in the technical literature of asymmetric membranes for fuel cells (e.g. multi-layers of different EW or incorporating barrier layers for methanol in the case of DMFC), symmetric membranes are the option widely used in practice for FCs.

One possibility to allocate FC PEMs according to their design is to distinguish 'dense' (or 'unsupported') membranes and 'reinforced' (or 'supported') membranes. Dense membranes are homogenously constituted through their thickness by the ionomer, normally alone, or eventually in intimate mixtures with other polymers doped with scavenging molecules. Reinforced membranes, instead, contain a microporous support, which has the function of stabilizing the membrane mechanically. The support is usually embedded inside the membrane, leaving two peripheral layers of dense ionomer. Dumbo membranes can be isotropic or anisotropic in the plane, according to their production procedure. Typically, membranes obtained past melt extrusion are anisotropic owing to the stretching that occurs in machine direction during the extrusion procedure. This anisotropy is readily detected by, for instance, unlike linear swelling upon soaking in water and different mechanical properties in the 2 directions of the plane. Solvent-bandage membranes are instead typically isotropic in the aeroplane.

Reinforced membranes are typically isotropic or moderately anisotropic in the plane, in relation to the properties of the support material. For instance, when biaxially expanded films are used as reinforcement, differences in the stretching ratio in the two directions will define the level of anisotropic behaviour of the final membrane product.

ePTFE (expanded polytetrafluoroethylene) is the near well known and well studied microporous fabric for reinforcement of FC membranes. It was introduced for the purpose in the 1990s (Verbrugge et al., 1992; Kolde et al., 1995; Bahar et al., 1996). Although not mechanically outstanding, this cloth is considered ideal for a number of its properties: very loftier void volume (> 80%), very fine and regular pore construction divers by sparse fibrils, good compatibility with PFSA ionomers, extremely high chemic inertness and extremely low thickness availability (down to <   10   μm).

Figure 15.13 shows stress–strain curves for dissimilar membrane types. Comparison is made between cast membranes (Nafion® NR), extruded membranes (Aquivion® E87) and an experimental reinforced membrane obtained by impregnating ePTFE with a commercial ionomer dispersion. On 1 hand information technology can be seen that extruded membranes show a college stress than cast membranes later the yield signal and a lower strain at break. This is due to the fact that the measurement was taken in the machine management, that is the direction in which the material is oriented during processing. On the other hand, information technology can exist seen that the reinforced membrane shows both a high modulus and an elevated strain at interruption, that is overall improved mechanical properties. This is due to the interaction of the PFSA ionomer with the fine fibrillated PTFE structure which creates a composite structure in the membrane, that is 2 extensively interacting solid phases.

fifteen.xiii. Stress–strain curves for cast Nafion® membranes (NR111, N112), extruded Aquivion® membranes (E87-03, E87-05) and an experimental ePTFE-based reinforced membrane. Exam conditions: 23   °C, 50% RH.

Other microporous materials are under investigation as reinforcing materials, especially targeting improved mechanical backdrop of the membrane. Examples are porous bi-stretched polyethylene (Mallant et al., 1998) and porous PVDF (Nasef et al., 2006). Higher durabilities tin be obtained by introducing a microporous reinforcement in the membrane. Effigy 15.14 shows the result of a durability examination (OCV hold) for an experimental reinforced membrane produced with EW   =   830   grand/eq Aquivion® compared to a number of other dense Aquivion® membranes obtained by cook extrusion with dissimilar ionomers and thicknesses (the first 2 digits after the 'E' represent the EW and the final two digits the thickness in tens of micrometres, for example E87-05 has an EW of 870   g/eq and a thickness of 50   μm; the last 'South' stands for stabilized ionomer). Despite the fact that the ionomer in this reinforced membrane is not stabilized and that the membrane is in the low thickness range, the outcome of the reinforcement is axiomatic in limiting the disuse nether these test weather. Really, while the ionomer in a dense membrane is at the same time delivering functional and mechanical characteristics, in a supported membrane these are at to the lowest degree partially subdivided between ionomer (functional) and reinforcement (mechanical). Therefore, even if the mechanical characteristics of the ionomer are degraded by chain scission under the chemically aggressive conditions of the test in Fig. 15.fourteen, the reinforcement is still able to confer sufficient mechanical stability to the membrane. However, past virtue of the composite nature of the membrane, if the ionomer is extremely degraded, a reinforced membrane with a highly inert support textile will besides neglect.

15.fourteen. OCV hold durability test for an experimental Aquivion® reinforced membrane (25   μm thickness) compared to Aquivion® extruded (E) membranes with different EWs and thicknesses. Examination weather condition as in Fig. fifteen.12.

Annotation that while extruded membranes are typically not fit to survive under the dry high voltage test weather shown in Fig. 15.14 (failure in few 100   hours), they tin guarantee very high lifetimes under high RH atmospheric condition with current constantly fatigued from the a cell (typical stationary application conditions): a prison cell performance of 20 000   hours has been recently accomplished on an Aquivion® E87-05S membrane with no detectable membrane deposition (Merlo et al., 2010).

While introduction of reinforcement can deliver significant immovability improvements, as shown above, it evidently affects the conductivity of the membrane, owing to the presence of the inert support material. It was also recognized in early on studies that water permeability is reduced (Verbrugge et al., 1992). Proper optimization of the membrane construction (choice of support, impregnation parameters, etc.) can limit these drawbacks. Moreover, the introduction of the support allows lower thicknesses without compromising durability, which helps to compensate for electrical conductivity and water permeability losses. Figure 15.15 shows that better performances (voltage at given current) are achieved with a reinforced membrane (experimental membrane of thickness 25   μm) compared to an extruded 30   μm Aquivion® E79-03S membrane.

xv.15. Polarization curve for an experimental Aquivion® reinforced membrane (25   μm thickness) compared to an Aquivion® extruded E79-03S membrane (30   μm thickness, EW   =   790   grand/eq). Test conditions: H₂ and air, cell temperature   =   75   °C, cell pressure   =   2.5   bar abs, anode inlet RH   =   cathode inlet RH   =   100%, Pt loading anode   =   Pt loading cathode   =   0.5   mg   cm^{−   2}.

In contempo years, the general trend for membranes in H₂/air FC applications, specially for automotive applications, has been to movement to lower thicknesses. Ultra-thin membranes (<   x   μm) have been shown to exist able to preserve the cell voltage under very dry conditions if electrical electric current is drawn from the cell. For instance, Kinoshita and Shimoda (2008) have shown limited voltage losses in H_ii/air operation at 10% inlet RH, 95   °C, 150   kPa and ii   A   cm^{−   2} with v   μm thick membranes. This is related to the efficient ship by the sparse membrane of the water produced at the cathode to go on the whole MEA well hydrated.

Membranes with such low thickness plain pose the trouble of college gas crossover and lower immovability. The latter is obviously related to the lower membrane force but also to the higher gas permeability, which enhances the radical degradation mechanisms described in Section 15.3.ii. Significant advances in materials and design must exist made before ultrathin membranes tin can achieve the lifetimes required to exist considered mature enough for introduction in fuel cell systems.

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Medical Biotechnology and Healthcare

A.L. Zydney , R. van Reis , in Comprehensive Biotechnology (2nd Edition), 2011

5.twoscore.2.2.1 Hollow fiber, apartment sheet, chemistry, and pore structures

MF membranes can have either an isotropic or asymmetric pore structure. Asymmetric membranes are used with the peel-side facing the feed to minimize surface fouling. MF membranes are made from a variety of polymers including polyethersulfone, polysulfone, polypropylene, cellulose and mixed cellulose esters, and hydrophilized polyvinylidene fluoride [xiv]. These materials are ofttimes surface modified to increase hydrophilicity and reduce fouling, and they can be bandage as mixed polymers (eastward.g., with polyvinylpyrrolidone to increase wettability).

Narrow diameter hollow-cobweb membranes for tangential flow MF typically have inner diameters ranging from 0.ii to 1.8   mm, providing laminar flow with moderate wall shear rates [14]. Most hollow fibers take an asymmetric construction with the dense skin at the lumen side of the fiber. The fibers are self-supporting, so they can typically be cleaned by backflushing from the filtrate side. Presterilized disposable hollow-fiber modules have as well been developed, eliminating the need for cleaning and regeneration. Flat-canvas membranes are straight bonded or glued to plates or sealed using appropriate gaskets. Open up channel systems are commonly employed for tangential catamenia MF to minimize plugging past cell aggregates and droppings.

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Why Are Cell Membranes Asymmetrical,

Source: https://www.sciencedirect.com/topics/engineering/asymmetric-membrane

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