Modulational instability: Difference between revisions

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'''Electrofiltration''' is a method that combines [[Membrane technology|membrane filtration]] and [[electrophoresis]] in a dead-end process.
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Electrofiltration is regarded as an appropriate technique for concentration and fractionation of [[biopolymer]]s. The film formation on the filter membrane which hinders filtration can be minimized or completely avoided by the application of [[electric field]], improving [[filtration]]’s performance and increasing selectivity in case of fractionation. This approach reduces significantly the expenses for [[downstream processing]] in bioprocesses.
 
==The Technique==
[[File:Electrofiltration_chamber_setup-EN.svg|thumb|400px|Figure 1: Schematic representation of an electrofiltration chamber]]
Electrofiltration is highly innovative state of the art technique for separation, respectively concentration of colloidal substances - for instance [[biopolymer]]s. The principle of electrofiltration is based on overlaying [[electric field]] on a standard [[dead-end filtration]]. Thus the created polarity facilitates electrophoretic force which is opposite to the resistance force of the filtrate flow and directs the charged [[biopolymer]]s. This provides extreme decrease in the film formation on the micro- or ultra-filtration membranes and the reduction of filtration time from several hours by standard [[filtration]] to a few minutes by electrofiltration. In comparison to [[cross-flow filtration]] electrofiltration exhibits not only increased permeate flow but also guarantees reduced shear force stress which qualifies it as particularly mild technique for separation of [[biopolymer]]s that are usually unstable.
 
The promising application in purification of biotechnological products is based on the fact that [[biopolymer]]s are difficult for filtration but on the other hand they are usually charged as a result of the presence of amino and carboxyl groups. The objective of electrofiltration is to prevent the formation of filter cake and to improve the filtration kinetic of products difficult to filtrate.
 
The [[electrophoresis]] of the particles and the [[electro-osmosis]] become essential when the filtration process is overlaid with [[electric field]]. By electrofiltration the conventional [[filtration]] is overlaid with an [[electric field]] (DC) which works parallel with the filtrate’s flow direction. When the electrophoretic force ''F<sub>E</sub>'', oppositely directed to flow, overruns the hydrodynamic resistance force ''F<sub>W</sub>'', the charged particles migrate from the filter medium, thus reducing significantly the thickness of the [[filter cake]] on the membrane.
 
When the solid particles, subject to separation, are negatively charged they migrate towards the [[anode]] (positive pole) and deposit on the situated there filter cloth. As a results on the [[cathode]] side’s membrane (negative pole) there is only a very thin film allowing nearly the whole filtrate to efflux through this membrane.
 
Figure 1 presents schematic description of electrofiltration chamber with flushing [[electrode]]s. For the flushing circulation a [[buffer solution]] is used. This approach has been patented.<ref>{{patent|WO|02051874|“Electrofiltration of Biopolymers”}}</ref>
 
==Fundamental==
[[File:Electrofiltration filterplate.jpg|thumb|Figure 2: Filter cake of xanthan on filter plate]]
The hydrodynamic resistance force is evaluated following the [[Stokes’ law]].
 
:<math>F_W = 6\cdot\pi\cdot\eta\cdot\text{r}_{H}\cdot\nu</math>
 
The electrophoretic force is evaluated following the [[Coulomb’s law]].
 
:<math>F_E = 4\cdot\pi\cdot\varepsilon_{0}\cdot\varepsilon_{r}\cdot\text{r}_{H}\cdot\zeta\cdot\text{E}</math>
 
In these equations ''r<sub>H</sub>''  presents the hydrodynamic radius of the [[colloid]]s, <math>\nu</math>  – the speed of electrophoretic migration, <math>\eta</math> – the dynamic [[viscosity]] of the solutions, <math>\varepsilon_{0}</math> – [[dielectric constant]] in vacuum, <math>\varepsilon_{r}</math> is water’s relative dielectric constant at 298&nbsp;K, <math>\zeta</math> is the [[zeta potential]], ''E'' is the [[electric field]]. The hydrodynamic radius is the sum of particles’ radiuses and the stationary solvent interface.
 
By steady state electrophoretic migration of charged [[colloid]]s the electrophoretic force and the hydrodynamic resistance force are in equilibrium, described by:
 
:''F<sub>W</sub>'' + ''F<sub>E</sub>'' = 0
 
Those effects influence the electrofiltration of [[biopolymer]]s, which could be also charged, not only by the hydrodynamic resistance force but also by the electric field force. Focusing on the [[cathode]] side reveals that the negatively charged particles are affected by the electric field force, which is opposite to the hydrodynamic resistance force. In this manner the formation of [[filter cake]] on this side is impeded or in ideal situation [[filter cake]] is not formed at all. In this case the electric field is referred as critical [[electric field]] ''E''<sub>crit</sub>. As a result of the equilibrium of those forces, liquids subjected to the influence of electric force become charged. In addition to the applied hydraulic pressure ∆pH the process is influenced also by the electro-osmotic pressure ''P<sub>e</sub>''.
 
Modifying the [[Darcy's law|Darcy’s basic equation]], describing filter cake formation, with electro-kinetic effects by integration under assumption of using the constants of electro-osmotic pressure ''P<sub>e</sub>'', the critical electric field ''E''<sub>krit</sub> and the electric field ''E'' results:
 
:<math>\frac{t}{V_L} = \frac{\eta\cdot\alpha_\text{c}\cdot c\cdot\frac{\left(E_\text{crit}-E\right)}{E_\text{crit}}}{2\cdot\left(\Delta P_H+P_e\right)\cdot A^2}\cdot V_L</math>
 
In this equation <math>\alpha_\text{c}</math> represents the mass specific cake resistance, ''c'' – concentration, ''A'' is filtration’s surface, ''V<sub>L</sub>'' – volume of the filtrate, <math>\Delta P_H</math> is the hydraulic pressure.
 
Previous scientific works conducted in the [http://www.bio-ag.de/ Dept. of Bioprocess Engineering, Institute of Engineering in Life Sciences, University of Karlsruhe] demonstrated that electrofiltration is effective for the concentration of charged [[biopolymer]]s. Very promising results concerning purification of the charged [[polysaccharide]] [[xanthan]] are already obtained.<ref>{{cite journal
| title = Improvement of dead-end filtration of biopolymers with pressure electrofiltration | author = Hofmann R., Posten C.
| journal = Chemical Engineering Science | volume = 58 | year =2003
| issue = 17 | pages = 3847 | doi=10.1016/S0009-2509(03)00271-9}}</ref> Figure 2 represents xanthan filter cake.
 
==References==
<references/>
 
==Literature==
*Vorobiev E., Lebovka N., (2008). Electrotechnologies for Extraction from Food Plants and Biomaterials, ISBN 978-0-387-79373-3.
 
{{Separation processes}}
 
[[Category:Filtration]]
[[Category:Membrane technology]]

Latest revision as of 00:47, 12 November 2014

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