Porous media charged

In this chapter, we will briefly present basic mass transfer mechanisms in polymer membranes and the mechanisms dominating in some membrane separations. In the first part of the chapter, we give a brief description of general transport mechanisms of solutes (charged or not) through a porous media (charged or not). In the second part, we discuss in detail some membranes processes and the transfer mechanisms, interesting from the theoretical point of view. 

One prominent example of rods with a soft interaction is Gay-Berne particles. Recently, elastic properties were calculated [89,90]. Using the classical Car-Parrinello scheme, the interactions between charged rods have been considered [91]. Concerning phase transitions, the sohd-fluid equihbria for hard dumbbells that interact additionally with a quadrupolar force was considered [92], as was the nematic-isotropic transition in a fluid of dipolar hard spherocylinders [93]. The influence of an additional attraction on the phase behavior of hard spherocylinders was considered by Bolhuis et al. [94]. The gelation transition typical for clays was found in a system of infinitely thin disks carrying point quadrupoles [95,96]. In confined hquid-crystalline films tilted molecular layers form near each wall [97]. Chakrabarti has found simulation evidence of critical behavior of the isotropic-nematic phase transition in a porous medium [98]. 

Edwards, DA, Charge Transport Through a Spatially Periodic Porous Medium Electrokinetic and Convective Dispersion Phenomena, Philosophical Transactions of the Royal Society of London A 353, 205, 1995. 

Generalized local Darcy s model of Teorell s oscillations (PDEs) [12]. In this section we formulate and study a local analogue of Teorell s model discussed previously. The main difference between the model to be discussed and the original one is the replacement of the ad hoc resistance relaxation equation (6.1.5) or (6.2.5) by a set of one-dimensional Nernst-Planck equations for locally electro-neutral convective electro-diffusion of ions across the filter (membrane). This filter is viewed as a homogenized aqueous porous medium, lacking any fixed charge and characterized... 

Abstract A general theoretical and finite element model (FEM) for soft tissue structures is described including arbitrary constitutive laws based upon a continuum view of the material as a mixture or porous medium saturated by an incompressible fluid and containing charged mobile species. Example problems demonstrate coupled electro-mechano-chemical transport and deformations in FEMs of layered materials subjected to mechanical, electrical and chemical loading while undergoing small or large strains. 

Soft biological structures exhibit finite strains and nonlinear anisotropic material response. The hydrated tissue can be viewed as a fluid-saturated porous medium or a continuum mixture of incompressible solid (s), mobile incompressible fluid (f), and three (or an arbitrary number) mobile charged species a, (3 = p,m, b). A mixed Electro-Mechano-Chemical-Porous-Media-Transport or EMCPMT theory (previously denoted as the LMPHETS theory) is presented with (a) primary fields (continuous at material interfaces) displacements, Ui and generalized potentials, ifi ( , r/ = /, e, to, b) and (b) secondary fields (discontinuous) pore fluid pressure, pf electrical potential, /7e and species concentration (molarity), ca = dna/dVf or apparent concentration, ca = nca and c = Jnca = dna/dVo. The porosity, n = 1 — J-1(l — no) and no = no(Xi) = dVj/dVo for a fluid-saturated solid. Fixed charge density (FCD) in the solid is defined as cF = dnF/dV , cF = ncF, and cF = cF (Xf = JncF = dnF/d o. 

MEASUREMENTS OF DEFORMATIONS AND ELECTRICAL POTENTIALS IN A CHARGED POROUS MEDIUM... 

Considering a charged porous medium containing monovalent electrolyte, the electrical current (Ie) carried by ions (per unit area) is related to the ion fluxes and given by [4, 8, 12]... 

Electrophoresis Separation of large, charged molecules in an electric field across a porous medium Identification of the components of a mixture... 

The third relaxation process is located in the low-frequency region and the temperature interval 50°C to 100°C. The amplitude of this process essentially decreases when the frequency increases, and the maximum of the dielectric permittivity versus temperature has almost no temperature dependence (Fig 15). Finally, the low-frequency ac-conductivity ct demonstrates an S-shape dependency with increasing temperature (Fig. 16), which is typical of percolation [2,143,154]. Note in this regard that at the lowest-frequency limit of the covered frequency band the ac-conductivity can be associated with dc-conductivity cio usually measured at a fixed frequency by traditional conductometry. The dielectric relaxation process here is due to percolation of the apparent dipole moment excitation within the developed fractal structure of the connected pores [153,154,156]. This excitation is associated with the selfdiffusion of the charge carriers in the porous net. Note that as distinct from dynamic percolation in ionic microemulsions, the percolation in porous glasses appears via the transport of the excitation through the geometrical static fractal structure of the porous medium. 

Repulsive potential energy between two identical spheres of same charge Volume of voids in porous medium Dimensionless applied voltage,... 

Even without molecular sieving or charge retardation associated with the support, observed electromigration velocities will generally be affected by electroosmotic flow and by capillary flow through the porous medium. These flow effects make the process unsuitable for mobility measurements. However, by somewhat empirical means, it is today the principal analytical procedure used for protein and amino acid analysis because it is simple, cheap, enables complete separation of all electrophoretically different components, and because small samples can be studied, which is often important for biochemical analyses. 

In 1809, Reuss observed the electrokinetic phenomena when a direct current (DC) was applied to a clay-water mixture. Water moved through the capillary toward the cathode under the electric field. When the electric potential was removed, the flow of water immediately stopped. In 1861, Quincke found that the electric potential difference across a membrane resulted from streaming potential. Helmholtz first treated electroosmotic phenomena analytically in 1879, and provided a mathematical basis. Smoluchowski (1914) later modified it to also apply to electrophoretic velocity, also known as the Helmholtz-Smoluchowski (H-S) theory. The H-S theory describes under an apphed electric potential the migration velocity of one phase of material dispersed in another phase. The electroosmotic velocity of a fluid of certain viscosity and dielectric constant through a surface-charged porous medium of zeta or electrokinetic potential (0, under an electric gradient, E, is given by the H-S equation as follows ... 

Consider electroosmotic motion in a porous medium. We can model this medium by a system of parallel cylindrical microcapillaries. Consider one of such capillaries and assume that its wall carries a charge. The motion of Uquid in the... 

The phenomenon of electro-osmosis has already been mentioned in connection with electrochemical realkalization (Section 7.8). It is well known that when a porous medium like concrete contains a solution, then an electric current applied between an anode and a cathode will move the water from the anode to the cathode. This leads to drying of anodes for pipelines in soils. The basis of the phenomenon is that when a compound dissolves, water molecules attach themselves to it. This happens more for positively charged metal ions than for negatively charged ions. Therefore more water is carried by the positive ions towards the negative cathode. 

An inverse phenomenon streaming potential), generation of an electric field inside the membrane, takes place if the solution passes through this porous medium due to an imposed hydrostatic pressure. This time it is the flow of the fluid inside the pores that induces the displacement of the mobile part of the EDL at the surface of capillaries, with respect to the charges attached to the surface. These dipoles create an electric field, which, under stationary conditions, prevents the farther displacement of the mobile charges. The resulting potential difference across the membrane, A(p, is proportional to the excessive hydrostatic pressure, AP ... 

Here dw( ) is the macroscopic EOF velocity (Darcy velocity) field through the neutrally charged porous medium inside the microcapillary. < ) = < )(r) is the local porosity distribution of the porous medium, determined by Eq. 9. The Darcy permeability K is defined by the Carman-Kozeny equation [7], K = a — ( )), and the inertial coefficient F =, with a = 150 and b = 1.75... 

Chromatography performs separation according to the size, charge, and affinity of the analyte, based on the different velocities that each compound is carried by a solvent in an appropriate porous medium. In electrophoresis, the separation is based on the electrokinetic mobility of... 

Some simple and useful examples are worked out in Sec. IV. First, the simultaneous motions of fluid and charges through a spatially periodic porous medium are analyzed linearization enables us to summarize the results by means of four electro-osmotic tensors that relate the fluxes of charge and matter to the potential and pressure gradients. The cases of a semi-finite void space limited by a plane solid wall and of plane or circular channels are briefly addressed the symmetry properties deduced from the general Onsager theorem are verified these simple configurations are further used to check the numerical routines. 

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