Membrane transport hydrodynamic flow

Two passive processes move water through membranes diffusion and hydrodynamic flow. A semipermeable membrane is a membrane that will allow certain molecules (i.e., water) or ions to pass through it by diffusion. If the concentrations of a substance for which the membrane is impermeable are different on the two sides of the membrane, then water will be transported to equilibrate concentrations, for example, a stream of water toward the higher concentration is driven by osmotic pressure. 

Gas separation, desalination, ultra- and microfiltrarion, ion transport, electrodialysis, and pervaporation processes rely on membrane fabrication methods that can deliver robust and selective membranes. These processes require fabrication methods that can produce membranes that are defect-free so that hydrodynamic flow does not occur over that expected for the specific pore diameter of the membrane owing to... 

As follows from the hydrodynamic properties of systems involving phase boundaries (see e.g. [86a], chapter 2), the hydrodynamic, Prandtl or stagnant layer is formed during liquid movement along a boundary with a solid phase, i.e. also at the surface of an ISE with a solid or plastic membrane. The liquid velocity rapidly decreases in this layer as a result of viscosity forces. Very close to the interface, the liquid velocity decreases to such an extent that the material is virtually transported by diffusion alone in the Nernst layer (see fig. 4.13). It follows from the theory of diffusion transport toward a plane with characteristic length /, along which a liquid flows at velocity Vo, that the Nernst layer thickness, 5, is given approximately by the expression,... 

Ralf Kuriyel (Millipore Corporation) addressed some of the issues related to the use of Dean vortices, formed during the flow of fluids in curved conduits, to enhance the performance of cross-flow filters by increasing the back transport of solutes. Results were presented on coiled hollow fibers with a varying radius of curvature, fiber diameter, and solution viscosity, to characterize the relationship between the back transport of solutes and hydrodynamic parameters. A performance parameter relating back transport to the Dean number and shear rate was derived, and a simple scaling methodology was developed in terms of the performance parameter. The use of Dean vortices may result in membrane systems with less fouling and improved performance. 

Most of hydrodynamic methods have focused on increasing the particle back transport from the membrane-liquid interface by increasing the shear rate and the flow instability in the boundary layer. These techniques include secondary flows, spacers and inserts, pulsed flow, high shear rate devices, vibrations, and two-phase flow. The physical methods that are currently been tested to enhance filtration performance of membranes include the application of electric fields and ultrasound. 

The mass flux of a solute can be related to a mass transfer coefficient which gathers both mass transport properties and hydrodynamic conditions of the system (fluid flow and hydrodynamic characteristics of the membrane module). The total amount transferred of a given solute from the feed to the receiving phase can be assumed to be proportional to the concentration difference between both phases and to the interfacial area, defining the proportionality ratio by a mass transfer coefficient. Several types of mass transfer coefficients can be distinguished as a function of the definition of the concentration differences involved. When local concentration differences at a particular position of the membrane module are considered the local mass transfer coefficient is obtained, in contrast to the average mass transfer coefficient [37]. 

In membrane filtration, some components (dissolved or particulate) of the feed solution are rejected by the membrane and these components are transported back into the bulk by means of diffusion. The rate of diffusion will depend on the hydrodynamics (laminar or turbulent) and on the concentration of solutes. If the concentration of solute at the surface is above saturation (i.e., the solubility limit) a gel is formed. This increases the flow resistance with consequential flux decrease. This type of behavior, for example, is typical of UF with protein solutions. 

The mass transfer resistances strongly depend on the nature of the hydrodynamics in the contacting device and the mode of operation. Many devices have been used to study two-phase mass transfer at or near the liquid-liquid interface. Hence, the hydrodynamic characteristics of ion transport through a membrane were presented to evaluate the feasibility that this permeation system can be calibrated as a standardized liquid-liquid system for studying the membrane-moderated PT-catalyzed reaction. The individual mass transfer coefficients and diffusivities for the aqueous phase, organic phase, and membrane phase were determined and then correlated in terms of the conventional Sh-Re-Sc relationship. The transfer time of quaternary salt across the membrane and the thickness of the hydrodynamic diffusion boundary layer are calculated and then the effect of environmental flow conditions on the rate of membrane permeation can be accurately interpreted [127]. 

This phenomenon is denoted feed-side concentration polarization and, in practice, affects mainly the fluxes of compounds of high sorption coefficient, even under turbulent hydrodynamic conditions over the membrane, as their permeability (and hence flux across the membrane) is high. It should at this point be emphasized that contrary to the non-ideal transport phenomena discussed earlier, feed-side concentration polarization is not a membrane-intrinsic phenomenon, but stems from poor design of the upstream flow conditions in practice it may in fact not be overcome owing to module design limitations (Baker et ah, 1997). 

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