Pressure driven species transport

In this book, pressure-driven species transport in porous electrode layers is not considered and we will always assume diffusion transport caused by a concentration gradient. Moreover, this transport will always be described by Pick s diffusion equation ... 

In the past, the most common method used for microsolute removal has been batch dialysis. The solution to be dialyzed was placed in seamless regen-erated-cellulose tubing ("sausage bags") and suspended in the dialysate allowing salts to diffuse across the membrane. With diafiltration, the same degree of salt removal can be accomplished much more rapidly with smaller volumes of dialysate. The pressure driven convective transport of solutes across the membrane is much faster than concentration driven diffusion (particularly at low salt concentrations). In addition, with diafiltration, all solutes (saltsand alcohol) are removed at the same rate independent of the size and diffusivity of the various species this makes the process more predictable and controllable. 

The most common membrane systems are driven by pressure. The essence of a pressure-driven membrane process is to selectively permeate one or more species through the membrane. The stream retained at the high pressure side is called the retentate while that transported to the low pressure side is denoted by the permeate (Fig. 11.1). Pressure-driven membrane systems include microfiltration, ultrafiltration, reverse osmosis, pervaporation and gas/vapor permeation. Table ll.l summarizes the main features and applications of these systems. 

In addition to conventional pressure driven flow, electrokinetic flow is also a commonly used means of transporting liquids in microfluidic devices. One type of electrokinetic flow, electroosmotic flow, relies on the presence of an electrical double layer at the solid-liquid interface. A negatively charged surface in a flow channel will attract cationic species from the fluid to form an electrical double layer at the surface. Application of an external voltage can pull those cationic species through the flow channel inducing bulk flow. The electroosmotic flow velocity can be described... 

In this problem, we calculate the time-averaged axial transport rate for the special case of an oscillating pressure-driven flow in a straight wall channel with a cross-sectional shape that we denote as S and a wall that we denote as B. We consider a two-component system consisting of a carrier gas and a second dilute species whose concentration we denote as c. The latter is assumed to have a uniform gradient in the axial direction that we denote as ft, i.e., dc/dz = j. We assume that this second component is sufficiently dilute that the velocity field is wholly determined by the carrier gas, which is modeled as an incompressible, Newtonian fluid with a density p and viscosity //. The pressure gradient is assumed to take the form... 

A range of membrane processes are used to separate fine particles and colloids, macromolecules such as proteins, low-molecular-weight organics, and dissolved salts. These processes include the pressure-driven liquid-phase processes, microfiltration (MF), ultrafiltration (UF), nanofiltration (NF), and reverse osmosis (RO), and the thermal processes, pervaporation (PV) and membrane distillation (MD), all of which operate with solvent (usually water) transmission. Processes that are solute transport are electrodialysis (ED) and dialysis (D), as well as applications of PV where the trace species is transmitted. In all of these applications, the conditions in the liquid boundary layer have a strong influence on membrane performance. For example, for the pressure-driven processes, the separation of solutes takes place at the membrane surface where the solvent passes through the membrane and the retained solutes cause the local concentration to increase. Membrane performance is usually compromised by concentration polarization and fouling. This section discusses the process limitations caused by the concentration polarization and the strategies available to limit their impact. 

As the initially injected sample plug is normally a distance away from the capillary inlet in capDlaiy electrophoresis, the entrance region should have negligible influence on the species transport. In the region of fully developed (denoted by the subscript fd) flow field, the thermally induced pressure-driven flow causes additional hydrodynamic dispersion to the species diffusion. Analogous to Eq. 17, the effective dispersion coefficient is given by... 

Currently, analytical approaches are still the most preferred tools for model reduction in microfluidic research community. While it is impossible to enumerate all of them in this entry, a generalized analytical model on species transport under pressure-driven flow in rectangular microchaimel with arbitrary aspect ratio will be discussed [10]. The nonuniform velocity profile along the cross section of the microchaimel under the pressure-driven flow results in unique and complex species transport phenomena including Taylor dispersion, heterogeneous transport rate, and position-dependent diffusion scaling law. 

One of the main goals of the GDL is the transport of gaseous species. From an experimental point of view the determination of the gas permeability (pressure-driven flow) is easier than the determination of the diffusion (driving force concentration difference) of gases. This might be the reason that, in the literature, values for the permeability for GDL material can be found much more often than diffusion coefficients or structural parameters of the materials necessary for the determination of the effective diffusion coefficient. Especially when looking in the specification for GDLs provided by manufacturers, one will find values for gas permeation but no data relevant for gas diffusion. 

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