Pressure-driven convection

Possible driving forces for solute flux can be enumerated as a linear combination of gradient contributions [Eq. (20)] to solute potential across the membrane barrier (see Part I of this volume). These transbarrier gradients include chemical potential (concentration gradient-driven diffusion), hydrostatic potential (pressure gradient-driven convection), electrical potential (ion gradient-driven cotransport), osmotic potential (osmotic pressure-driven convection), and chemical potential modified by chemical or biochemical reaction. 

In PEMFC systems, water is transported in both transversal and lateral direction in the cells. A polymer electrolyte membrane (PEM) separates the anode and the cathode compartments, however water is inherently transported between these two electrodes by absorption, desorption and diffusion of water in the membrane.5,6 In operational fuel cells, water is also transported by an electro-osmotic effect and thus transversal water content distribution in the membrane is determined as a result of coupled water transport processes including diffusion, electro-osmosis, pressure-driven convection and interfacial mass transfer. To establish water management method in PEMFCs, it is strongly needed to obtain fundamental understandings on water transport in the cells. 

Pressure-driven convective flow, the basis of the pore flow model, is most commonly used to describe flow in a capillary or porous medium. The basic equation covering this type of transport is Darcy s law, which can be written as... 

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. 

Pore-flow model In pore-flow model, permeates are separated by pressure-driven convective flow through tiny pores. Separation is achieved between different permeates because... 

Convection is a process by which a substance is dragged along by the flow of fluid hence the term solvent drag is used to describe this type of transport. The flow is powered by osmotic or hydrostatic pressure gradients which exist across tissue boundaries. The kidney is an example of an organ which depends on hydrostatic pressure-driven convection for filtration of substances by the glomerulus and osmotic-pressure driven convection for solute reabsorption in the proximal tubule. Filtration and reabsorption by blood capillaries depends on Starling s relationship ... 

Water flux owing to the pressure-driven convection flow is given as... 

If pressure-driven convection is neglected, then the equation reduces to... 

For a Nafion polymer membrane, the Nemst-Planck s equation without the pressure-driven convection term is written in terms of water content in the membrane as... 

Gas permeation through the porous membranes may be driven by pressure or concentration gradient. Under a pressure or concentration gradient, gas will permeate through the membrane in a convective or a diffusive flow, respectively. In general, the pressure-driven convective fluxes are much higher than the concentration-driven diffusion fluxes. 

Ihe membranes were assembled in a dead-end filtration module and the results obtained under convective flow conditions were compared with those obtained in a batch reactor. The PCB degradation rate under pressure-driven convective flow conditions benefited from narrow pore size, high intrinsic reaction rate and high diffusivity. 

This velocity profile is commonly called drag flow. It is used to model the flow of lubricant between sliding metal surfaces or the flow of polymer in extruders. A pressure-driven flow—typically in the opposite direction—is sometimes superimposed on the drag flow, but we will avoid this complication. Equation (8.51) also represents a limiting case of Couette flow (which is flow between coaxial cylinders, one of which is rotating) when the gap width is small. Equation (8.38) continues to govern convective diffusion in the flat-plate geometry, but the boundary conditions are different. The zero-flux condition applies at both walls, but there is no line of symmetry. Calculations must be made over the entire channel width and not just the half-width. 

Any material that provides adequate protection against water should at least limit convective soil gas movement. Properly applied waterproofing materials should help block pressure-driven entry of soil gas. 

Dialysis continues to meet certain specialized applications, particularly those in biotechnology and the life sciences. Delicate substances can be separated without damage because dialysis is typically performed under mild conditions ambient temperature, no appreciable transmembrane pressure drop, and low-shear flow. While slow compared with pressure-driven processes, dialysis discriminates small molecules from large ones reliably because the absence of a pressure gradient across the membrane prevents convective flow through defects in the membrane. This advantage is significant for two... 

In practice, UF operation is usually limited by cake formation In all pressure-driven membrane processes both the solvent (water) and solutes are carried convectively to the membrane surface. In UF, only the solvent and microsolutes pass through the membrane. The macromolecules are rejected and, became of their small... 

Permeability is the resistance of a material to bulk or convective, pressure-driven flow of a fluid through it. 

Problem 3-35. Temperature Distribution in a Combined Plane Couette and Poiseuille Flow with a Linearly Increasing Wall Temperature. In this problem you will examine convective heat transfer in a combined plane Couette and Poiseuille flow. Suppose we have the channel depicted in the figure. The upper wall moves with a velocity U and the lower wall is fixed. In addition to the shear flow there is a pressure-driven backflow resulting in the purely quadratic dependence of velocity on y (e.g., the shear rate at the lower wall is zero). 

The subject of hydrodynamic stability theory is concerned with the response of a fluid system to random disturbances. The word hydrodynamic is used in two ways here. First, we may be concerned with a stationary system in which flow is the result of an instability. An example is a stationary layer of fluid that is heated from below. When the rate of heating reaches a critical point, there is a spontaneous transition in which the layer begins to undergo a steady convection motion. The role of hydrodynamic stability theory for this type of problem is to predict the conditions when this transition occurs. The second class of problems is concerned with the possible transition of one flow to a second, more complicated flow, caused by perturbations to the initial flow field. In the case of pressure-driven flow between two plane boundaries (Chap. 3), experimental observation shows that there is a critical flow rate beyond which the steady laminar flow that we studied in Chap. 3 undergoes a transition that ultimately leads to a turbulent velocity field. Hydrodynamic stability theory is then concerned with determining the critical conditions for this transition. 

Convective or pressure-driven fluid flow is remarkably efficient for carrying agents over large distances (i.e. > 1 cm) and for mixing agents within the human body. 

In many situations, drug transport due to bulk flow can be neglected. This assumption (v is zero) is common in previous studies of drug distribution in brain tissue [17]. For example, in a study of cisplatin distribution after continuous infusion into the brain, the effects of bulk flow were found to be small, except within 0.5 mm of the site of Infusion [24]. In the cases considered here, since drug molecules enter the tissue by diffusion from the polymer implant, not by pressure-driven flow of a fluid, no flow should be introduced by the presence of the polymer. With fluid convection assumed to be negligible, the general governing equation in the tissue. Equation 10-17, reduces to ... 

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