Transport mechanisms, flow-through

FIGt 22-48 Transport mechanisms for separation membranes a) Viscous flow, used in UF and MF. No separation achieved in RO, NF, ED, GAS, or PY (h) Knudsen flow used in some gas membranes. Pore diameter < mean free path, (c) Ultramicroporoiis membrane—precise pore diameter used in gas separation, (d) Solution-diffusion used in gas, RO, PY Molecule dissolves in the membrane and diffuses through. Not shown Electro-dialysis membranes and metallic membranes for hydrogen. 

At any instant, pressure is uniform throughout a bubble, while in the surrounding emulsion pressure increases with depth below the surfaee. Thus, there is a pressure gradient external to the bubble which causes gas to flow from the emulsion into the bottom of the bubble, and from the top of the bubble back into the emulsion. This flow is about three times the minimum fluidization velocity across the maximum horizontal cross section of the bubble. It provides a major mass transport mechanism between bubble and emulsion and henee contributes greatly to any reactions which take place in a fluid bed. The flow out through the top of the bubble is also sufficient to maintain a stable arch and prevent solids from dumping into the bubble from above. It is thus responsible for the fact that bubbles can exist in fluid beds, even though there is no surface tension as there is in gas-liquid systems. 

The main emphasis in this chapter is on the use of membranes for separations in liquid systems. As discussed by Koros and Chern(30) and Kesting and Fritzsche(31), gas mixtures may also be separated by membranes and both porous and non-porous membranes may be used. In the former case, Knudsen flow can result in separation, though the effect is relatively small. Much better separation is achieved with non-porous polymer membranes where the transport mechanism is based on sorption and diffusion. As for reverse osmosis and pervaporation, the transport equations for gas permeation through dense polymer membranes are based on Fick s Law, material transport being a function of the partial pressure difference across the membrane. 

The research group led by Dr. Djilali at the University of Victoria has developed an ex situ experimental technique using fluorescent microscopy to study the liquid water transport mechanisms inside diffusion layers and on their surfaces [239-243]. The diffusion layer is usually placed between two plates (the top plate may or may not have a channel) the liquid water, which is pumped through a syringe pump, flows from the bottom plate through the DL. Fluorescein dye is added to the water for detection with the microscope. 

The first term on the right-hand side is the diffusive flux relative to the volume average velocity. The second term represents a contribution due to bulk flow. It should be emphasized here that the separation of the total flux into two contributions is always possible regardless of the actual transport mechanism through the membrane. In other words, Eq. (7) is purely phenomenological and does not require any specific transport model. 

The previous section introduced the first situation in this book where spatial distribution has been relevant. Even so, the only transport process was that imposed by the fluid flow no molecular transport mechanisms were invoked, except perhaps through the hoped-for perfect radial mixing. 

Figure 2.1 Molecular transport through membranes can be described by a flow through permanent pores or by the solution-diffusion mechanism...

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