Channel flow with permeation

Figure 19.4. The spiral wound membrane module for reverse osmosis, (a) Cutaway view of a spiral wound membrane permeator, consisting of two membranes sealed at the edges and enclosing a porous structure that serves as a passage for the permeate flow, and with mesh spacers outside each membrane for passage of feed solution, then wound into a spiral. A spiral 4 in. dia by 3 ft long has about 60 sqft of membrane surface, (b) Detail, showing particularly the sealing of the permeate flow channel, (c) Thickness of membranes and depths of channels for flows of permeate and feed solutions.

Spiral-wound elements, as shown in Figure 2, consist primarily of one or more membrane "leaves, each leaf containing two membrane layers separated by a rigid, porous, fluid-conductive material known as the "permeate channel spacer." The permeate channel spacer facilitates the flow of the "permeate", an end product of the separation. Another channel spacer known as the "high pressure channel spacer" separates one membrane leaf from another and facilitates the flow of the high pressure stream through the element. The membrane leaves are wound around a perforated hollow tube, known as the "permeate tube", through which the permeate is removed. The membrane leaves are sealed with an adhesive on three sides to separate the feed gas from the permeate gas, while the fourth side is open to the permeate tube. 

The characteristic feature of flow FFF is the superimposition of a second stream of liquid perpendicular to the axis of separation. This cross-flow drives the injected sample plug toward a semipermeable membrane that acts as the accumulation wall. The cross-flow liquid permeates across the membrane and exits the channel, whereas the sample is retained inside the channel in the vicinity of the membrane surface. Sample displacement by the cross-flow is countered by diffusion away from the membrane wall. At equilibrium, the net flux is zero and sample clouds of various thicknesses are formed for different sample species. As with other FFF techniques, a larger diffusion coefficient D leads to a thicker equilibrium sample cloud that, on average, occupies a faster streamline of the parabolic flow profile and subsequently elutes at a shorter retention time t,. For well-retained samples analyzed by flow FFF, t, can be related to D and the hydrodynamic diameter d by... 

Mainly four types of membrane modules are used plate-and-frame, spiral-wound, tube-in-shell, and hollow fiber. The plate-and-frame module consists of a series of membranes (10-500 pm thick) sandwiched between spacers that act as flow channels (Figure 5.69). (The membranes are often laminated on a porous support that offers no flow resistance.) The feed flows in one set of channels and the permeate, with or without carrier fluid, flows in alternate channels. Plate-and-frame modules find use in ultrafiltration and dialysis applications which include hemodialysis and electrodialysis. 

Flat-sheet membranes are normally assembled in plate-and-frame devices together with porous support plates and spacers forming the feed flow channels. The feed solution is pressurized in the housing and forced across the membrane (Fig. 2.3a). The support plate provides a flow channel for the permeate that is collected from a tube on the side of the plate. Feed channel heights vary from 0.3 to 0.75 mm depending on the viscosity of the feed solution to be filtered. 

Parallel-Leaf Cartridge. A parallel-leaf cartridge consists of several flat plates, each having membrane sealed to both sides (Fig. 13). The plates have raised (2—3 mm) rails along the sides in such a way that, when they are stacked, the feed can flow between them. They are clamped between two stainless-steel plates with a central tie rod. Permeate from each leaf drains into an annular channel surrounding the tie rod (33). 

TFF membrane systems generally use a common feed distributed among parallel modules with a collection of common retentate and common permeate streams. In some applications, it is also useful to plumb TFF modules with the retentate in series where the retentate flow from one module provides the feed flow to the next module. This type of configuration is equivalent to increasing the length of the retentate channel. Permeate flows may or may not be plumbed together. 

Equations (20-66) and (20-67) present single-pass formulas relating retentate solute concentration, retentate crossflow, permeate flow, and membrane area. For relevant low-feed-concentration applications, polarization is minimal and the flux is mainly a function of pressure. Spiral or hollow fiber modules with low feed channel and permeate pressure drops are preferred. 

Membrane gas-separation systems have found their first applications in the recovery of organics from process vents and effluent air [5]. More than a hundred systems have been installed in the past few years. The technique itself therefore has a solid commercial background. Membranes are assembled typically in spiral-wound modules, as shown in Fig. 7.3. Sheets of membrane interlayered with spacers are wound around a perforated central pipe. The gas mixture to be processed is fed into the annulus between the module housing and the pipe, which becomes a collector for the permeate. The spacers serve to create channels for the gas flow. The membranes separate the feed side from the permeate side. 

A flattened membrane tube, or two sheet membranes sealed at both edges (and with a porous backing material inside if necessary), is wound as a spiral with appropriate spacers, such as mesh or corrugated spacers, between the membrane spiral. One of the two fluids - that is, the feed (and retentate) or the permeate - flows inside the wound, flattened membrane tube, while the other fluid flows through the channel containing spacers, in cross flow to the fluid in the wound membrane tube. 

Based on previous works on Homeopathy we have hypothesized that the primary target of a homeopathic potency in an organism is the water-channel protein or aquaporin (Sukul and Sukul, 2001). Aquaporins occur in all life forms and facilitate permeation of water across biological membranes. We have discussed in details about the structure and function of aquaporins and their relation to health and disease in chapter IV. There are several types of aquaporins (AQP) and one type AQP1 occurs abundantly in red blood cells of vertebrates. If the primary target of a homeopathic potency is aquaporin, application of a homeopathic potency on cell membranes would affect water flow into the cells. In order to test this hypothesis we treated red blood cells of a fresh water fish (Clarius batrachus) with Mercuric chloride 30 (Merc cor 30) and Nux vomica 30 (Nux vom 30) separately in a hypotonic medium. In the control red cells were treated with Ethanol 30. The diluent medium in all the three potencies consisted of 90% ethanol and 10% distilled water. 

They concluded that the surface charge of HS controlled their recovery, and any carrier component decreasing the effective surface charge of HS led to a sorption increase. Furthermore, the cross-flow rate influenced recovery dramatically, which supports the idea that either sorption to membrane or permeation through it is responsible for losses. Finally, other channel components play a minor role. The authors recommendations were to use 0.005 M TRIS-buffer (pH 9.1) as a carrier solution (recovery of about 85-90%) and use a regenerated cellulose membrane with a 5-kDa cutoff as the accumulation wall. 

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