Membranes Pinch points

One can see from Figure 9.8 that the profile intersects the pinch point locus at an ta value of about 2. However, it is evident that the profile does not pinch at this point. The reason for this is that there is still material present in the retentate for permeating. Even though there is an intersection between the profile and the locus, this is only instantaneous. A moment later (down the length of membrane), the value will decrease, and thus search for another stable node. Therefore, the profile does not terminate if it intersects with the pinch point locus, unless has gone to zero. 

Osmotic Pinch Ejfect Feed is pumped into the membrane train, and as it flows through the membrane array, sensible pressure is lost due to fric tion effects. Simultaneously, as water permeates, leaving salts behind, osmotic pressure increases. There is no known practical alternative to having the lowest pressure and the highest salt concentration occur simultaneously at the exit of the train, the point where AP — AH is minimized. This point is known as the osmotic pinch, and it is the point backward from which hydrauhe design takes place. A corollary factor is that the permeate produced at the pinch is of the lowest quality anywhere in the array. Commonly, this permeate is below the required quahty, so the usual prac tice is to design around average-permeate quality, not incremental quahty. A I MPa overpressure at the pinch is preferred, but the minimum brine pressure tolerable is 1.1 times H. 

Both endocytosis of material at the plasma membrane and exocytosis from the Golgi apparatus involve the formation of clathrin-coated pits and vesicles. On the cytosolic side of the membrane these structures have an electron-dense coat consisting mainly of the protein clathrin, the polypeptides of which form a three-legged structure known as a triskelion. The clathrin triskelions assemble into a basket-like convex framework that causes the membrane to invaginate at that point and eventually to pinch off and form a vesicle. In endocytosis these clathrin-coated vesicles migrate into the cell where the clathrin coats are lost before delivering their contents to the lysosomes. 

This means that when the retentate runs out of material, the very last permeate composition will be that of (or x ). This result is intuitive, since aU the material has transferred through the membrane. One can simply use the permeation model to determine the composition of the last drop of retentate (refer to Equation 9.6). Using the o( -values selected and = [0.3,0.3], the pinch will occur at = [0.15,0.45]. This corresponds to the last point on the curve in Figure 9.8. The position of the pinch is fixed for a chosen X and flux model. All curves will terminate at this point, irrespective of x (see Section 9.6.7). 

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