Transmembrane hydrostatic pressure

Generally, the pure-water flux through a membrane layer, uw is directly proportional to the applied hydrostatic pressure difference (transmembrane pressure, AP) according to Darcy s law as follows ... 

Consider Figure 1, which depicts the conventional hemodialysis system in counter-current mode. This dlalyzer set-up maximizes the concentration difference across the membrane and thus ensures maximum solute transfer. However this configuration also maximizes the transmembrane hydrostatic pressure difference and thus, maximizes the water flux. During hemodialysis the hydrostatic pressure of the blood must always be higher than the pressure of the dialysate to ensure sterility in the event of a membrane rupture. One has the following constraints during... 

Figure 7. Decay of UF rate with time at various fixed transmembrane hydrostatic pressures and per meters squared of membrane...

Figure 1.26 Transmembrane flux and salt rejection of a membrane prepared from a solution of 25% cellulose acetate, 45% acetone and 30% formamide by precipitation in water as a function of the past precipitation annealing temperature. (Test conditions 1% NaCI-solution, 100 bar hydrostatic pressure).

A decrease in hydrostatic pressure along the fiber due to resistance to substrate solution flow occurs so that at a definite distance from the inlet, say Lc, transmembrane pressure is nil. Fiber-to-shell solution flux from that point on is negative and becomes a shell-to-fiber flux. Neglecting the shell pressure drop, the overall fiber-to-shell ultrafiltration net flow rate can then be obtained upon integration of the flux equation over the length of the fiber from the inlet to Lc, that is ... 

Here J and J are the transmembrane fluid and solute flux densities Xp and Att are the hydrostatic and osmotic pressure differences (inside minus outside) across the fiber wall C is the "wall" concentration i.e., solute concentration ImmeSiately adjacent to the solution-membrane interface within the fiber annulus C is local filtrate or product concentration at the outer surfice of the fiber and 8 is the transmembrane Pdcldt... 

Efforts to stabilize BLMs by the use of polymerizable lipids have been successful, but the electrochemical properties of these membranes were greatly compromised and ion channel phenomena could not be observed [21]. Microfiltration and polycarbonate filters, polyimide mesh, and hydrated gels have been used successfully as stabilizing supports for the formation of black lipid films [22-25] and these systems were observed to retain their electrical and permeability characteristics [24]. Poly(octadec-l-ene-maleic anhydride) (PA-18) was found to be an excellent intermediate layer for interfacing phospholipids onto solid substrates, and is sufficiently hydrophilic to retain water for unimpeded ion transfer at the electrode-PA-18 interface [26]. Hydrostatic stabilization of solventless BLMs has been achieved by the transfer of two lipid monolayers onto the aperture of a closed cell compartment however, the use of a system for automatic digital control of the transmembrane pressure difference was necessary [27]. 

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