Osmotic pressure difference across membrane

The pressure difference between the high and low pressure sides of the membrane is denoted as AP the osmotic pressure difference across the membrane is defined as Att the net driving force for water transport across the membrane is AP — (tAtt, where O is the Staverman reflection coefficient and a = 1 means 100% solute rejection. The standardized terminology recommended for use to describe pressure-driven membrane processes, including that for reverse osmosis, has been reviewed (24). 

Physical methods such as osmotic shock, in which the cells are exposed to high salt concentrations to generate an osmotic pressure difference across the membrane, can lead to cell-wall disruption. Similar disruption can be obtained by subjecting the cells to freeze/thaw cycles, or by pressuriziug the cells with an inert gas (e.g., nitrogen) followed by a rapid depressurization. These methods are not typically used for large-scale operations. 

As a result of Internal concentration polarization, the effective osmotic pressure difference across the membrane can be significantly below the osmotic pressure difference between the bulk solutions. The effective osmotic pressure can be calculated from the salt permeation coefficient and the salt diffusion resistance in the porous membrane substrate. The highest power output for a membrane is obtained at an operating pressure equal to about one half of the effective osmotic pressure. 

The high rejection of these compounds may lead to significant osmotic pressure differences across the membrane, which decreases the actual driving force for... 

RO occurs when a solution is pressurized against a solvent-selective membrane, and the applied pressure exceeds the osmotic pressure difference across the membrane. Water is the solvent in most existing reverse osmosis applications the solutes may be salts or organic compounds. 

The delivery profile of the pump is controlled by the characteristics of the semi-permeable membrane (such as permeability, pore size, and thickness), the osmotic pressure difference across the membrane and the dimensions of the orifice. 

Using the van t Hoff equation, the osmotic pressure difference across the membrane is estimated by... 

When both solutes and water traverse the same barrier, we should replace the classical thermodynamic approach with one based on irreversible thermodynamics. The various forces and fluxes are then viewed as interacting with each other, so the movement of water across a membrane influences the movement of solutes, and vice versa. Using this more general approach, we will show that the osmotic pressure difference effective in causing a volume flux across a membrane permeable to both water and solutes is generally less than the actual osmotic pressure difference across that membrane. 

By definition, UF membranes are freely permeable to inorganic salts and other molecules with MW less than about 1000. Because it is these species that generally create most of the osmotic pressure of solutions, the net osmotic pressure difference across UF membranes is generally quite small and therefore small applied pressures can be used. Because these membranes are more open than RO membranes, there is less necessity to produce very thin membranes in order to achieve high water fluxes. 

An interesting behavior of this kind of membrane is its response to feed-water salinity and operating pressure. This type of membrane will show changes in flux and salt rejection as ionic strength of the feedwater is varied. This is illustrated in Figures 5.8 and 5.9 for two types of salts, sodium chloride and magnesium sulfate. The changes in membrane flux as a function of feedwater salinity are not explained by osmotic pressure differences across the membrane. 

Dialysis A separation process in which a colloidal dispersion is separated from a noncolloidal solution by a semipermeable membrane, that is, a membrane that is permeable to all species except the colloidalsized ones. Osmotic pressure difference across the membrane drives the separation. The solution containing the colloidal species is referred to as the retentate or dialysis residue. The solution that is free of colloidal species is referred to as the dialysate or permeate at equilibrium (no osmotic pressure difference), this solution is referred to as the equilibrium dialysate. See also Ultrafiltration. 

The Osmotic Pressure Model, as shown in (3.6), is an equivalent description for macromolecules according to Wijmans et al. (1985). AfT is the osmotic pressure difference across the membrane. 

The Irreversible Thermodynamics Model (Kedem and Katchalsky (1958)) is founded on coupled transport between solute and solvent and between the different driving forces. The entropy of the system increases and free energy is dissipated, where the free energy dissipation function may be written as a sum of solute and solvent fluxes multiplied by drivir forces. Lv is the hydrodynamic permeability of the membrane, AII v the osmotic pressure difference between membrane wall and permeate, Ls the solute permeability and cms the average solute concentration across the membrane. 

Plant and prokaryotic cells are surrounded by a rigid cell wall that protects them against osmotic stress, but eukaryotic cells exist in vivo in tissues where the extracellular medium has very similar osmolarity to that inside the cells thus there is normally no net osmotic pressure difference across the plasma membrane. 

An interesting comparison is the variation in the solvent flux for the two different systems under exactly the same conditions 40 bar, 0.33 M, and cell flow rate 120-150 L h . The toluene flux in the docosane-toluene system is 20.7 L m h and in the TOABr-toluene system is 36.7 L m h. This is in spite of the higher viscosity and lower mass transfer in the TOABr-toluene system. Thus it can be seen that the nonideaUty of the TOABr-toluene system actually assists the filtration process by reducing the osmotic pressure difference across the membrane and thus allowing a higher flux. 

The osmosis phenomenon, stemming from biological systems with biological semipermeable membrane, initially represents a nature net transport of solvent molecules from a region of higher water chemical potential (e.g., dilute solution) to a region of lower water chemical potential (e.g., concentrate solution). The driving force is the pure chemical potential difference, i.e., osmotic pressure difference, across the membrane. 

Equation 20 evidently shows that when the imposed pressure difference is equal to half of the effective osmotic pressure difference across the membrane, the power density reaches its maximum value, namely. 

The driving force depends upon the type of membrane separation. For gas permeation the driving force is the difference in partial pressure of the transferring species across the membrane. For RO the driving force is the pressure difference minus the osmotic pressure difference across the membrane. For UF the driving force is the same as for RO, but this usually simplifies to the pressure difference across the membrane since osmotic pressures are small. These driving force effects are specific to each membrane separation and are discussed in more detail in the later sections. 

The driving force for solvent flux in RO is the difference between the pressure drop across the membrane and the osmotic pressure difference across the membrane (Ap - An). Then the mass flux of solvent is... 

The flux equations also allow some characteristic coefficients to be derived. When there is no osmotic pressure difference across the membrane (An = 0 => c, = C2 or Ac = 0), eq. V - 29 indicates that a volume flow occurs because of a pressure difference (AP). This flow can be described as ... 

In practice, the membrane may be a little permeable to low molecular solutes and hence the real osmotic pressure difference across the membrane is not An but c An, where o is the reflection coefficient of the membrane towards that particular solute (see also chapter V). When R < 100%, then o < 1 and eq. VI - 21 now bwomes... 

Here, AP is the hydraulic pressure difference and An the osmotic pressure difference across the membrane. The vdue of An is determined by the concentration at the membrane surface c, and not by the bulk concentration Cj,. 

Strength O.6., as well as the schematic representation of the liposome at each time. First, liposomes condensed into a non-spherical shape at 24 min after exchange, and then showed an outward protrusion of the liposome membrane at 30 min. This deformation is due to an osmotic pressure difference across the liposome membrane because of a difference in the MES concentration through the semipermeability liposome membrane. 

---