Membrane Henry coefficient

Yif Pi being valid for solutions of i. It must be noticed that the activity coefficient Yi f varies with the concentration of i in the feed soluhon. For dilute solutions of i the product Yif P is constant and may be described by the Henry coefficient. Hi. In vapor permeation the value of pn may be increased by compressing the feed vapor before processing it through the membrane unit. If the partial permeate pressure Pi -p of solute i is negligible in view of its partial feed pressure p f (but not necessarily when the total permeate pressure Pt is close to zero, as is often stated in the literature), then it follows that... 

Equation (9) illustrates that in comparison to the selectivity of a simple liquid-vapor equilibrium based on the ratio of the respective volatilities, here expressed in terms of the Henry coefficients of solutes i andj, respectively, the membrane introduces a further selectivity given by the ratio of the permeabilities of the respective compounds i andj (assuming all the above assumptions to be valid). In other words, whilst the driving force for solute transport is identical in processes based on the vapor-liquid equilibrium and in vapor permeation or pervaporation, the latter can exceed the vapor-liquid equilibrium selectivity whenever... 

Each term on the right side of Equation 4.2 represents an individual resistance. Hollow-fiber diameters are Henry coefficient (liquid-gas equilibrium constant) for the species in question. With liquid-liquid contact, the term H in Equation 4.2 should be replaced by OTd, the equilibrium distribution coefficient between the tube-side liquid and the shell-side liquid. The membrane transfer coefficient is a function of (1) the diffusion coefficient in the phase occupying membrane pores and (2) the various geometric parameters of the membrane. Assuming pure Eickian... 

The reciprocal value of the Henry coefficient is also denoted as gas solubility. For a given diffusion coefficient in the membrane material, the molar flux per unit cross-sectional area is ... 

If tire diffusion coefficient is independent of tire concentration, equation (C2.1.22) reduces to tire usual fonn of Pick s second law. Analytical solutions to diffusion equations for several types of boundary conditions have been derived [M]- In tlie particular situation of a steady state, tire flux is constant. Using Henry s law (c = kp) to relate tire concentration on both sides of tire membrane to tire partial pressure, tire constant flux can be written as... 

Permeability P, can be expressed as the product of two terms. One, the diffusion coefficient, reflects the mobility of the individual molecules in the membrane material the other, the Henry s law sorption coefficient, reflects the number of molecules dissolved in the membrane material. Thus equation 9 can also be written as equation 10. 

Permeation of gases in glassy polymers can also be described in terms of the dual sorption model. One diffusion coefficient (Do) is used for the portion of the gas dissolved in the polymer according to the Henry s law expression and a second, somewhat larger, diffusion coefficient (DH) for the portion of the gas contained in the excess free volume. The Fick s law expression for flux through the membrane has the form... 

In 1879, von Wroblewski showed that the solution of gases in rubber followed Henry s law, Eq. (1), and he defined an absorption coefficient as the lumber of cubic centimeten of gas measured at STP which dissdved in 1 cubic centimeter of rubber at one atmosphere pressure. Combining this with Pick s law, Eq. (2) he showed that the steady state permeation flux throu a membrane of thickness is given by Eq. (3) ... 

By inserting Henry s law (Equation 4.6) into Pick s law (Equation 4.1), integrating across the membrane and remembering the definition of the permeability coefficient (Equation 4.5), Equation 4.2 was developed as the standard equation for transport through a dense polymeric membrane. 

Membrane phase concentration of component i in the feed side, Cg, can be calculated from its bulk concentration by Henry s equation (Equation 5.8) provided it is present in trace amount in the feed solution. For higher concentration of component i, Cg can be obtained from experimental sorption data. Membrane phase concentration on the permeate side of component i, i.e., Cpi may be neglected due to the low pressure the activity of the component in the downstream side is very low. Thus, Equation 5.28 can be readily solved to calculate the theoretical flux and diffusion coefficient of i or j component employing any of the above equations relating the diffusion coefficient and concentration. Equations 5.14 through 5.25 depending on its best matching with the experimental data. 

Ki denotes overall mass-transfer coefficient (m/s) ki denotes liquid mass-transfer coefficient (m/s) kg denotes gas mass-transfer coefficient (m/s) feiji denotes membrane mass-transfer coefficient (m/s) H denotes Henry s constant... 

Here, the transport rates depend on the partition coefficient Kfp only. The solute concentration in the membrane can often be related to the gas phase partial pressure using Henry s law or a similar equilibrium relationship. At higher pressures, vapor-liquid equilibrium or gas-polymer absorption data are necessary to determine the concentration gradient in the membrane. 

Table 9.6 summarizes the relative ease of VOC separation using silicone rubber membranes in pervaporation mode. As the Henry s Law coefficient decreases, pervaporation becomes less selective and less competitive to other approaches, such as steam stripping. 

Class Henry s Law coefficient (atm/mole frac.) Solubility in water (wt%) Pervaporation separation factor with silicone rubber membranes Ease of separation by pervaporation Examples... 

Temperature influence is unanimously described as enhancing removal efficiency with higher temperature due to the increase in Henry s law constant and diffusion coefficient in water and the membrane material with temperature. An inhibiting effect on the removal efficiency with temperature is solely the decreasing sorption in the membrane material with increasing temperature [36,128-130]. 

On photolysis, co-polymers of vinyl(methylcymantrene) with octyl methacrylate have been shown to lose CO and generate polymers 45 possessing 16-electron Mn centers, which coordinate to N2 to yield 46 (Equation (16)). The coordination is reversible and can be used to prepare membranes that exhibit facilitated transport of this gas. Comparison of the diffusion coefficient for normal Henry-mode diffusion and the facilitated Langmuir-mode diffusion, due to the mediation of the manganese centers which function as N2 carriers, showed that the latter mechanism contributes substantially. Moreover, as expected for this interpretation, the contribution from the facilitated transport mode increased as the loading of the Mn sites became higher. 

The Henry s law constant is an important criteria in determining the extent to which an organic compound will distribute into the atmosphere from water and vice versa. Another important environmental process is the extent to which a compound will distribute into a hydrophobic region. It will be shown that soil organic matter controls sorption of organic compounds in soil, while movement into an organism involves passage across the hydrophobic barrier of the membrane. This tendency is indicated by the octanol-water partition coefficient, Xqw... 

Studies on the sorption of some hydrocarbons have shown that above the transition temperature of EBBA (331 K) the isotherms obey Henry s law and the solubility coefficients S can be calculated. The sorption and desorption curves are similar in shape which indicates that these systems follow Fickian sorption. This fact indicates that steady state surface equilibrium is reached and that the diffusion coefficient for hydrocarbons is a function of concentration only. It follows that the membranes containing 60 wt.% of EBBA are homogeneous from the view point of gas permeation at the temperature above transition in EBBA. The permeability coefficients P show a distinct jump in the vicinity of transition temperature from crystal to nematic phase. This phenomenon was observed for hydrocarbon gases, noble gases like He, and for inert gases like N2. 

Thus, in the simplest limiting case of a membrane-permeant system, one in which Henry s law and Pick s laws are observed, the coefficients of permeability P, solubility 5, and diffusion D are related as follows P = D x 5. 

The pure gas (99.99% or higher purity) transport properties were tested with an instrument (GKSS, Geesthacht, Germany) with eonstant permeate volume described elsewhere [14], The short response time of the instrument allows one to record transient permeation behaviours of less than 1 second. The pure gas permeability is the amount of gas permeating in the unit time, multiplied by the thickness of the membrane and normalized for the membrane surface and the pressure gradient. The recorded pressure vs. time plots were used to derive diffusion coefficients from the initial transient permeation, and permeability at the steady state. The time-lag 9 is the intercept of the linear part of the pressure vs. time curve with the axis of time. In a homogeneous membrane in which the solubility of a gas obeys Henry s law, its diffusion coefficient D can be calculated from the ratio ... 

The diffusion and permeabihty are closely interconnected with the solubility of a polymer. The permeation of the permeants through polymeric membrane film occurs in three stages (1) Sorption includes the initial adsorption, absorption, penetration, and dispersal of penetrant into the voids of the polymer membrane surface and cluster formation. The distribution of permeant in the membrane may depend on penetrant size, concentration, temperature, and swelling of the matrix as well as on time. The extent to which permeant molecules are sorbed and their mode of sorption in the polymer depends upon the enthalpy and entropy of permeant-polymer mixing, i.e., upon the activity of the permeant within the polymer at equilibrium. When both polymer-permeant and permeant-permeant interactions are weak relative to polymer-polymer interactions, i.e., dilute solution occurs, Henry s law is obeyed. The solubihty coefficient S is a constant independent of sorbed concentration at a given temperature. (2) Diffusion includes the transfer of the penetrant through the polymer membrane which depends on penetrant concentration that leads to a plasticization effect, penetrant size and shape, polymer Tg, time, and temperature. The diffusion coefficient is determined by Pick s first law of diffusion. (3) Desorption includes release of the penetrant from the opposite side of the membrane face. 

A porous poh propylene membrane with a thickness of 20 pm and a porosity of 50% is filled with w ater. Which is the fraction of the oxygen flux that permeates through the water. Henry s law constant of oxygen in water at 298 K is 3.3 10 mmHg and the diffusion coefficient of oxygen in water is 2.1 10 - em /s. The oxygen permeabilit) in polypropylene is P = 1.6 Barren... 

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