Permeability coefficient definition

A system with clearly defined disperse (A) and continuous (B) component phases is afforded by copolymers of styrene (A) grafted onto a polydimethyl siloxane matrix (B)101 Lack of appreciable interaction between the components was indicated by gas solubility and Tg measurements. The permeability coefficient of propane and other paraffins over a composition range vA = 0 — 0.55 followed the trend described by Eqs. (30)—(33) (with PA = 0, in view of the fact that the polystyrene phase is practically impermeable). Of particular relevance to the present discussion is the close agreement with the Bruggeman, and definite deviation from the Bottcher, equations at higher vA (cf. Fig. 11). Corresponding block copolymer membranes with vA = 0.34 also fitted into this pattern, except in one case where the structure was found to be lamellar and P was considerably lower. 

The dimensionless partition coefficient K = cp/cl = Sr, also known as a relative solubility coefficient, is defined as the ratio of the concentration of a substance in the polymer cP to that in the liquid (food) cLat equilibrium. While D is practically independent of the liquid phase in contact with the polymer in these measurements, the K values are determined by the nature of the polymer and liquid contact phases. From the definition Sr = K, a relative peremeability coefficient can be calculated, Pr = Sr D, with the dimension D. Here, accordingly to Eq. (9-2) and the solubility constant in the polymer and in the liquid phases expressed as SP = cP/p and Sl = C Jp, respectively, the following relationship results between the absolute and relative permeability coefficients ... 

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. 

Table 1 includes additional mathematical definitions of effective membrane permeability coefficient for various transport mechanisms. 

Alternative definitions for the permeability coefficients have been utilized in Eqs. (12.13) and (12.14) for the purpose of explicitly representing the dependence on membrane thickness h and viscosity x. They are related to their counterparts in Eqs. (12.9) and (12.10) ... 

How would a 40 A thick layer of lipid molecules comprise a barrier to solute diffusion Consider now Fig. 2, which represents a lipid phase separating two aqueous phases and acting as a permeability barrier between those two phases. The net flux of molecules from side 1 to side 2 of this barrier is v and, from the definition of permeability coefficient given above, is given by... 

For membrane reactors, many cmcial phenomena have to be included, as membrane permeability mechanism and hydrogen flux, reactions kinetics, heat and mass transport inside the reactor and from the external to the reactor. Therefore, a proper simulation certainly requires a deep study and a careful evaluation and definition of the system. The model developers have to work in a strict connection with test drivers, since reliable model parameters and coefficients definition is crucial designers can address reactors experimentation clarifying which information from test-benches are required. At the same time, a proper model development allows the number of experimental tests to be reduced drastically to those ones required for a complete reactor vahdation. 

The driving force of a membrane for gas separation is the pressure difference across the membrane. The yield of the separated gas can be expressed in terms of membrane permeance, which can be characterised by the amount of permeated gas that passes through a certain membrane area in a given time at a definite pressure difference. The values of permeability are often quoted in Barter (1 Barter=10 cm s cm cm Hg = 3.35 x 10 mol m m s Pa STP, standard temperature and pressure). Gas permeation phenomena can be described by a simple solution diffusion model, which involves (l) sorption or dissolution of the permeating gas in the membrane at the higher pressure side, (2) diffusion through the membrane and (3) desorption or dissolution at the lower pressure side. Thus, the permeability coefficient P can be determined by the product of the solubility coefficient S and the mutual diffusion coefficient D [eqn (5.1)] ... 

Polyethylene terephthalate) (PET), with an oxygen permeability of 8 iiiuol/(ius-GPa), is not considered a barrier polymer by die old definition however, it is an adequate barrier polymer for holding carbon dioxide in a 2-L bottle for carbonated soft drinks. The solubility coefficients for carbon dioxide are much larger than for oxygen. For the case of the PET soft drink bottle, the principal mechanism for loss of carbon dioxide is by sorption in the bottle walls as 500 kPa (5 atm) of carbon dioxide equilibrates with the polymer. For an average wall thickness of 370 pm (14.5 mil) and a permeabdity of 40 nmol/(m-s-GPa), many months are required to lose enough carbon dioxide (15% of initial) to be objectionable. 

Partition coefficient, 9, 10 Partition ratio, 11 time optimization of, 57-58 Peak, definition of, 69 Peak capacity, 18, 19 Pellicular supports, 157 Permeability, 63-64 Phase selection diagrams, 218-219 Phase volume ratio, 11 Pinkerton (ISRP) columns, 225-226 Plate height, 17 Plate number, 14-16 Plate theory, 3, 28 Polarity index, 210, 211 Pore size of LC supports, 157 Porosity, 27 Precision, 99-100 Preparative scale ... 

As for the permeability measurements, most techniques based on the analysis of transient behavior of a mixed conducting material [iii, iv, vii, viii] make it possible to determine the ambipolar diffusion coefficients (- ambipolar conductivity). The transient methods analyze the kinetics of weight relaxation (gravimetry), composition (e.g. coulometric -> titration), or electrical response (e.g. conductivity -> relaxation or potential step techniques) after a definite change in the - chemical potential of a component or/and an -> electrical potential difference between electrodes. In selected cases, the use of blocking electrodes is possible, with the limitations similar to steady-state methods. See also - relaxation techniques. 

The following symbols are used in the definitions of the dimensionless quantities mass (m), time (t), volume (V area (A density (p), speed (u), length (/), viscosity (rj), pressure (p), acceleration of free fall (p), cubic expansion coefficient (a), temperature (T surface tension (y), speed of sound (c), mean free path (X), frequency (/), thermal diffusivity (a), coefficient of heat transfer (/i), thermal conductivity (/c), specific heat capacity at constant pressure (cp), diffusion coefficient (D), mole fraction (x), mass transfer coefficient (fcd), permeability (p), electric conductivity (k and magnetic flux density ( B) ... 

The Dykstra-Parsons coefficient is a normalized measure of the spread of a permeability distribution that is bounded between zero and one. The formal definition is... 

Beginning with the definition of permeability in Eq. (20.1-3), one can proceed without the simplifying assumption in Eq. (20.1-5) that the diffusion and soiptkm coefficients are constants. In this case we find... 

A closer inspection of the definition of membrane permeability suggests additional methods to correlate the permeability with other properties of the diffusing species. The permeability, called or P, is related to the equilibrium partition coefficient, K, the diffusion coefficient in the membrane, D, and the thickness of the membrane, L ... 

By extending our definition of a membrane, we can include liquids. If we view a membrane as a semlpermeable barrier between two phases, then an immiscible liquid can serve as a membrane between two liquid or gas phases. Different solutes will have different solubilities and diffusion coefficients In a liquid. The product of these two terms is a measure of the permeability. A liquid can yield selective permeabilities and, therefore, a separation. Because the diffusion coefficients in liquids are typically orders of magnitude higher than in polymers, a larger flux can be obtained. 

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