Permeability constants, definitions

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 ... 

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) ... 

Definition of Kerr Constants. In the presence of an external electric field E, the electric pemuttivity e( ) and magnetic permeability n(E) become functions of the field strength. As a consequence the refractive index n also depends on E ... 

Measurements are usually made after stationary state conditions have been established, i.e. the rate of loss or gain in weight has become constant. A quantitative estimate of the transport characteristics of the system may be made on the basis of the well known diflEusion equations. The equations which form the basis of the quantitative study of linear diflEusion processes and from which the definitions of diflEusion and permeability are derived are... 

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... 

The scaled surface area and its variation with d> are of crucial importance in the definition and evaluation of the osmotic pressure , H, of a foam or emulsion. We introduced the concept in Ref 37, where it was referred to as the compressive pressure , P. It has turned out to be an extremely finitful concept (22,27,38). The term osmotic was chosen, with some hesitation, because of the operational similarity with the more familiar usage in solutions. In foams and emulsions, the role of the solute molecules is played by the drops or bubbles that of the solvent by the continuous phase, although it must be remembered that the nature of the interaetions is entirely different. Thus, the osmotic pressure is denned as the pressure that needs to be applied to a semipermeable, freely movable membrane, separating a fluid/fluid dispersion from its continuous phase, to prevent the latter from entering the former and to reduce thereby the augmented surface free energy (Fig. 4). The membrane is permeable to all the components of the continuous phase but not to the drops or bubbles. As we wish to postpone diseussion of compressibility effects in foams until latter, we assume that the total volume (and therefore the volume of the dispersed phase) is held constant. 

In aerosol van der Waals forces, the central role played by the material properties of both the particle and whatever it interacts with is clearly illustrated in the above considerations where the polarizability or electric susceptibility a and the dielectric constant (or permeability) e are used alternatively. Provided that a represents the material s susceptibility, not the molecular polarizability, the usual definition... 

As a result of this definition, the fundamental constant magnetic field constant po (also known as the permeability of free space) is fixed at exactly 4 tx10- N/a2. 

Permeability is defined as the product of the diffusion constant and the solubility coefficient. Water vapor permeability (WVP] is defined as the time rate of water vapor transmission through unit area of flat material with a definite unit thickness induced by unit vapor pressure difference between two specific surfaces, and under indicated temperature and humidity conditions. (ASTM E 96, Standard Test Method for Water Vapor Transmission of Materials]. 

A different representation makes use of the definition of effective permeabilities or effective rate constants (cf. general treatment in Section 6.7). Whereas the values, which are proportional to the exchange cmrent densities, denote the ratio... 

The definition given in Equation D.9 also includes the value of/cM in terms of the permeability of free space, Mo- The unit for charge in the SI unit system becomes I [As] and is defined as the coulomb [Gj. Using Equation D.6, the proportionality constant in Equation D.4 becomes ... 

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