The effective solubility coefficients
were then estimated using Eq.
In two-phase mixtures, such as 50% of octane and 50% of water, the ozone solubility coefficients
in both phases were close to each other, and for the whole range of the inlet ozone concentration in gas were equal to 0.25 [+ or -] 0.11 for water ([[alpha].sub.W]) and to 0.20 [+ or -] 0.10 for octane ([[alpha].sub.OCT]).
Table 1: Values of diameters and force constants ([epsilon]/k) of [C.sub.1]-[C.sub.4] hydrocarbon gases for the calculation of a solubility coefficient
The apparent gas diffusion and solubility coefficients
of the UV-cured membranes as a function of UV irradiation time are presented in Fig.
The solubility coefficients
, S, were then calculated from
Since permeation is a solution-diffusion process, the permeability, P, is the product of the diffusion and solubility coefficients
and can be expressed by the following equation:
[K.sub.H] = 3.61 x [10.sup.-5] mole [multiplied by] [N.sup.-1] [multiplied by] [m.sup.-1]
Equation 3 can be solved using the Newton-Raphson technique, and it shows that the equilibrium bubble size depends neither on the hydrodynamic nor the diffusional aspects of the bubble growth process, but rather on the initial conditions, temperature, final pressure, surface tension, gas molecular weight, and solubility coefficient
. For example, a polymer/gas system with the following parameters: [P.sub.sat] = [p.sub.g0] = 9.9 MPa: [P.sub.[infinity]] = 0.1 MPa; K = 0.164 [cm.sup.3] (STP) / g .
As the simplest practical cases of m = 2 and m = 3, with stepwise distribution of both diffusion coefficients and solubility coefficients
at the boundary between respective layers, the diffusion properties in the transient state are analyzed in detail.
In fact, while in certain cases, researchers ascribed the low permeability values to surprisingly low solubility coefficients
(14-18), in one case the low value of permeability was attributed to a low diffusion coefficient (19).
It uses an automated constant-volume sorption technique that provides the effective diffusion and solubility coefficients
independently in a single test.
On the other hand, the diffusion coefficients of gases in membranes often change less than the solubility coefficients
. Therefore, more condensable gases are more permeable through the PDMS membrane which is a rubbery polymer.