In the first step, gas is adsorbed from adjacent space at the outer membrane surface at Ra [m] (outer membrane radius). Once the gas molecule is adsorbed, desorption or absorption will occur depending on the energetics of selleck chem Trichostatin A the surface. Absorption (which is considered as dissolution process) is the rate limiting step compared to the fast adsorption process. Inside the membrane the gas molecules diffuse according to the concentration gradient along the membrane radius. Its flux density j (r,t) [mol/m2/s] is described by Fick’s first law j(r,t) = ?D ? C (D [m2/s] �C diffusion coefficient of gas, r [m] �C radius, t [s] �C time). If the gas molecules reach the inner membrane surface at Ri [m] (inner membrane radius), the mass transfer proceeds in reverse order: gas leaves the membrane phase and is subsequently desorbed into the gas phase.

Since both the adsorption-desorption processes and the gas diffusion processes outside the membrane are fast compared to the diffusion process within the solid membrane phase, an adsorption-desorption equilibrium and constant concentrations in both adjacent gas spaces can be assumed.At sufficiently Inhibitors,Modulators,Libraries low concentrations, the generally non-linear adsorption isotherm can be approximated by a linear Henry isotherm C|Ra = Sa pa ��a /(RT) where C|Ra [mol/L] is surface concentration at the membrane, pa [Pa] denotes gas pressure in the external space (index ��a��), xa [mol/mol] is the unknown mol fraction of gas and Sa [m3(gas)/m3(membrane)] is solubility of the gas in the membrane which is related to the dimensionless inverse Henry constant (R = 8.

3145 Inhibitors,Modulators,Libraries J/K/mol �C gas constant, T [K] �C temperature). The corresponding boundary condition for the interior Inhibitors,Modulators,Libraries space (index ��i��) is given by C|Ri = Si pi ��i /(RT) Furthermore, we only consider symmetrical membranes so that: S = Si = Sa. For constant boundary conditions a dynamic equilibrium will be establish. Near this steady state the gas flow 2��?r?L?j (r) [mol/s] through the membrane will be constant (L [m] �C length of the tubular membrane). Assuming that both the solubility and the diffusion coefficient are independent of the concentration, the number of moles dv that permanently permeate the membrane in the time dt is:d��=PpaRT2��?Lln(Ra/Ri)(��a?�æ�i)?dt,(1)where the material parameter Inhibitors,Modulators,Libraries P = SD [m2/s] is called permeability and �� = pi/pa is the ratio of gas pressures inside and outside the membrane tube.

Using the ideal gas law V0 (p0 + dp) = p0 (V0 + dV) = RT (v0 + dv) where Drug_discovery V0 [m3] is the volume, p0 [Pa] is the pressure, and v0 [mol] the number of moles inside the measuring membrane tube (index ��0�� indicates the initial state) one can substitute v0 in Equation (1) to obtains two measurable quantities: the volume change for isobaric conditions (dV = RT/p0?dv) and the equivalent pressure change (dp = RT/V0?dv) for isochoric conditions.2.2. Multi Gas AnalysisDifferent measurement methods can be used Perifosine molecular weight to determine this change of pressure or volume.