Transient aqueous pores

Figure 5. Theoretical estimate of the transport of propidium iodide (Pi) across an artificial planar bilayer membrane. The molecule was treated as a circular disk with charge zs = +2. Only transient aqueous pores are used in this version of the model Future versions should include metastable pores and estimates of the contributions of diffusion and convection.

Weaver JC, Powell KT, Mintzer RA, Ling H, Sloan SR (1984) The electrical capacitance of bilayer membranes the contribution of transient aqueous pores. Bioelectrochem Bioenerg 12 393-412... 

As organic and aqueous phases are macroscopically separated by the membrane, HFM offer several hydrodynamic advantages over other contactors, such as the absence of flooding and entrainment, or the reduction of feed consumption (160, 161). The flowsheets tested in HFM were similar to those developed for centrifugal contactor tests. Computer codes based on equilibrium (162) and kinetics data, diffusion coefficients (in both phases and in the membrane pores), and a hydrodynamic description of the module, were established to calculate transient and steady-state effluent concentrations. It was demonstrated that, by selecting appropriate flow rates (as mass transfer is mainly controlled by diffusion), very high DFs (DI A 11 = 20,000 and DFrm = 830) could be achieved. Am(III) and Cm(III) back-extraction efficiency was up to 99.87%. 

In a third paper by the Bernard and Holm group, visual studies (in a sand-packed capillary tube, 0.25 mm in diameter) and gas tracer measurements were also used to elucidate flow mechanisms ( ). Bubbles were observed to break into smaller bubbles at the exits of constrictions between sand grains (see Capillary Snap-Off, below), and bubbles tended to coalesce in pore spaces as they entered constrictions (see Coalescence, below). It was concluded that liquid moved through the film network between bubbles, that gas moved by a dynamic process of the breakage and formation of films (lamellae) between bubbles, that there were no continuous gas path, and that flow rates were a function of the number and strength of the aqueous films between the bubbles. As in the previous studies (it is important to note), flow measurements were made at low pressures with a steady-state method. Thus, the dispersions studied were true foams (dispersions of a gaseous phase in a liquid phase), and the experimental technique avoided long-lived transient effects, which are produced by nonsteady-state flow and are extremely difficult to interpret. 

The rate of transmembrane diffusion of ions and molecules across a membrane is usually described in terms of a permeability constant (P), defined so that the unitary flux of molecules per unit time [J) across the membrane is 7 = P(co - f,), where co and Ci are the concentrations of the permeant species on opposite sides of membrane correspondingly, P has units of cm s. Two theoretical models have been proposed to account for solute permeation of bilayer membranes. The most generally accepted description for polar nonelectrolytes is the solubility-diffusion model [24]. This model treats the membrane as a thin slab of hydrophobic matter embedded in an aqueous environment. To cross the membrane, the permeating particle dissolves in the hydrophobic region of the membrane, diffuses to the opposite interface, and leaves the membrane by redissolving in the second aqueous phase. If the membrane thickness and the diffusion and partition coefficients of the permeating species are known, the permeability coefficient can be calculated. In some cases, the permeabilities of small molecules (water, urea) and ions (proton, potassium ion) calculated from the solubility-diffusion model are much smaller than experimentally observed values. This has led to an alternative model wherein permeation occurs through transient hydrophilic defects, or pores , formed by thermal fluctuations of surfactant monomers in the membrane [25]. 

Rodriguez, N., Cribier, S., and Pincet, F. (2006) Transition from long- to short-lived transient pores in giant vesicles in an aqueous medium. Physical Review E, 74 (6), 061902. 

Transient Displacement. Experimental displacement results for the simultaneous injection of aqueous surfactant solution and nitrogen into a core initially saturated with a surfactant solution are shown in Figures 12 and 13. Darcy velocities relative to the exit pressure of 4.8 MPa are 0.43 m/day (1.4 ft/day) for gas and 0.046 m/day (0.15 ft/day) for liquid yielding a gas fractional flow or foam quality of 90%. Figure 12 provides the transient liquid saturation profiles. Experimental data points are connected by dashed lines. Time is expressed nondimensionally in pore volumes, PV, which is the ratio of total volumetric flow rate (at exit pressure) multiplied by elapsed time and divided by the void volume of the core. 

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