Boundary conditions cylindrical pore model

Simulations of water in synthetic and biological membranes are often performed by modeling the pore as an approximately cylindrical tube of infinite length (thus employing periodic boundary conditions in one direction only). Such a system contains one (curved) interface between the aqueous phase and the pore surface. If the entrance region of the channel is important, or if the pore is to be simulated in equilibrium with a bulk-like phase, a scheme like the one in Fig. 2 can be used. In such a system there are two planar interfaces (with a hole representing the channel entrance) in addition to the curved interface of interest. Periodic boundary conditions can be applied again in all three directions of space. 

Further, Imdakm and Matsuura [61] have developed a Monte Carlo simulation model to smdy vapor permeation through membrane pores in association with DCMD, where a three-dimensional network of interconnected cylindrical pores with a pore size distribution represents the porous membrane. The network has 12 nodes (sites) in every direction plus boundary condition sites (feed and permeate). The pore length / is assumed to be of constant length (1.0 p,m), however, it could have any value evaluated experimentally or theoretically [62]. 

The unit cell and coordinates are illustrated in Figure 10.14(b). As with the array of microdiscs model, the unit cell is cylindrically symmetrical about an axis that passes through the centre of the pore, perpendicular to the electrode surface. The problem may thus be reduced from a three-dimensional one to a two-dimensional one. As with the microdisc electrode, this is a two-dimensional cylindrical polar coordinate system, and Pick s second law in this space is given by Eq. (9.6). The simulation space for the unit cell with its attendant boundary conditions is shown in Figure 10.15. 

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