Stack potential, equation

The linear and slower decrease of stack potential with current shown in Fig. 3.5 can be simply explained with the Ohm s law, then the voltage losses due to this effect are described by the following equation ... 

Analysis of equations The length of mirroring Equation for stack potential... 

Physically, the transition from Eq. (5.158) to Eq. (5.162) or Eq. (5.165) means that the distribution of individual cell potentials stepwise along 2 is replaced by the smooth stack potential V)j. Note that in Eq. (5.162) the resistivities Rp are not smoothed they form a layered structure (Figure 5.19). Each cell is characterized by its own Rp x, y) and the adjacent cells are separated by BPs with the constant resistivity Rp (Figure 5.19). In the general case, (5.162) is the equation with the stepwise coefficient CiRp/Rp-. along the first module BP + MEA this coefficient is C Rp/Ri, and along the second module it is etc. 

Equations (5.172) mean symmetry at f = 0 and the absence of normal current through the side surface of the stack, respectively. Equations (5.173) describe the disturbance of potential at 2 =0 and the decay of this disturbance at large distance. We assume that the damping length is much smaller than the stack length. 

As stated earlier the C value in micropores will be large due to the overlapping wall potentials. Under these circumstances, the surface Will be covered well over 90% by stacks of adsorbate not in excess of two molecules in depth as shown by equation (4.45) and Table 4.1. Therefore, the close proximity of the walls offer no special condition which is not already allowed for by the BET theory. 

The role of thermal fluctuations for membranes interacting via arbitrary potentials, which constitutes a problem of general interest, is however still unsolved. Earlier treatments G-7 coupled the fluctuations and the interaction potential and revealed that the fluctuation pressure has a different functional dependence on the intermembrane separation than that predicted by Helfrich for rigid-wall interactions. The calculations were refined later by using variational methods.3 8 The first of them employed a symmetric functional form for the distribution of the membrane positions as the solution of a diffusion equation in an infinite well.3 However, recent Monte Carlo simulations of stacks of lipid bilayers interacting via realistic potentials indicated that the distribution of the intermembrane distances is asymmetric 9 the root-mean-square fluctuations obtained from experiment were also shown to be in disagreement with this theory.10... 

We have obtained the useful equation for the potential energy between the single atom or molecule and the lattice plane. Now we turn to the case whereby the solid is composed of stacked lattice layers, which we hereafter call it slab (Figure... 

The system of equations (5.142) and (5.149) written for all cells and BPs determines cell currents and BP potentials in the stack. Iterations are required to find the self-consistent distribution of currents and potentials. Starting from uniform potentials we calculate cell currents using Eqs (5.155) and (5.153), as described in the previous section. These currents are then used to calculate new BP potentials with Eq. (5.142). This procedure is repeated until convergence is achieved. 

The most computationally intense procedure is a solution of the 2D Poisson equation (5.142). The algorithm of stack simulation can thus be effectively parallelized each stack module cell - - BP can be solved on a separate processor. Upon completion of an iteration step, adjacent modules exchange with the information (the cell currents and BP potentials) required for the next iteration. 

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