Constriction factor

In such a large column, the weir constriction factor (Figure 8-105) is not significant and is not applied to the above ho. ... 

One must be very careful in reviewing the older, and some more recent, literature in consideration of the tortuosity and constriction factors some work has attempted to separate these two factors however, more modem developments show that they cannot be strictly decoupled. This aspect will be particularly important when reviewing the barrier and tortuous-path theories of electrophoresis, as discussed later. 

Figure 26 shows plots of this constriction factor verses porosity for various values of L. As observed in Figure 21 for the Michaels model of diffusion in such a cell, the percolation limits are seen where the constriction factor goes to zero at = L/(l + L). 

It follows from a comparison of Eqs. 1.51 and 1.52 that in the calculation of the actual EOF mobility, the effect of tortuosity is taken into account so that peo, packed can be used to calculate the zeta potential of the packing. In the literature of electroki-netic phenomena in porous media [44], constriction factor is employed to describe the effect arising from the variability of cross-section along a given flow path. However, in packed CEC columns this factor is estimated to be in the range 0.93-1.0 and so may be neglected in the following treatment. 

The constriction factor accounts for the variation in the cross-sectional area that is normal to diffusion. It is a function of the ratio of maximum to minimum pore areas (Figure 12-2a).When the two areas, Aj andA2, are equal, the constriction factor is unity, and when P = 10, the constriction factor is approximately 0.5. 

Van Brakel, J. and Heertjes, P.M., Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor, Int. J. Heat Mass Transfer, 17 1093-1103, 1974. 

Here, we distinguish three different contributions due to water-filled pores in the ionomer (radius r, corresponding water volume portion e ,), micropores (radius r ), and mesopores (radius r )- is a constrictivity factor and t is a... 

In this expression, a percolation dependence is assumed in the mesopore space 5 is a constrictivity factor and t is a tortuosity factor (Dullien, 1979). 

Selection of appropriate values for the free p>arameters of PSO plays an important role in the algorithm s performance. In our study, the parameters setting is presented in Table 1, and the constriction factor j is determined by Eq.(6). The PSOt Toolbox (Birge 2003) was used for implementation of PSO. 

Particle Swarm Optimization (PSO) is a stochastic optimization method evolved from Swarm Theory and Evolutionary Computation [4]. It is instigated by animals natural swarming behavior [5]. PSO has been proven to be a suitable technique for solving various optimization problems [6, 7]. Among the advantages of PSO are that it allows efficient and rapid optimization of the problem, due to its parallel nature, it requires only basic mathematical operators for optimization and it provides low computational and memory costs for each iteration [8]. Many variants of the PSO algorithm exist, such as PSO with inertia weight [9], PSO with constriction factor [10], and mutative PSO [11]. 

For both algorithm, the constriction factor method was used. The values of and C2 were both set to 2.05 [14], since the values cannot violate the rule set in Eq. (7). Based on the values of and C2, the value of x equal to 0.7290 was used throughout the optimization course. 

R. C. Eberhart and Y. Shi, "Comparing inertia weights and constriction factors in particle swarm optimization," in Proc. Congress of Evolutionary Computation, San Diego, CA, 2000, pp. 84-88. 

Wasan et al. [12,13] discuss the tortuousity effect and define a constriction factor which they include to account for the varying cross-... 

---