Separators tortuosity factor

With increasing tortuosity factor T and lower porosity P, R increases sharply. The electrical resistance of a separator is proportional to the thickness d of the membrane and is subject to the same dependence on temperature or concentration as... 

Influence on Electrolyte Conductivity In porous separators the ionic current passes through the liquid electrolyte present in the separator pores. Therefore, the electrolyte s resistance in the pores has to be calculated for known values of porosity of the separator and of conductivity, o, of the free liquid electrolyte. Such a calculation is highly complex in the general case. Consider the very simple model where a separator of thickness d has cylindrical pores of radius r which are parallel and completely electrolyte-filled (Fig. 18.2). Let / be the pore length and N the number of pores (all calculations refer to the unit surface area of the separator). The ratio p = Ud (where P = cos a > 1) characterizes the tilt of the pores and is called the tortuosity factor of the pores. The total pore volume is given by NnrH, the porosity by... 

Tortuosity. Tortuosity is the ratio of mean effective capillary length to separator thickness. The tortuosity factor, r of a separator can be expressed... 

This parameter is widely used to describe the ionic transport by providing information on the effect of pore blockage. A tortuosity factor r = 1, therefore, describes an ideal porous laody with cylindrical and parallel pores, whereas values of r > 1 refer to more hindered systems. Higher tortuosity is good for dendrite resistance but can lead to higher separator resistance. 

The definition of tortuosity factor in Eq. 3.5.b-2 includes both the effect of altered diffusion path length as well as changing cross-sectional areas in constrictions for some applications, especially with two-phase fluids in porous media, it may be better to keep the two separate (e.g., Van Brakel and Heertjes [39]). This tortuosity factor should have a value of approximately 3 for loose random pore structures, but measured values of 1.5 up to 10 or more have been reported. Satterfield [40] states that many common catalyst materials have a t 2 3 to 4 he also gives further data. 

The macropores are not straight cylinders but bounded with changing widths and sometimes narrow slits or dead-end pores. Therefore, a tortuosity factor is introduced in the balance equations. Principally speaking, the tortuosity factor should be dependent only on the inner geometry of the adsorbent pellet but not on operation parameter of fluid properties such as the pressure, the temperature, the density, the viscosity, or the molar fluxes of the components. However, this is not true for some publications because of the difficulty to clearly separate the contributions from the particle porosity Sp and the Knudsen diffusion. Therefore, the tortuosity factors published in the literature are often greater than 3 up to 6 which can be expected due to the inner structure of the porous material. 

Experiments on the separation of CO2 from CH4 by the supported liquid membranes containing aqueous amines such as monoethanolamine, diethanolamine and ethylenediamine hydrochloride were performed, and tfie data were discussed quantitatively on the basis of facilitated transport theory. The effects of the chemical properties of amines such as the reaction rate constant and chemical equilibrium constant and also the effect of the CO2 partid pressure on the permeation rate of CO2 could be interpreted by the proposed theory. It was propos to use L as the effective diffusional path length in the calculation of the facilitation factor, where L is the membrane thickness and x is the tortuosity factor of the microporous support membrane. The permeation rates of CH4 was found to provide useful information for evaluating the solubilities of CO2 in the reactive membrane solutions. 

In Equation 4.1, the tortuosity factor (T) is given for different separator types, and d is the thickness of the substrate in the direction that is perpendicular to the electrode surface [6]. The path length of the pore (L) can only be equal to or larger than the value of d. The larger the tortuosity factor, the more deviations in the path length of the pore as compared to the distance of the substrate thickness. 

Table 10,1 Contributions to ASR for a Rise-type anode-supported cell (Nl-YSZ/YSZ/tSM-YSZ) at 8S0°C tested in a plug flow-type configuration at S and 8S% fuel utilisation (FU). Rehji is calculated using a specific conductivity of YSZ of 0.045 S/cm, Sconnect is an estimation, Rp.eichem is the sum of typical anode and cathode polarisation resistances measured in separate electrode experiments, Rp.aiff is calculated using a diffusion coefficient of 10 cm /s, 30% porosity, a tortuosity factor of 3 and a thickness of 0.1cm, and fip,conver is Calculated using Eq. (10) with i = 0,5 A/cm ...

Due to the visualization of a porous medium as an ensemble of large dust molecules in the Dusty G ls Model pore structure properties such as porosity, tortuosity, and pore size distribution are not directly included. All information on pore structure characteristics is contained in the permeability constants Co, Ci, and Ca. Heteroporosity as originating from a wide pore size distribution is not accounted for specifically. On the other hand the Dusty Gas Model has the etdvantage to allow a separation of the influence of pore structure characteristics on the different transport mechanisms. The influence of the adsorbent material pore structure on gas phase mass transport is incorporated through the parameters Co, Ci, and C2 resp. They are determined by flux experiments for the specific adsorbent material (refs. 4, 6). The values for the different trstructural parameters such as representative pore diameter dp, porosity p, and tortuosity factor Tp by the expressions ... 

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. 

Diffusion Through Separators Like current flow, the diffusion of dissolved components through separators will be delayed by decreasing porosity and increasing tortuosity. The attenuation factor of diffusion, 8d (= DID f), usually coincides with that of conduction. 

The tortuosity is also included in the geometric factor to account for the tortuous nature of the pores. It is the ratio of the path length which must be traversed by molecules in diffusing between two points within a pellet to the direct linear separation between those points. Theoretical predictions of r rely on somewhat inadequate models of the porous structure, but experimental values may be obtained from measurements of De, D and e. 

Way, Noble and Bateman (49) review the historical development of immobilized liquid membranes and propose a number of structural and chemical guidelines for the selection of support materials. Structural factors to be considered include membrane geometry (to maximize surface area per unit volume), membrane thickness (<100 pm), porosity (>50 volume Z), mean pore size (<0.1)jm), pore size distribution (narrow) and tortuosity. The amount of liquid membrane phase available for transport In a membrane module Is proportional to membrane porosity, thickness and geometry. The length of the diffusion path, and therefore membrane productivity, is directly related to membrane thickness and tortuosity. The maximum operating pressure Is directly related to the minimum pore size and the ability of the liquid phase to wet the polymeric support material. Chemically the support must be Inert to all of the liquids which It encounters. Of course, final support selection also depends on the physical state of the mixture to be separated (liquid or gas), the chemical nature of the components to be separated (inert, ionic, polar, dispersive, etc.) as well as the operating conditions of the separation process (temperature and pressure). The discussions in this chapter by Way, Noble and Bateman should be applicable the development of immobilized or supported gas membranes (50). 

The item here called a conductivity factor has various names— permeability, diffusivity, etc.— that sometimes emphasize the host material (e.g., permeability of sandstone ) and sometimes emphasize the traveling material (e.g., diffusivity of hydrogen ). The factor in reality always depends on both host and traveler it is a property of the transport situation as a whole. Sometimes it is useful to separate out two components such as mobility of the diffuser and tortuosity of the matrix but for present purposes we shall stay with a single comprehensive factor. The terms permeability and diffusivity may be used from time to time, but we shall try to maintain the view that any conductivity factor is acceptable, under whatever name, as long as its units are clearly in view. 

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