Long tortuosity factor

The reduction of the long-range diffusivity, Di by a factor of four with respect to bulk water can be attributed to the random morphology of the nanoporous network (i.e., effects of connectivity and tortuosity of nanopores). For comparison, the water self-diffusion coefficient in Nafion measured by PFG-NMR is = 0.58 x 10 cm s at T = 15. Notice that PFG-NMR probes mobilities over length scales > 0.1 /rm. Comparison of QENS and PFG-NMR studies thus reveals that the local mobility of water in Nafion is almost bulk-like within the confined domains at the nanometer scale and that the effective water diffusivity decreases due to the channeling of water molecules through the network of randomly interconnected and tortuous water-filled domains. ... 

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. 

This equation shows that wider pores with 9 greater than 90° would produce smaller capillary pressure. For tortilla chips, Moreira et al. (1997) showed that smaller pores led to higher fat uptake than bigger pores. Pores with an average radius of 1 pm are reported to have pressure equivalent to 1 atm. This implies that when pore radius is less than 1 pm, oil can be absorbed even if there is water vapor inside the pore (Mellema, 2003). The tortuosity and depth of pores are additional factors that determine the degree of oil uptake by capillary pressure, such that long and continuous pores would allow more oil absorption. 

Zhao and Benziger were able to determine the contribution of the tortuous network for water diffusion through Nafion. They determined the effective diffusion coefficient of water with the PGSE NMR method at short delay times, where the diffusion was limited by short-range molecular interactions. They also determined diffusion coefficients at long delay times, where diffusion allowed the molecules to move through the hydrophilic domain network. The ratio of these two diffusion coefficients is the tortuosity of the hydrophilic domains, which is shown in Fig. 10. Tortuosity decreases by more than a factor of ten as water activity increases. The tortuosity follows a similar trend with water activity as the free volume of water absorption. Tortuosity, free volume, and proton conductivity are related to the evolution of the connectivity of the hydrophilic domains. 

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