An analytical model for gas diffusion though nanoscale and microscale fibrous media

Significance Statement

Nanofibrous and microfibrous materials such as electrospun fibers are good candidates for breathable protective clothing due to high moisture diffusivity and convective resistance. In general, moisture diffusion slows when diffusive molecules must follow tortuous pathways in randomly layered electrospun fibers. Moreover, the diffusion of molecules is hindered due to their frequent collisions with the solid wall of fibers. When the path size is much larger than the mean free path of molecules (λ), molecule-molecule collisions predominate and the diffusion coefficient is close to a constant. When the path size is comparable with λ , however, molecule-wall collisions increase and Knudsen diffusion occurs with the diffusivity decreasing with the decrease in path size. Therefore, the diffusion mechanism is dependent on the path size and the tortuosity of the random pathways.

We employ fractal theory to overcome the challenge of predicting the size-dependent diffusivity of electrospun fibers with random and complex geometry. Microstructures of disordered fibrous media can be described by fractal geometry, analogous to a class of natural objects such as rivers, coastlines, and lakes. They are randomly generated and difficult to describe using Euclidean geometry with integer dimensions 0-3. Nevertheless, these objects are observed to demonstrate statistically self-similar patterns, or fractal. A fractal object is always related to the length scale by a power law, where  is the fractal dimension, which can take non-integer values; M(l) can be a quality, or length, or volume, or area of the object, and  is the length scale.

M(l) ∞ lD


The pore size distribution and the tortuosity of pores, which are the integration of various structural parameters such as fiber orientation and disorder of fiber distribution, are well characterized by fractal geometry. Our model is verified by effective diffusivities measured by an inverted-cup method and those reported in the literature for carbon fiber gas diffusion layers in fuel cells. As well, structural parameters such as fiber radius and porosity are analyzed. In particular, electrospun fibers are found to be less diffusive than, but in the same magnitude as, nonwoven microfibers due to Knudsen diffusion in nanoscale pores. However, electrospun fibrous nets are much thinner and lighter. Thus, we show here in a model and an experiment that a thin item of electrospun protective clothing with a very high convective resistance can be as breathable as commercial microfiber nonwovens.

analytical model gas diffusion though nanoscale and microscale fibrous media - advances in engineering








Journal Reference

Microfluidics and Nanofluidics,  2014, Volume 16, Issue 1-2, pp 381-389.

Dahua Shou, Jintu Fan, Maofei Mei, Feng Ding.

1. Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong and

2. Centre for Advanced Materials Technology (CAMT), School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW, 2006, Australia and

3. Department of Fiber Science and Apparel Design, College of Human Ecology, Cornell University, Ithaca, NY, USA.


Gas diffusion in nanofibrous and microfibrous materials is of great interest in microfluidics. In this work, an analytical model is proposed, based on fractal theory, to quantify gas diffusion across fibrous media composed of nanofibers and microfibers. The fractal model is expressed in terms of pore area and tortuosity fractal dimensions, allowing statistical quantification of the geometrical structures of fibrous media. Knudsen diffusion in nanoscale pores is considered. To validate this model, moisture vapor diffusion rate through electrospun nanofibrous webs was measured using the inverted-cup method. The diffusivities predicted from the proposed model agree well with the experimental measurements in the present investigation and those reported in the literature for effective diffusivities of gas diffusion layers in fuel cells. Based on the model, the effect of porosity, fiber radius, and the ratio between the minimum and the maximum pore sizes on the effective diffusivity is analyzed.

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