A model for roughness statistics of heterogeneous fibrous materials

We present a theory giving the standard roughness metrics and of stochastic fibrous materials in terms of their porosity and the thickness of the constituent fibres. Our treatment shows also that and are linearly dependent on each other with gradient depending on the skewness of the surface depth profile. Comparison of our theory with experiments on laboratory-formed paper samples and with data from the literature for industrially manufactured paper and carbon fibre nonwovens for use in fuel cells is excellent. The theory has applicability to generic families of stochastic fibrous materials and has relevance, for example, to printing of devices on paper.