Abstract
AbstractWe perform numerical simulations of Stokes flow through ordered arrays of fibers of square cross‐section. The results for the permeability of single‐size‐fiber arrays are in very good agreement with the well‐known correlation of Jackson and James, provided that an effective radius of equivalent cylindrical fibers is used with the same cross‐sectional area. Then, we consider arrays of mixtures of different‐sized fibers and test several mixing rules, proposed for estimating the composite permeability. The two most well‐known, namely, the unweighted‐ and the volume‐averaged resistivity rules give good predictions for not too large size‐ratios, yet they systematically overestimate and underestimate the numerical results, respectively. Then, it appears almost self‐evident that a combination of the above two mixing rules would provide a better prediction. Indeed, the geometric mean gives excellent agreement with the numerical results over an extended range of size ratios and relative volume fractions.
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