Influence of mean distance between fibers on the effective gas thermal conductivity in highly porous fibrous materials

The paper considers the problem of definition of characteristic length parameter and Knudsen number in the calculation of the effective coefficient of thermal conductivity of highly porous fibrous materials. As the characteristic length it is proposed to use the parameter of average distance between fibers instead of the commonly used parameter of the average pore size. We introduced the technique for determining the average distance between fibers in the fibrous highly porous structures with different spatial orientation, volume content, diameter and length of fibers. The technique is based on the direct measurements of the distances between the fibers in representative volume elements (RVE) of fibrous structures. The requirements for the minimum size of the RVE are established. It is shown the convergence of the algorithm whenever we increase the number of measurements in various similar RVE of the same structure. We held the calculations of the average distance between the fibers in the three-dimensional isotropic structures with different volume content and diameter of the fibers. It is shown that the average distance between the fibers is always greater than the average pore size that determined on the basis of geometric methods or based on the known approximate analytical evaluations. It is proposed the modification of a simple analytical formula for the prediction of the average distance between the fibers in the highly porous structures. It is shown that the use of the parameter of average distance between fibers instead of the average pore size leads to the 2-3 times increase of the estimated gas effective thermal conductivity in the pores of the fibrous structure under low pressure.