On the theory of conductivity of anisotropic composites: A linear-concentration approximation of inclusions

Tracer diffusion inside fibrinogen layers

“…Such problems were investigated for several different geometries of inclusions. For small concentration of obstacles the diffusivity D of the system is well-described by the perturbative approaches [28,29], and its anisotropy vanishes (which corresponds to A = 1), as also seen in Fig.12.…”

“…If they are oriented, the final diffusion coefficient is anisotropic. As a measure of anisotropy the quotient of the values of diffusivity (or, otherwise of the MSD components) parallel and perpendicular to the orientation of obstacles [1,29] can be taken: A = D /D ⊥ , which changes in the interval 1 ≤ A ≤ ∞. The problem of finding the anisotropy of the diffusion coefficient in a system with obstacles is similar to the problem of finding the heat conductivity or the electric conductivity in similar settings.…”

Evaluation of Effective Heat Transport and Temperature Gradients in Thermally Anisotropic Particulate Arrangements

“…For example, the percolation threshold of a honeycomb lattice is 0.69, whereas, for a random closed packing, it is 0.27 . Percolation thresholds for different lattice types, with and without the influence of the local environment, have been calculated. ,, The percolation threshold is further affected by the intrinsic properties of the single constituents. , Several studies investigate the percolation behavior using components with elliptical particles, i.e., anisotropic shapes. ,, In addition, rod-like systems are the focus of current research. − …”

“…37,40,41 The percolation threshold is further affected by the intrinsic properties of the single constituents. 42,43 Several studies investigate the percolation behavior using components with elliptical particles, 44 i.e., anisotropic shapes. 42,45,46 In addition, rod-like systems are the focus of current research.…”

“…This enables the calculation of the conductivity for an isotropic system with noncircular inclusions. 43 Furthermore, an initially highly anisotropic composite becomes almost completely isotropic as the concentration of inclusions approaches the percolation threshold. 55,56 Another way to incorporate anisotropy in matrix-filler systems is based on a simple extension of an all-symmetric EMT.…”