Effective diffusivity in membranes with tetrakaidekahedral cells and implications for the permeability of human stratum corneum

The stratum corneum, the outermost layer of the skin, acts as the main barrier of human skin. This membrane consists of flat and thin corneocyte cells which are embedded into an intercellular lipid matrix. A previous study elucidated how tetrakaidekahedral-shaped cells influence the barrier properties of the membrane. It remained an open question whether the mathematical tools from homogenization theory can be applied to this case. We show (i) how the method of asymptotic expansion can be used to homogenize membranes consisting of tetrakaidekahedral-shaped cells and calculate the effective diffusivity. Furthermore, numerical results confirm that (ii) the resulting tensor is of diagonal shape, and (iii) the transversal and lateral diffusivity can be described uniformly with different coefficients.