Thermal properties of composite two-layer systems with a fractal   inclusion structure
  In this work, we study the thermal transport properties of platelike composite two-layer samples made of polyester resin and magnetite inclusions. By means of photoacoustic spectroscopy and thermal relaxation, their effective thermal diffusivity and conductivity were experimentally measured. The composite layers were prepared under the action of a static magnetic field, resulting in anisotropic inclusion structures with the formation of chains of magnetite particles parallel to the faces of the layers. In one kind of bilayers, a composite layer was formed on top of a resin layer while their relative thickness was varied. These samples can be described by known models. In contrast, bilayers with the same concentration of inclusions and the same thickness on both sides, where only the angle between their inclusion structures was systematically varied, show a nontrivial behaviour of their thermal conductivity as a function of this angle. Through a lacunarity analysis, we explain the observed thermal response in terms of the complexity of the interface between the layers. 
J. J. Reyes-Salgado, V. Dossetti, B. Bonilla-Capilla, J. L. Carrillo
cond-mat.mtrl-sci