Clinton DeW. Van Siclen
Physicist. Runner. Negroni connoisseur.
This site gives access to many of my papers, representing a variety of physics research areas.
Walker diffusion method for calculation of transport properties of composite materials
The morphology of a multiphase microstructure greatly influences the macroscopic transport properties of the composite material. These properties are shown to be related to the diffusion coefficient of a random nonbiased walker. The proper diffusion rules are found by considering an isomorphic image of the micro-structure in which distinct populations of walkers correspond to the phase domains, with the walker density of a population proportional to the transport coefficient of the corresponding domain. To demonstrate the method, it is applied to disordered two-phase percolating composites.
Anomalous walker diffusion through composite systems
Diffusion of a non-biased walker through a composite (multi-phase) system is shown to be anomalous for length scales less than the correlation length ξ (i.e., when the path length is measured with a ruler of length less than ξ) and Gaussian for length scales greater than ξ. The values of ξ and the fractal dimension dw of the walker path in the anomalous regime reflect the phase properties and phase domain morphology of the composite. They are related to the diffusion coefficient Dw for walker diffusion in the Gaussian regime by Dw ∝ξ2−dw, and to the macroscopic transport coefficient σ through the relation σ ∝Dw. The correlation length ξ thus gives the size above which the composite is effectively homogeneous with respect to the transport property of interest. Walker behaviour is compared for disordered (random), particulate–matrix, and labyrinthine two-phase microstructures.
Walker diffusion method for calculation of transport properties of finite composite systems
A heterogeneous medium may be represented by a scalar field of local transport coefficients e.g., conductivity or by a ‘‘resistor network’’ derived from that scalar field. In either case the effective macroscopic and local microscopic transport properties may be calculated by the walker diffusion method. Some sample calculations for disordered systems are presented to demonstrate the method.