The method of spatio-temporal variable diffusivity (STVD) for coupled diffusive processes.

• A new model for coupled diffusive processes with a TLP bonding application. • Model framed within the theory of partial differential equations of a mixed order. • Comparison between single interlayer, separate and nanocomposite interlayers. • Spatial distribution variance of concentration as a measure of the diffusive process. A model for coupled diffusive processes is framed within the theory of partial differential equations of mixed order. Its numerical implementation is achieved by a technique that does not require additional tools beyond the standard procedures for the solution of the diffusion equation. The interface between the diffusant and the substrate retains its sharpness during the bulk of the diffusive process. The results demonstrate that, as expected in pharmaceutical and diffusion bonding applications, the amount of material made available for diffusion is controlled by the area of the interface and, therefore, the use of nanoparticle layers may greatly accelerate the rate of the overall process. [ABSTRACT FROM AUTHOR]