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This paper presents a simple tool for characterising the timescale forcontinuum diffusion processes through layered heterogeneous media. Thismathematical problem is motivated by several practical applications such asheat transport in composite materials, flow in layered aquifers and drugdiffusion through the layers of the skin. In such processes, the physicalproperties of the medium vary across layers and internal boundary conditionsapply at the interfaces between adjacent layers. To characterise the timescale,we use the concept of mean action time, which provides the mean timescale ateach position in the medium by utilising the fact that the transition of thetransient solution of the underlying partial differential equation model, frominitial state to steady state, can be represented as a cumulative distributionfunction of time. Using this concept, we define the characteristic timescalefor a multilayer diffusion process as the maximum value of the mean action timeacross the layered medium. For given initial conditions and internal andexternal boundary conditions, this approach leads to simple algebraicexpressions for characterising the timescale that depend on the physical andgeometrical properties of the medium, such as the diffusivities and lengths ofthe layers. Numerical examples demonstrate that these expressions provideuseful insight into explaining how the parameters in the model affect the timeit takes for a multilayer diffusion process to reach steady state.

Characteristic time scales for diffusion processes through layers and across interfaces