Many Uses for Diffusion Waves

The article on diffusion waves by Andreas Mandelis was a refreshing and interesting look at some applications of these waves, which are governed by a linear, parabolic partial differential equation. Readers may be interested in some other applications that arise from extensions of this governing equation in classical continuum mechanics. In porous media transport, for example, diffusion wave theories have variously been used to describe propagation in poroelastic media, ¹ the wave-driven dynamics of reacting solutes in homogeneous media ² and in mixed media characterized by composite heterogeneity, or by interfaces at which discontinuities in the wave field are maintained. ³

In the related field of ground-water hydrology, the wave field is identified with hydraulic head and is typically forced by tidal effects in surface water bodies, by Earth tides or by seasonal effects. The governing equation ensures that high frequency modes are strongly damped in aquifers, while low frequency modes are passed.

Of particular interest are nonlinear diffusion waves, which are often relevant for groundwaters near beaches, river banks, and so forth, and which display unusual characteristics. ⁴ Various examples of nonlinear diffusion waves are described in refs. and .

Mandelis concentrated his discussion on applications close to modern physicists’ hearts, including materials science, photonics, and so forth. What I hope to have shown is that these peculiar waves are also important in other areas, reinforcing Mandelis’s conclusion that diffusive propagation is a topic worthy of further study.