Instability and reaction-di�usion transport of bacteria

Bacterial transport in saturated–unsaturated soils is an important process in environmental science and
hydrology. A mechanistic model for bacterial transport in geomaterials is presented here. The model
equations comprise a pair of fully coupled non-linear parabolic partial di�erential equations that describe
the concentration of microbes in the liquid water and solid surfaces. The model equations not only describe the bacteria sorption and desorption processes, but also take into account the retention of bacteria at the liquid–water interface and the dynamic reproduction characteristics of the bacteria. The instability and travelling waves for the coupled equations are analysed.