TRAVELING WAVES DURING THE TRANSPORT OF REACTIVE SOLUTE IN POROUS-MEDIA - COMBINATION OF LANGMUIR AND FREUNDLICH ISOTHERMS

Recently, it has been shown that in the case of nonlinear solute adsor ption the displacement may be in the form of a travelling wave. In thi s paper, we investigate whether a travelling wave type of behaviour ca n be expected when two different types of sorption sites can be distin guished with different isotherms and kinetics. Illustrations are given for cases where the overall isotherm comprises two contributions that follow the Langmuir and the Freundlich equations, respectively. Bound ary conditions are chosen that ensure a decrease in concentration in t he direction of flow. Depending on the value of the Freundlich power ( p) the travelling wave may exist. For p less-than-or-equal-to 1, the t ravelling wave always exists, whereas for 1 < p less-than-or-equal-to 2 it depends on the values of the other adsorption parameters and whet her a lower bound of the upstream concentration (at x = -infinity) is exceeded. For p greater-than-or-equal-to 2, the existence of the trave lling wave requires that the upstream concentration does not exceed an (specified) upper bound. Besides illustrating some waves we show that two different rate functions that have the Freundlich isotherm as the ir limit for an infinite rate parameter result in qualitatively differ ent travelling waves.