Are there some cases which have increasing of the removal percent in adsorption with increasing of the initial concentration of the dye ? If so, what is the scientific explanation of this phenomenon ?
It depends on the reaction rate order with respect to the concentration of a dye. The reaction mechanism of dye bleaching is commonly very complex resulting in different reaction kinetics
Not necessarily Mohamed, It only holds true if the dye removal is non-destrucitve e.g. it achieved by disolving the dye. Please also consider the case where the abdorption process is close to or has reached saturation level
The increase in removal percentage with increase of starting concentration may be observed in the case of sigmoid adsorption isotherm (or S-isotherm), which results from cooperative adsorption, see the review of G. Limousin et al. Sorption isotherms...
doi:10.1016/j.apgeochem.2006.09.010
This happens typically to non-polar organic compounds and thus probably not to dyes.