Singularity in a mathematical model of emulsion liquid membrane

An earlier paper of ours presented a mathematical model to study metal recovery from wastewater with emulsion liquid membrane and the analytical solution resulting from the model. In this paper, we point out that in a certain parameter range the eigenvalue equation has a singularity that gives rise to an additional term in the analytical solution, whose impact is strongest in the initial phase of metal recovery. This paper examines the origin and consequence of the additional term associated with the singularity.