On the multiplicity of solutions of the nonlinear reactive transport model

• Main Author: Elyas Shivanian
• Format: Article
• Language: English
• Published: Elsevier 2014-06-01
• Series: Ain Shams Engineering Journal
• Subjects: Reactive transport model; Michaelis–Menten reaction; Exact analytical solution; Multiple solutions
• Online Access: http://www.sciencedirect.com/science/article/pii/S2090447914000082

The generalization of the nonlinear reaction–diffusion model in porous catalysts the so called one dimensional steady state reactive transport model is revisited. This model, which originates also in fluid and solute transport in soft tissues and microvessels, has been recently given analytical solution in terms of Taylor’s series for different families of reaction terms. This article considers the mentioned model without advective transport in the case of including Michaelis–Menten reaction term and shows that it is exactly solvable and furthermore, gives analytical exact solution in the implicit form for further physical interpretation. It is also revealed that the problem may admit unique or dual or even more triple solutions in some domains for the parameters of the model.