Professor Tim Myers (Centre de Recerca Matemàtica, Barcelona, Spain) – Mathematical Modelling of Adsorption Processes

Abstract. Adsorption is a ubiquitous chemical process where atoms, ions, or molecules from a fluid attach to the surface of a solid. Adsorption processes lie at the heart of many technologies, for example contaminants bind to porous media in water‑treatment columns, gases are selectively captured in purification and separation processes or for hydrogen storage, chromatography is based on the different adsorption-desorption rates of distinct materials, and organic molecules adsorb onto metal surfaces to form protective corrosion‑inhibiting films. Although these systems appear in very different technological settings, they share a common feature: their performance is governed by interfacial interactions whose kinetics, equilibria and transport are highly nonlinear. Understanding and predicting these behaviours requires mathematical models capable of linking microscopic adsorption mechanisms to macroscopic transport.

In this talk we will investigate the development and analysis of mathematical models for environmental contaminant capture in adsorption columns and also the application of corrosion inhibitors to pipes. The first couples an advection–diffusion equation, governing the transport of contaminants through the column, with a kinetic equation describing mass loss due to adsorption onto the solid phase. The second deals with the attachment of multiple layers of molecules to a substrate, described by a system of ODEs which, in certain cases, permit simple, closed form solutions.

The work demonstrates how classical and modern analytical techniques can yield simple solutions to complex physical problems, so permitting an understanding of the dominant physical processes and paving the way for process optimisation.