Direct Numerical Simulation of Marangoni Flows: Dynamical Regimes and Transitions

Abstract

Marangoni flows are free-surface flows driven by gradients of surface tension. Because surface tension depends on chemical composition, Marangoni flows may be generated by the uneven distribution of surface-active species at an interface. The primary goal of this thesis is to develop a rigorous computational framework for the simulation of the fluid dynamical and interfacial phenomena underlying the physics of Marangoni flows. The focus is on characterizing the different dynamical regimes generated by the presence of surface-active species (surfactants) at an interface. The computational framework was developed using direct numerical simulation, that is, by simultaneously solving the full system of partial differential equations governing the free-surface flow and the surfactant transport on a continually deforming interface. Results from the simulations enabled detailed examination of the interfacial mechanisms of surfactant transport and provided a comprehensive picture of the free-surface flow. Analysis of the results established limits of applicability of scaling solutions previously proposed in the literature, calculated the necessary corrections, and also lead to the discovery of previously unobserved scaling laws in viscous Marangoni flows. New findings from this research not only enhance the fundamental understanding of the physics of Marangoni flows, but also the ability to accurately predict the behaviour of Marangoni flows and the associated transport of surface-active species, which is critical to the understanding of important natural and biomedical processes, ranging from the surfactant-driven propulsion of insects and microorganisms to the spreading of drugs and natural surfactants (proteins) in the eye and lungs. Controlled Marangoni transport of chemical species is also relevant to a wide range of environmental and technological processes, with applications ranging from cleaning of oil spills to coating of microfluidic devices.