| Summary: | <p>This thesis puts forward methods for the computation of transport of mass, momentum and heat in multicomponent flows, systems which involve the transport of two or more chemical species in a common thermodynamic phase. Although commonplace in nature, problems of this type remain relatively unstudied in the numerical literature.</p>
<p>The transport problems considered in this thesis are formulated in terms of the Onsager--Stefan--Maxwell equations, which describe multi-species molecular diffusion in fluids, and the Navier--Stokes equations, which account for convection. Under some mild assumptions, we prove existence and uniqueness of solutions to some linearized systems. Effective numerical methods using finite elements are then obtained and analyzed to provide a general methodology for simulation.</p>
<p>The scope of the thesis is broader than numerical analysis. It contains original reformulations of transport problems within the framework of linear irreversible thermodynamics. The theory of fluid thermodiffusion is consolidated and cast into a new form, which allows for straightforward simulation of heat transfer alongside molecular diffusion. In addition we provide original and substantial detail on how to extend the framework to encompass transport in electrolytic materials under the assumption of electroneutrality, which generalizes some of the equations arising in porous electrode theory.</p>
<p>The power of the framework developed is illustrated throughout the thesis. We employ it to simulate a diverse range of examples, such as oxygen diffusion in the lungs, the mixing of flowing hydrocarbons streams, thermal separation of gases and transport in electrolytes.</p>
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