Final Report Summary - CIF (Complex Interfacial Flows: From the Nano- to the Macro-Scale) A wide variety of natural phenomena and technological applications involve flow, transport and chemical reactions taking place on or near fluid-solid or fluid-fluid interfaces. From gravity currents under water and lava flows to heat and mass transport processes in engineering applications and to the rapidly developing field of micro- and nanofluidics. Both equilibrium properties of a fluid and transport coefficients are modified in the vicinity of interfaces. The effect of these changes is crucial in the behaviour of fluids in confinement such as microchannels of micro-electromechanical systems, but is essential as well in macroscopic phenomena involving interfacial singularities, such as thin-film rupture and motion of three-phase contact lines associated e.g. with droplet spreading.Interface boundaries are mesoscopic structures. While material properties vary smoothly at macroscopic distances from an interface, gradients in the normal direction of conserved parameters, such as density, are steep with strong variations as the molecular scale in the neighbourhood of the interface is approached. This brings about a contradiction between the need in macroscopic description and a necessity to take into consideration microscopic factors that come to influence the fluid motion and transport on incommensurately larger scales.The primary aim of CIF was to develop a class of novel continuous models bridging the gap between molecular dynamics and conventional hydrodynamics and applicable at mesoscopic distances from gas-liquid and fluid-solid interfaces. A combination of analytical techniques, numerical modelling and computer-aided multi-scale analysis was employed for the development of models that bridge the micro- to the macroscale. The results of the proposed work have greatly contributed to the fundamental understanding of mesoscopic non-equilibrium phenomena in the vicinity of interfaces and to the development of novel computational methods combining the advantages of molecular and continuous models.In particular, by using elements from the statistical mechanics of classical fluids, namely dynamic density-functional theory (DDFT) we have been able to provide the first rigorous, rational and systematic and efficient description (from first principles) of fluid problems involving topological transitions and singularity formation, such as moving contact lines.However, to make progress several challenges and at times formidable difficulties had to be overcome. And these constitute the major contributions and outcomes of the project.Specifically: (i) Previous DDFTs neglected inertia or hydrodynamic interactions (HI), or both, the combined effect of which is often crucial in dynamics. Within CIF we developed a new DDFT formalism that nicely unifies previous DDFTs and carefully and systematically accounts for both inertia and HI, a crucial step towards accurate and predictive modelling of physically relevant systems.(ii) Previous DDFTs were restricted to colloidal fluids. We extended our new DDFT formulation to simple (atomic or molecular) fluids, leading to a Navier-Stokes(NS)-like equation with non-local terms associated with a free-energy functional; (iii) The resulting governing equations are highly non-local/integro-differential equations necessitating the development of novel computational techniques for their solution. These techniques represent a tour de force in numerical analysis; (iv) We undertook the matched asymptotic analysis of these equations so as to connect the microscale to the macroscale/usual hydrodynamic/NS description for contact line problems, a highly non-trivial task; (v) The resulting NS-like equation suffers the problem of closure for its transport coefficients, not surprising as it represents an effective coarse-grained model of microscopic systems, and necessarily some information from the microscale is lost in the effective description. These coefficients, strong functions of density in the vicinity of boundaries and interfaces (such as fluid-fluid and fluid-wall interfaces), have been benchmarked with molecular dynamics (MD) simulations. Alternative and more ambitious approaches which will not resort on MD and are based on “data-driven” and “equation-free” methodologies are currently being exploited.
