Hybrid molecular and continuum fluid dynamics models for micro and nanofluidic flows

From molecules to living organisms and from atoms to planets a variety of physical phe- nomena operate at different temporal and spatial scales. Understanding the nature of those phenomena is crucial for advancing new technologies in many disciplines. In micro and nanofluidics as the operational dimensions are downsized to smaller scales the surface-to- volume ratio increases and the surface phenomena become dominant. Numerical modelling is the key for obtaining a better insight into the processes involved. The Achilles heel of fine grain microscopic numerical simulations is their computational cost. Simulating a multiscale phenomenon with an accurate microscopic description is extremely demand- ing computationally. On the contrary, simulations of multiscale phenomena based only on macroscopic descriptions cannot fully capture the physics of the multiscale systems. In order to confront this dilemma multiscale frameworks, called hybrid codes, have been de- veloped to couple the microscopic and macroscopic description of a system and to facilitate the exchange of information. The aim of this research project is to establish and implement a robust hybrid molecular- continuum method for micro- and nano-scale fluid flows. Towards that direction a hybrid multiscale method named as Point Wise Coupling (PWC) has been developed. PWC aims to circumvent the limitations of the existing hybrid continuum/atomistic approaches and deliver a modular and applicable methodology. In the PWC, the whole domain is covered with the macroscopic solver and the microscale model enters as a local refinement. Ad- ditionally, numerical techniques based on neural networks are employed to minimise the cost of the molecular solver and reduce the outcomes’ variability induced by the fluctuating nature of the atomistic data. Molecular studies have been performed (i) to obtain a better insight of the interfacial phenomena in the solid/liquid interfaces, and (ii) to study the parametrisation of the molec- ular models and mapping of atomistic information to hybrid frameworks. Specifically, the impact of parameters, such as surface roughness and stiffness, to slip process is studied. PWC framework has been employed to study a number of fundamental test cases in- cluding Poiseuille flow of polymeric fluids, isothermal slip Couette flow and slip Couette flow with heat transfer. Attention is drawn to the boundary condition transfer from the continuum solver to the atomistic description. In the performed hybrid studies the effects of the numerical optimisation techniques (linear interpolation, neural networks) to simu- lations’ accuracy, stability and efficiency are studied. The outcomes of the simulations suggest that the neural networks scheme enhance the simulation’s efficiency by minimising the number of atomistic simulations and at the same time act as a smoothing operator for reducing the oscillations’ strength of the atomistic outputs.