Research into how nanoscale membranes and nanofluidic devices can be used in medicine, process engineering, and environmental science has flourished in recent years, with reports of experiments that are increasingly more sophisticated. One area of interest is the use of membranes for the purification of water, where increases in efficiency and reductions in cost could make fresh water available to many more people around the world. This work focusses on the molecular modelling of transport properties of water, and how they can be best utilised to achieve better membrane performance. Three main themes are covered: the accurate determination of transport properties in molecular fluids, the effects of strong confinement on fluid mobility, and the importance of such considerations in membrane design.

The bulk viscosity of molecular fluids is calculated through the consideration of a theoretical term, related to the relaxation of the internal degrees of freedom, and a configurational term, taking into account long-range intermolecular interactions as calculated from equilibrium molecular dynamics. Both atomistic and coarse-grained force fields for water, CO2 and n-decane are considered. Comparison to experimental data, where present, demonstrates that atomistic force fields in general achieve more accurate results than the corresponding coarse-grained counterparts. The internal degree of freedom contribution is only non-negligible in the case of CO2, leading to bulk viscosities orders of magnitude larger than the shear viscosity, both in the gas and liquid phase. In the remaining cases, the configurational term dominates and the bulk-to-shear viscosity ratio is approximately 3.

The diffusivity, and both the bulk and shear viscosities of water confined between two graphene sheets are calculated using equilibrium molecular dynamics. A particular focus is placed on determining the fluid structure in strong confinement. It is shown that there exists a range of channel separations, where water forms rhombic monolayer ice structures. The mobility of water molecules in this frozen regime is consequently reduced by several orders of magnitude. The extent of the frozen regime is strongly dependent on the average channel density, and by extension tangential pressures, with higher densities resulting in both monolayer and bilayer ice structures observed over a larger range of separations.

Finally, the flow behaviour of water through a membrane consisting of stacked, porous graphene sheets is studied using non-equilibrium molecular dynamics. Energy barriers upon entry and exit are examined by calculating the potential of mean force. The permeability depends strongly on the membrane geometry; only for a stacking of three or more sheets is traditional membrane behaviour recovered. For small slits in the sheets, large energy barriers inhibit flow. It is suggested that filtration could be modulated by controlling the separation of the graphene sheets in order to minimise energy penalties upon membrane entry.

The combined results of this thesis aid in developing a truly multi-scale modelling strategy for flow in the presence of confinement.