This research grant was awarded “to establish and test the science underpinning a new model for microfluidics”. This aim has been achieved by developing a range of new mathematical models able to capture the important physics of gas microflows (in particular, the physics due to the combined molecular/continuum nature of these flows) with much less computational effort than molecular dynamics simulations. These models have been validated against independent molecular simulations and experimental data. They fit naturally into the hierarchy of tools that engineers can now deploy to model non-equilibrium gas flows, and in which there is substantial and growing international interest. This research established a strong and ongoing collaboration between researchers at Strathclyde University and Daresbury Laboratory. The grant supported two PhD students and a Visiting Fellowship, and has resulted so far in 11 journal publications, 16 conference publications, a two-day international research colloquium attracting over 110 delegates, and numerous invited seminars/talks in the UK and overseas.