By considering velocity fluctuations in interfacial transport, we have shown that the constitutive assumption in-built with the 'standard' forms of the Navier-Stokes-Fourier equations need to be extended from a rather fundamental perspective, to render them applicable for fluid flows with strong local gradients of density and temperature. We have demonstrated a physically-based model of the underlying picture leading towards a new derivation of the extended form of Navier Stokes equation by drawing analogy with the mean and fluctuating components of velocity and temperature as in the case of turbulent transport. Based on these fundamental axiomatic propositions, he subsequently described the pre-constitutive forms of the pertinent conservation equations. In particular, we have derived modified constitutive models, based on the continuum manifestations of the underlying molecular-level phenomena. With appropriate linearization, these forms are shown to be in exact agreement with the constitutive hypotheses postulated by Brenner. The additional terms featuring in the extended equations, as compared to the standard constitutive forms, are expected to be of significant consequences in the analysis of compressible flows with high gradients in the local thermodynamic properties, as well as 'slip' flows in microchannels and nanochannels. We have also demonstrated that predictions from this model agree well with predictions from Monte Carlo Simulation (Microfluidics and nanofluidics 2014).
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