The theory of nonlocal isothermal hydrodynamics near a solid object derived microscopically in the study by Camargo et al. [J. Chem. Phys. 148, 064107 (2018)] is considered under the conditions that the flow fields are of macroscopic character. We show that in the limit of macroscopic flows, a simple pillbox argument implies that the reversible and irreversible forces that the solid exerts on the fluid can be represented in terms of boundary conditions. In this way, boundary conditions are derived from the underlying microscopic dynamics of the fluid-solid system. These boundary conditions are the impenetrability condition and the Navier slip boundary condition. The Green-Kubo transport coefficients associated with the irreversible forces that the solid exert on the fluid appear naturally in the slip length. The microscopic expression for the slip length thus obtained is shown to coincide with the one provided originally by Bocquet and Barrat [Phys. Rev. E 49, 3079 (1994)].
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Very useful discussions with Aleks Donev and Diego Duque-Zumajo are highly appreciated. Diego Camargo is grateful to COLCIENCIAS-Colombia through a Doctoral Scholarship program and CIDI-UPB Montería for supporting this work. This research was supported by the Ministerio de Economía y Competitividad of Spain (MINECO) under Grant Nos. FIS2013-47350-C5-1-R, FIS2017-86007-C3-3-P, and FIS2013-47350-C5-3-R.
© 2019 Author(s).