Boundary conditions derived from a microscopic theory of hydrodynamics near solids

Abstract

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)].

Fast transport of water in carbon nanotubes: a review of current accomplishments and challenges

“…In most of the previous studies on fluid flow in nanochannels this variation in spatial viscosity, which could affect the effective shear viscosity, was not taken into consideration. This could be one of the factors accountable for the discrepancies observed in slip length and flow rate enhancement, and efforts should be directed towards addressing this challenge [156][157][158][159][160][161].…”

Full characterization of the hydrodynamic boundary condition at the atomic scale using an oscillating channel: Identification of the viscoelastic interfacial friction and the hydrodynamic boundary position

“…We considered 6400 molecules for the liquid and 8192 atoms for the walls. All the quantities in the present study are shown in LJ reduced units based on the liquid molecular mass m f and two parameters σ f f and ε f f for the LJ potential LJ (r 6 ] between the liquid molecules, where r i j was the distance between molecules i and j. We added a quadratic function to LJ so that LJ (r i j ) and LJ (r i j ) smoothly vanished at the cutoff distance r i j = 3.50.…”

“…The Navier BC involves two free parameters, the FC λ and the hydrodynamic position of the wall surface, z s , where the BC applies [2], i.e., where the slip velocity and wall shear rate are defined. This position differs in general from the physical position of the wall surface [3][4][5][6][7]. The Navier BC is often rewritten as a kinematic relation on the velocity field, and referred to as the partial slip BC: u s = b(∂u/∂z)| z=z s , where b = η/λ is the so-called slip length.…”

“…It is of critical importance to understand and optimize liquid-solid slip, which can enhance dramatically the performance of micro-and nanofluidic systems [14][15][16][17]. Accordingly, the hydrodynamic BC has been an active field of research during the past decades, both on the experimental side [18][19][20][21] and on the modeling side [3,4,6,[22][23][24][25][26][27][28][29][30][31][32][33], where molecular dynamics (MD) simulation proved to be a powerful tool. However, determining both λ and z s that make up the Navier BC is delicate even in a MD simulation, and it is a common practice to assume that z s lies at some prescribed distance from the wall surface [32] or coincides with the position of the wall surface [23][24][25] and only the friction coefficient (or equivalently the slip length) is measured.…”

“…Few groups have attempted the complete determination of the Navier BC so far: for instance, Bocquet and Barrat [3] reported the gap between the wall surface and the hydrodynamic wall surface (hydrodynamic boundary) was 1.3σ by a Green-Kubotype formula and 1.6σ as a fit parameter to reproduce the measured autocorrelation function of the fluctuating liquid velocity confined between two walls, where σ is the liquid molecular diameter; Chen et al [4] measured between 2.2 and 2.5σ from an analysis of the equilibrium hydrodynamic fluctuations; and recently Herrero et al [34] measured varying between 0.6 and 1.1σ depending on the wall wettability from the analysis of the wall shear stress in Poiseuille flow simulations. Camargo et al [6] proposed an alternative derivation of the Navier BC without resorting to the linear response theory, including the definition of .…”