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

Abstract

Flows in nanofluidic systems are controlled by the hydrodynamic boundary condition (BC), involving the friction coefficient and the hydrodynamic wall position. Here we considered a liquid nanoslab confined between two walls, where we derived, from the Stokes equation and the Navier slip BC, analytical expressions for the liquid response to an oscillatory tangential motion of the walls in terms of the wall shear stress and mean fluid velocity. By fitting these expressions to molecular dynamics simulation results, we could extract both the viscoelastic friction coefficient and hydrodynamic wall position for walls with three different wettabilities, hence fully characterizing the frequency-dependent hydrodynamic boundary condition. The proposed method could be applied to a variety of liquid-solid interfaces of interest, e.g., for flows of complex fluids or fluids at a low temperature. It should also support methodological developments on the characterization of the hydrodynamic slip in general.

Fast increase of nanofluidic slip in supercooled water: the key role of dynamics

“…[26][27][28][29][30][31][32][33] Further work has been performed to study the impact on friction of different wall features such as wettability, 34,35 roughness, 36 crystallographic orientation, 37 electronic structure, [38][39][40] or electrostatic interactions. 41 Yet a large number of questions with regard to the interface properties, such as its viscoelastic or purely viscous nature [42][43][44] or the possible link with its interfacial thermal transport equivalents via wall's wetting properties, [45][46][47] remain open nowadays, limiting the perspectives for a rational search of optimal interfaces.…”

Theoretical framework for the atomistic modeling of frequency-dependent liquid-solid friction

“…Both works from the two groups involved elaborate mathematical manipulations, and only reported the pure viscous (Markovian) behavior of the Navier FC, for a Lennard-Jones (LJ) liquid on a simple model wall. However, non-Markovian behavior of the FC was recently reported for a LJ liquid on a fcc lattice [26] and it is plausible that more complex liquids such as water also show such behavior, in analogy with their bulk transport properties [27][28][29][30][31][32].…”

“…In this evaluation of Eqs. ( 7) and ( 8), we substituted λ(t) by the Maxwell-type model λ 0 exp(−t/t λ )/t λ with the parameters λ 0 = 0.1492 √ m f ε ff /σ 3 ff and t λ = 0.077σ ff m f /ε ff taken from the results of non-equilibrium simulations [26], whose simulation system and conditions were identical to the present study [42]. Here, the same λ was used regardless of the system height: this shows that there is no system size dependence in the estimation of λ from the MD simulation data by the present theory.…”

“…The motion of the liquid in response to the bottom wall motion (the top wall is fixed) can be described by Stokes equation for a wide frequency range [26] [34]:…”

“…The system temperature was controlled at 0.827ε ff /k B by a Langevin thermostat set on the second outermost layer of the walls, and the pressure was set to 0.094ε ff /σ 3 ff by a preliminary piston equilibration (see Ref. 26 for technical details). For the liquid-solid interaction, the LJ potential was adopted as well.…”