Discrete hydrodynamics near solid walls: Non-Markovian effects and the slip boundary condition

Area of Science:

• Physics
• Fluid Dynamics
• Computational Science

Background:

• Predicting fluid behavior near solid boundaries is crucial in various scientific and engineering fields.
• Discrete hydrodynamics offers a framework for simulating fluid at finer scales.
• Understanding wall effects, like friction and slip, is essential for accurate modeling.

Purpose of the Study:

• To present a simple Markovian theory for discrete hydrodynamics near parallel solid walls.
• To investigate the validity of the Markovian assumption at different scales.
• To derive microscopic expressions for slip length and wall hydrodynamic position.

Main Methods:

• Defining discrete momentum using finite element basis functions.
• Incorporating irreversible extended friction forces to model wall effects.
• Assessing the Markovian assumption via eigenvalue decay of the correlation matrix.
• Measuring nonlocal viscosity and friction kernels using Green-Kubo formulas and a plateau-problematic extraction procedure.

Main Results:

• Fluid dynamics near walls exhibit non-Markovian behavior at scales smaller than molecular dimensions, resolving density layering.
• Dynamics behave in a Markovian way for bins larger than molecular size.
• The nonlocal theory accurately predicts transverse momentum decay for plug flow using extracted transport kernels.
• A slip boundary condition is derived with microscopic expressions for slip length and hydrodynamic wall position.

Conclusions:

• The Markovian theory provides a robust framework for discrete hydrodynamics near walls.
• Scale-dependent Markovian and non-Markovian dynamics are observed near solid boundaries.
• The derived slip boundary condition offers microscopic insights into fluid-wall interactions, though initial plug flow stages show deviations.