Microscopic Slip Boundary Conditions in Unsteady Fluid Flows

Area of Science:

• Physics
• Fluid Dynamics
• Materials Science

Background:

• The Green-Kubo integral is crucial for calculating transport coefficients.
• An algebraic tail in this integral hinders accurate slip length determination in solid-fluid systems.
• Understanding solid-fluid friction is key for microfluidic and nanoscale applications.

Purpose of the Study:

• To explain the origin of the algebraic tail in Green-Kubo integrals for friction coefficients.
• To develop a theoretical framework for discrete nonlocal hydrodynamics near solid walls.
• To derive a microscopic expression for slip length and hydrodynamic wall position.

Main Methods:

• Developed a simple theory for discrete nonlocal hydrodynamics.
• Analyzed extended friction forces near parallel solid walls.
• Performed simulations of unsteady plug flow to validate the derived boundary conditions.

Main Results:

• Identified the origin of the algebraic tail in the Green-Kubo integral.
• Provided a solution to the plateau problem in Green-Kubo expressions.
• Derived a slip boundary condition with a microscopic slip length and hydrodynamic wall position.

Conclusions:

• The developed theory successfully addresses the algebraic tail issue in Green-Kubo integrals.
• The derived microscopic slip length expression offers a new method for characterizing fluid-wall interactions.
• Simulations confirm the validity of the theoretical framework for unsteady plug flow.