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An algebraic tail in Green-Kubo integrals complicates slip length calculations. This study introduces a discrete nonlocal hydrodynamics theory to resolve this issue, providing a microscopic slip length expression and validating it with flow simulations.

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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.