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Updated: May 26, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

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Published on: February 22, 2018

Beyond the no-slip boundary condition.

Howard Brenner¹

¹Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307, USA. hbrenner@mit.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 21, 2011

Summary

This summary is machine-generated.

This study proposes a new macroscopic method for fluid slip boundary conditions, suggesting the energy equation governs slip. The derived relation accurately predicts gas and liquid creep behavior at solid surfaces.

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Area of Science:

Fluid dynamics
Physical chemistry
Surface science

Background:

Determining the correct fluid slip boundary condition at solid interfaces is crucial for accurate fluid flow modeling.
Existing models often rely on the momentum equation, but its applicability to slip phenomena is debated.

Purpose of the Study:

To develop a simple macroscopic approach for fluid slip boundary conditions.
To identify whether the energy or momentum equation dictates the fluid-mechanical boundary condition for slip.

Main Methods:

A macroscopic theoretical framework was developed, focusing on the energy equation.
A constitutive relation for slip velocity was derived based on near-equilibrium linear thermodynamics.

Main Results:

The study proposes that the energy equation, not the momentum equation, determines the slip boundary condition.
A general constitutive relation for slip velocity was derived: (v(m))(slip)=-α∂lnρ/∂s|(wall).
This relation successfully explains experimental data for thermal and pressure-driven creep in gases and liquids.

Conclusions:

The energy equation provides a more accurate basis for fluid slip boundary conditions.
The derived constitutive relation offers a unified explanation for various creep phenomena at solid-fluid interfaces.
This work advances the understanding of fluid behavior at the nanoscale and microscale.