Limits of the hydrodynamic no-slip boundary condition

Area of Science:

• Fluid dynamics
• Surface science
• Rheology

Background:

• The no-slip boundary condition is a fundamental concept in fluid dynamics.
• The relative importance of surface roughness versus fluid-surface intermolecular interactions in determining boundary conditions remains debated.
• Understanding these factors is crucial for accurately modeling fluid behavior near surfaces.

Purpose of the Study:

• To experimentally differentiate the influence of surface roughness and intermolecular interactions on fluid flow boundary conditions.
• To quantify the critical surface roughness at which roughness effects become dominant over intermolecular interactions.
• To establish limits for existing theories on fluid-surface interactions.

Main Methods:

• Hydrodynamic forces were measured for Newtonian fluid flow over surfaces with varying roughness.
• Surface chemistry was kept consistent (poorly wetted) to isolate the effect of roughness.
• Deviations from the no-slip boundary condition were analyzed in relation to surface roughness (rms).

Main Results:

• Deviations from the no-slip boundary condition increased nearly exponentially with increasing surface roughness.
• A critical rms roughness of approximately 6 nm was identified where deviations became significant.
• Intermolecular interactions were found to dominate boundary conditions on very smooth surfaces.

Conclusions:

• Surface roughness becomes the dominant factor in fluid flow boundary conditions for surfaces rougher than approximately 6 nm rms.
• Intermolecular interactions play a more significant role in determining boundary conditions for very smooth surfaces.
• This study quantifies the transition point, providing critical insights into the interplay between surface topography and molecular forces in fluid dynamics.