No-slip condition
In
In the majority of fluid flows relevant to fluids engineering, the no-slip condition is generally utilised at solid boundaries.
Physical justification
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Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (adhesive forces) is greater than that between the fluid particles (cohesive forces). This force imbalance causes the fluid velocity to be zero adjacent to the solid surface, with the velocity approaching that of the stream as distance from the surface increases.
The no-slip condition is only defined for viscous flows and where the continuum concept is valid.
Slip behaviour
As the no-slip condition was an empirical observation, there are physical scenarios in which it fails. For sufficiently
While the no-slip condition is used almost universally in modeling of viscous flows, it is sometimes neglected in favor of the 'no-penetration condition' (where the fluid velocity normal to the wall is set to the wall velocity in this direction, but the fluid velocity parallel to the wall is unrestricted) in elementary analyses of inviscid flow, where the effect of boundary layers is neglected.
The no-slip condition poses a problem in viscous flow theory at contact lines: places where an interface between two fluids meets a solid boundary. Here, the no-slip boundary condition implies that the position of the contact line does not move, which is not observed in reality. Analysis of a moving contact line with the no slip condition results in infinite stresses that can't be integrated over. The rate of movement of the contact line is believed to be dependent on the angle the contact line makes with the solid boundary, but the mechanism behind this is not yet fully understood.
See also
References
- Proceedings of the Royal Society of London. 24 (164): 387–391.
- S2CID 55186899.
- .
- ^ Schamberg, R. (1947). The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems (Thesis).
- .
- PMID 9908755.
- ^ Kim Kristiansen; Signe Kjelstrup (2021). "Particle flow through a hydrophobic nanopore: Effect of long-ranged wall–fluid repulsion on transport coefficients". Physics of Fluids. 33 (10).
- ^ M. Kratzer; S. K. Bhatia; A. Y. Klimenko (2023). "Knudsen layer behaviour and momentum accommodation from surface roughness modelling". Journal of Statistical Physics. 190 (3).