No-slip condition
In fluid dynamics
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

, the no-slip condition for viscous fluids states that at a solid boundary, the fluid will have zero velocity relative to the boundary.

The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows.

Physical justification

Particles close to a surface do not move along with a flow when adhesion
Adhesion is any attraction process between dissimilar molecular species that can potentially bring them in close contact. By contrast, cohesion takes place between similar molecules....

 is stronger than cohesion
Cohesion (chemistry)
Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...



As with most engineering approximations, the no-slip condition does not always hold in reality. For example, at very low pressure (e.g., at high altitude), even when the continuum approximation
Continuum mechanics
Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modelled as a continuous mass rather than as discrete particles...

 still holds there may be so few molecules near the surface that they "bounce along" down the surface. A common approximation for fluid slip is:

where is the coordinate normal to the wall and is called the slip length. For an ideal gas, the slip length is often approximated as , where is the mean free path
Mean free path
In physics, the mean free path is the average distance covered by a moving particle between successive impacts which modify its direction or energy or other particle properties.-Derivation:...

. Some highly hydrophobic surfaces have also been observed to have a nonzero but nanoscale slip length.

While the no-slip condition is used almost universally in modeling of viscous
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

 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
Inviscid flow
In fluid dynamics there are problems that are easily solved by using the simplifying assumption of an ideal fluid that has no viscosity. The flow of a fluid that is assumed to have no viscosity is called inviscid flow....

, where the effect of boundary layer
Boundary layer
In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

s is neglected.

The no-slip condition poses a problem in viscous flow theory at contact lines
Capillary surface
In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different fluids. As a consequence of being a surface, a capillary surface has no thickness in slight contrast with most real fluid interfaces....

: 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
Contact angle
The contact angle is the angle at which a liquid/vapor interface meets a solid surface. The contact angle is specific for any given system and is determined by the interactions across the three interfaces. Most often the concept is illustrated with a small liquid droplet resting on a flat...

 the contact line makes with the solid boundary, but the mechanism behind this is not yet fully understood.

External links

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