No-slip condition

In fluid dynamics, the no-slip condition for viscous fluids assumes 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. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition.

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 brings down the fluid velocity to zero.

As with most of the 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 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 ${\displaystyle n}$ is the coordinate normal to the wall and ${\displaystyle \beta }$ is called the slip length. For an ideal gas, the slip length is often approximated as ${\displaystyle \beta \approx 1.15\ell }$, where ${\displaystyle \ell }$ is the mean free path. Some highly hydrophobic surfaces have also been observed to have a nonzero but nanoscale slip length.

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