Noslip

Noslip, or no-slip boundary condition, is a fundamental assumption in classical fluid dynamics stating that a viscous fluid in contact with a solid boundary has zero relative velocity with respect to that boundary. In practical terms, for a stationary wall the fluid velocity at the boundary is zero; for a moving wall it matches the wall’s velocity. This condition is applied at solid-fluid interfaces when solving the Navier–Stokes equations and leads to the formation of a velocity boundary layer adjacent to the wall, within which the fluid transitions from the wall velocity to the bulk flow velocity. The tangential shear stress at the wall is given by τ = μ (∂u/∂y) evaluated at the wall, where μ is the dynamic viscosity.

There are departures from no-slip in some systems. The Navier slip condition generalizes the idea by allowing finite slip: u_slip = b (∂u/∂n) at the boundary, where b is the slip length. If b = 0 the no-slip condition is recovered; if b > 0 some slip occurs, which can be relevant on hydrophobic surfaces, micro- or nano-scale channels, or in rarefied gas flows.

Historically, the no-slip boundary condition became a standard modeling assumption in the 19th and 20th centuries and remains widely used in engineering and physics. However, modern research in microfluidics and computational fluid dynamics continues to investigate the limits of the assumption and the circumstances under which slip must be incorporated.