No-slip condition

The boundary condition that sets a viscous fluid’s velocity equal to a solid surface’s velocity at their interface. It is a standard approximation in continuum fluid mechanics.

Boundary layer: A thin region near a surface where viscosity strongly affects fluid velocity. No-slip creates the wall-to-flow velocity gradient from which boundary layers develop.
Viscosity: A fluid’s resistance to deformation and flow, arising from internal momentum transport. Viscosity transmits the surface’s motion into the adjacent fluid.
Navier slip condition: A boundary condition relating tangential slip velocity to viscous stress at a surface. Unlike no-slip, it permits a finite difference between fluid and wall velocities.
Drag (physics): A force opposing an object’s motion through a fluid. No-slip creates near-surface shear that contributes to viscous drag.
Wall shear stress: The tangential viscous force per unit area exerted at a fluid boundary. The velocity gradient imposed by no-slip determines the shear exerted on the wall.
Continuum mechanics: The framework that models matter as continuously distributed rather than molecularly discrete. No-slip is imposed on the continuous velocity field at an idealized interface.
Free-slip boundary condition: A boundary condition allowing tangential fluid motion while preventing normal flow through a surface. It removes tangential resistance instead of matching fluid and wall velocities.
Lubrication theory: An approximation for thin-film flows in which pressure varies mainly along the film. Its standard wall constraints often impose no-slip on both bounding surfaces.
Navier–Stokes equations: Differential equations describing the motion of viscous fluids. No-slip supplies a boundary condition needed to solve these equations near solid walls.
Boundary condition: A constraint specifying a solution’s behavior at the boundary of a mathematical domain. No-slip is a velocity constraint applied at the fluid’s solid boundary.

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