# No-Slip Boundary Condition

Entry by Robin Kirkpatrick AP 225 2011

## Introduction

The no-slip boundary condition is the concept that fluid particles 'stick' to the solid surface and velocity as the surface as the surface moves. This no-slip condition is what accoounts for hydrodynamic coupling of surfaces, and much of the widely observed phenomena in fluid mechanics, coupled motion of particles, near-wall hindered diffusion, and boundary layers (in general).

In inviscid flows, we generally set the velocity of the fluid normal to the surface equal to the velocity of the surface, but leave the parlell components unrestricted (ie neglecting the concept of 'non-slip'). This leads to the concept of a boundary layer- a small distance from the surface over which viscosity is not negilgible and the no-slip condition becomes relevant.

## Validity

The no-slip condition is an ideal model, and is not always relevant. For instance, when nanobubbles are present on surfaces, it is believed that gas transfer between the fluid and bubbles and bubble deformation results in a "leaky matress effect" which results nonzero boundary velocities. In situations where the no-slip condition is not a good enough approximation, we can introduce the concept of a slip length by $u - u_{wall} = \beta \frac{\delta u}{\delta n}$ where n is the coordinate normal to the wall, u is the fluid velocity, and β is called the slip length.

The more worrying issues are slips that might occur when the liquid touches the solid surface.