1.4 Reynolds Number

The boundary condition on rigid surfaces is that the fluid immediately adjacent to the surface moves with the wall velocity. This is the no-slip condition. It says that there is no discontinuity in velocity at the wall. As a stationary wall is approached, the fluid velocity tends continuously to zero. This no-slip boundary condition is not indisputable. In rarified gases, and at the intersection of a gas fluid interface with a wall, it is violated. But at normal densities and pressures, and in homogeneous fluids, ^[*] it is correct. Certainly, if one stands in a stiff breeze, the air appears to flow freely over one s face. Nevertheless, in the immediate vicinity of a stationary body, the air velocity tends to zero. It does so across a thin boundary layer see Chapter 5. The sensation of airflow at the surface is due to pressure and heat transfer effects produced by the flow.

No-slip is certainly not an obvious condition. Early fluid dynamicists, including Stokes, were uncertain. The book Hydrodynamics by Horace Lamb was called the bible of fluid dynamics in the late 19th and early 20th centuries. It contains a section entitled on the question of slipping. The matter was resolved initially by comparing the predictions of flow through a pipe, allowing for the possibility slip, to experiment. The data implied no-slip: u = 0 at a stationary surface. Subsequently, high-resolution measurements of velocity proved no-slip beyond doubt.

The no-slip boundary condition is the...