Experimental observations indicate that a fluid
in motion comes to a complete stop at a solid surface and assumes a zero velocity
relative to the surface. A fluid in direct contact with a solid "sticks" to the surface due to viscous
effects, and there is no slip. This is the no-slip condition.
When a fluid
is forced to flow over a curved surface, such as the back side of a cylinder at sufficiently high velocity, the boundary layer can no longer remain attached to the surface, and at some point it separates from the surface—a process called flow separation. The no-slip condition applies everywhere along the surface, even downstream of the separation point.
In many applications of physics, boundary conditions have an essential role. The purpose of this paper is to examine from both a historical and philosophical perspective one such boundary condition, namely, the no-slip condition of fluid dynamics. The historical perspective is based on the works of George Stokes and serves as the foundation for the philosophical perspective. It is seen that historically the acceptance of the no-slip condition was problematic. Philosophically, the no-slip condition is interesting since the use of the no-slip condition illustrates nicely the use of scientific models. But more importantly, both the use and justification of the no-slip condition illustrate clearly how theories can holistically approach the world through model construction. Further, since much of the debate over scientific realism occurs in the realm of models, a case is made that an understanding of the role of the no-slip condition has something to offer to this debate.
he no-slip boundary condition represents a 200-year old unsolved problem. The official boundary condition is that the tangential component of velocity is continuous across a solid-liquid interface. So, if the solid is not moving, the tangential component of fluid velocity as the surface must also be zero. Because the solid-fluid interface does not deform, the normal component must also be zero. If the solid is moving, the tangential component of velocity of the fluid at the interface is the same as the velocity of the solid, and the normal component of velocity at the interface is still zero. "Stokes first problem" solves how a moving solid creates a velocity field in an initially stationary fluid. Now, for a fluid-fluid interface, all bets are off becasue the interface can deform. There can be a velocity jump across a fluid-fluid interface. The no-slip condition exists to ensure the stress tensor does not diverge. However, the no-slip condition is routinely violated all the time- web printing processes, droplet migration across my car windshield during a rainstorm, etc. etc. As I mentioned above, the no-slip boundary condition is a 200-year old unsolved problem.
The No Slip Condition (in Poiseuille Flow)
In the previous article, the Poiseuille velocity profile and pressure-flow relationship was derived for a Newtonian fluid in a straight cylindrical tube. At some point in the derivation, we invoke the "No Slip" condition
which states that the velocity of the fluid at the wall must be equal to the velocity of the wall, i.e. 0. Is that justified? What's the basis for it?
I'm going to try to explain this in a much more general way that has to do with the "continuum hypothesis"
of how materials behave, both fluids and solids. We all know that mattered is made up of particles. In most cases however, you would have to look very closely – at a very small length scale to determine that this is the case. Materials behave grossly as if they are continuous, not particulate. Correlates of this theory include the ability to treat all of the properties of the matter as continuous -- properties like temperature, concentration of a chemical within a fluid, density, and velocity e.g. if the material is moving or deforming.