The no-slip boundary value constraint for Navier-Stokes solutions was explained

Question

The no-slip boundary value constraint for Navier-Stokes solutions was explained in my fluid dynamics class as a requirement to match velocities at the interfaces.

Now that my class is done, I've been playing with solving an idealized fluid flow problem: figuring out the rate of "spin-down" of stirred fluid in a non-bottomless cylindrical container (ie: my coffee after being given a good stir).

For the non-time dependent portion of the problem, I'm not able to apply the no-slip condition as taught in class to my cup of coffee. Matching velocities to my stir stick (I've idealized that as a cylinder as in Acheson's bottomless tea example (pg 45) ), I've got a problem at the base of the cup: If I match velocities of the fluid to the "stir-stick", I can't also match velocities to the bottom of the cup (zero velocity) where the stir-stick touches the base.

I've been pointed to some journal articles to read, but won't be able to do so until the fall when I enroll in my next course (and get library access again). In the interim, I was wondering if I could get some pointers on an approach to deal with conflicting 'no-slip' conditions like this one (ie: any problem with a moving interface in contact with a static one has this trouble.)

Explanation / Answer

If you were to stir an ideal no-slip liquid, your spoon would get stuck if it is to touch the bottom. You can try taking 2 glass plates, dipping them in water, and moving them relatively to each other, then get them touching together and try moving again, the friction increases and for ideal no-slip liquid the force required to move surfaces at given speed would become infinite as the distance approaches zero.

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