Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

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.)

EDIT: I believe that I can work around the inconsistency problem with no-slip constraints for this problem by "stirring without touching the bottom of the cup" ... ie: set the stir depth to 1cm (say). This makes the non-time dependent solution uglier, since I have to treat three different regions:

  1. Below the stir stick (zero velocity no-slip condition on the inside of the cup in this region ; velocity matching the stir velocity along the circle at the stir radius at the stir depth).
  2. Between the center of the cup and the stir stick. "no-slip" conditions: match velocities below the stir stick. match the stir velocity at the stir radius.
  3. Between the stir stick and the edge of the cup. "no-slip" conditions: zero velocity on the cup edge. stir velocity at the stir radius.

This makes the problem much messier ... I already have Bessel functions to deal with, and now have to apply them separately in three regions.

I'm still interested to see if there's a better way to deal with the boundary value conditions ... ie: without forcing an artificial distance between a static and a dynamic interface so that they don't touch.

share|improve this question
add comment

1 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.

share|improve this answer
    
Do you know of a model that works better than "no-slip" for stirring that involves non-static interfaces in contact? –  Peeter Joot Jul 11 '12 at 20:31
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.