# continuum or rarefied?

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 March 8, 2007, 05:50 continuum or rarefied? #1 Dave Guest   Posts: n/a Hi, I'm investigating microflows and I need to know when to use the continuum or rarefied assumption? I have found that the knudsen number is low enough in most of the domain to use the continuum assumption but the flow has a high kn in parts of the flow. So which assumption can I use? I am investigating microchannels and micronozzles. Thanks for your help, Dave

 March 8, 2007, 10:37 Re: continuum or rarefied? #2 Harish Guest   Posts: n/a People use partial slip models for Kn in the range 10^-3 - 0.1 and sometimes upto 10.Take a look at the book fundamentals of microflows by karniadakis and beskok. So for that regime you can still use N-S with partial slip.

 March 9, 2007, 04:26 Re: continuum or rarefied? #3 Dave Guest   Posts: n/a Thanks Harish, If you wanted to determine the knudsen number of the flow in a micronozzle in order to decide whether to use th eno-slip or slip condition. What would you base it on, i.e. do you calculate the knudsen number at the throat and take that as the indicator? Thanks Dave

 March 9, 2007, 10:31 Re: continuum or rarefied? #4 Harish Guest   Posts: n/a Take the bigger of the Kn calculated from different geometric parameters in the problem.

 March 9, 2007, 15:00 Re: continuum or rarefied? #5 Robin Guest   Posts: n/a Interesting discussion... Do either of you know any well accepted validation data or such flows? Have you done any validation studies yourselves?

 March 9, 2007, 15:16 Re: continuum or rarefied? #6 Harish Guest   Posts: n/a I have done some sample validations.Simple examples can be found in the book of karniadakis and beskok, " An introduction to microflows". Also you can find papers for simple analytical solutuons for flows like couette flow ,poiseulle flow , drag on a sphere to mention a few.All of these are derived as some f(kn). The only problem is that the Knudsen number criterion is not universally accepted still.The thumb of rule is beyond Kn=0.1 you have problems.But some simulations have been demonstrated for lower kundsen numbers in few test cases and pretty good results were obtained.Some people go for the chapman expansion to use different constitutive relation to expand the range of Kn.

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