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March 16, 2001, 04:41 
About Stokes number

#1 
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Dear All,
Stokes number seems a frequently empolyed dimensionless number is fluidparticle twophase flows. Is there anyone who could kindly tell me the defination and physical meaning of this number? Many thanks! Jie Li 

March 16, 2001, 18:08 
Re: About Stokes number

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The Stokes number is a very powerful concept, and has been extended to included a heat transfer or mass transfer Stokeslike number.
The Stokes number is the characteristic response time of the fluid divided by the characteristic response time of the particle. If the Stokes number is small, that is much less than 1, it means that the particle motion is tightly coupled to the fluid motion that is the particle dispersal is the same as the fluid dispersal. This suggests that mixture theory can be used instead of full multiphase approach as there is little relative motion between phases locally. If the Stokes number is large, the particles are not influences by the fluid their response time is longer than the time the fluid has to act on it (the fluid time scale may be the rotation time of a characteristic eddy) and so the particle will pass through the flow without much deflection in its initial trajectory. The interesting case is where the Stokes number is about one now the particles migrate to the margins of the eddy and hence 'unmixes'. All very interesting. Here are some references I found very useful: This first paper is superb, full of physical insights: Raju & Meiburg, 1995, "The accumulation and dispersion of heavy particles in forced twodimensional mixing layers. Part 2. The effect of gravity", Phys. Fluids, v. 7, p. 12411264. Another good one with nice illustrations: Tang et al., 1992, "Selforganizing particle dispersion mechanism in free shear flows", Phys. Fluids, v. A4, p. 22442249. 

March 16, 2001, 18:14 
OPPPPS got it backwards

#3 
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Sorry everything I said in previous message is okay EXCEPT that the Stokes number is the ratio of the particle response time to the characteristic fluid time scale. I stated just the reverse above, and that was wrong.
Sorry all. 

March 20, 2001, 04:40 
Re: About Stokes number

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Dear George Bergantz,
Many thanks for your kind explanations which is helpful. Are you also involved in particulate twophase flow research. This seems a quite promising area and very interesting, Particularly the pattern formation. Thank you again. Jie 

November 8, 2010, 07:04 

#5 
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Hi i am modeling a naca0012 in heavy rain with fluent dpm model and steady state treatment(for particle and phase)..my question is
where can i find the τ (relaxation time) for my airfoil to calculate the stokes number? 

May 23, 2011, 23:13 
Stokes number

#6 
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viva
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hi,
Could you advice me how to calculate Stoke's number for a fluidparticle system? Thanks 

May 24, 2011, 10:02 
Re: Stokes number

#7 
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Nizkaya Tatiana
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Hello, viva!
The exact definition of Stokes number might differ slightly depending on the application area. Relaxation time for a small spherical particle in still fluid is: tau_p= 2/9 a^2/nu/R, where R=2*rho_f/(2*rho_p+rho_f), rho_p and rho_f are particle and fluid densities respectively, nu is kinelatic viscosity of the fluid. For aerosols (rho_f<<rho_p) R~rho_f/rho_p. The Stokes number is the ratio of relaxation time to hydrodynamic time: St=2/9 (a/L)^2 Re/R, where a is the particle radius, L is the hydrodynamic length scale (size of the computational domain) and Re=U0*L/nu is Reynolds of the flow. However, sometimes this parameter is called the "nondimensional response time" and Stokes is defined as St=2/9 (a/L)^2 Re. 

May 26, 2011, 17:20 

#8 
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viva
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Thanks alot Martlet. It was a great help. thanks


February 5, 2017, 07:55 

#9 
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@martlet can you please send me some literature hints regarding the stokes number for small solid particles?


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