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Jie March 16, 2001 05:41

About Stokes number
Dear All,

Stokes number seems a frequently empolyed dimensionless number is fluid-particle two-phase flows. Is there anyone who could kindly tell me the defination and physical meaning of this number?

Many thanks!

Jie Li

George Bergantz March 16, 2001 19:08

Re: About Stokes number
The Stokes number is a very powerful concept, and has been extended to included a heat transfer or mass transfer Stokes-like 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 two-dimensional mixing layers. Part 2. The effect of gravity", Phys. Fluids, v. 7, p. 1241-1264.

Another good one with nice illustrations:

Tang et al., 1992, "Self-organizing particle dispersion mechanism in free shear flows", Phys. Fluids, v. A4, p. 2244-2249.

George Bergantz March 16, 2001 19:14

OPPPPS- got it backwards
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.

Jie March 20, 2001 05:40

Re: About Stokes number
Dear George Bergantz,

Many thanks for your kind explanations which is helpful.

Are you also involved in particulate two-phase flow research. This seems a quite promising area and very interesting, Particularly the pattern formation.

Thank you again.


haris November 8, 2010 08:04

Hi i am modeling a naca0012 in heavy rain with fluent dpm model and steady state treatment(for particle and phase) question is

where can i find the τ (relaxation time) for my airfoil to calculate the stokes number?:confused:

viva May 23, 2011 23:13

Stokes number

Could you advice me how to calculate Stoke's number for a fluid-particle system?


martlet May 24, 2011 10:02

Re: Stokes number
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 "non-dimensional response time" and Stokes is defined as St=2/9 (a/L)^2 Re.

viva May 26, 2011 17:20

Thanks alot Martlet. It was a great help. thanks

map February 5, 2017 08:55

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

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