Understanding the Importance of Particle Reynolds Number in Fluid Dynamics

In summary, Reynolds number is a measure of the resistance of a bubble or drop of fluid to movement. This resistance is due to the fluid deforming and flowing around the particle. Reynolds number is used to study the flow around a particle.
  • #1
min_ht
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1
Hello,

The particle Reynolds number makes me confused and I hope someone can help me on this please!

Normally (as I read in every books and papers) that when a bubble or drop rises in a fluid, the bubble/drop Reynolds number is calculated by:

Re = ρUD/μ

where U is particle velocity, D can be particle diameter, and ρ and μ are density and viscosity of continuous fluid

my question is why don't use ρ and μ of bubble/drop? why use them of surrounding fluid?
what is the physical meaning of this Re?

Thanks in advance.
 
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  • #2
The particle is supposed to be solid, so it has no ##\mu##: the fluid has to move around the particle and not the other way around. :smile:
 
  • #3
BvU said:
The particle is supposed to be solid, so it has no ##\mu##: the fluid has to move around the particle and not the other way around. :smile:

Thank you for your reply
Actually the term "particle" refers to all solid particle, liquid drop or gas bubble (book: Bubbles, Drops, and Particles of Clift et al. 1978)
just normally people use particle for solid body :)
and that equation for Re applies for all of them
in my case it is liquid droplet, so it has μ, and that's why I don't really understand :(
 
  • #4
The resistance to the particle movement is caused by the fluid deforming. As reckoned from the frame of reference of particle, the fluid is flowing past. So it is the fluid deformation and flow around the particle that determines the drag on the particle. That's why the focus is on the fluid.
 
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  • #5
min_ht said:
in my case it is liquid droplet, so it has μ, and that's why I don't really understand

In the case of something like a liquid droplet falling through air, you would make the assumption that the droplet is a spherical particle with no deformation. The Reynolds number still applies to the surrounding fluid flowing around the particle, not the other way around.

https://en.wikipedia.org/wiki/Sediment_transport#Particle_Reynolds_Number
 
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  • #6
If your goal is to study the flow around a particle, why would you use conditions inside the particle in your study?
 
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  • #7
Thank you all
I think I got your points and they help a lot
very appreciated!
 
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What is the definition of Particle Reynolds number?

The Particle Reynolds number (Rep) is a dimensionless quantity used in fluid mechanics to characterize the flow of a fluid around a particle. It is defined as the ratio of inertial forces to viscous forces acting on the particle, and is given by the equation Rep = (ρuL)/μ, where ρ is the fluid density, u is the fluid velocity, L is the characteristic length of the particle, and μ is the fluid viscosity.

What is the significance of Particle Reynolds number in fluid dynamics?

The Particle Reynolds number is an important parameter in fluid dynamics as it determines the type of flow regime around a particle. At low Rep values, the flow is dominated by viscous forces and is called Stokes flow. At high Rep values, the flow is dominated by inertial forces and is called turbulent flow. The transition between these two regimes is known as the critical Reynolds number.

How does Particle Reynolds number affect particle behavior in a fluid?

The behavior of a particle in a fluid is strongly influenced by the value of Particle Reynolds number. At low Rep values, particles tend to follow the flow of the fluid and have a smooth trajectory. At high Rep values, particles experience erratic motion due to the turbulent nature of the flow. This can result in increased mixing and collisions between particles.

What are some practical applications of Particle Reynolds number?

Particle Reynolds number is used in a wide range of practical applications, including fluidized bed reactors, sediment transport in rivers and oceans, and aerosol science. It is also commonly used in the design of industrial processes involving particle-fluid interactions, such as filtration, mixing, and spray drying.

How can Particle Reynolds number be calculated or measured?

Particle Reynolds number can be calculated using the equation Rep = (ρuL)/μ, where the values of ρ, u, L, and μ can be obtained from experimental measurements or theoretical models. It can also be measured directly using specialized instruments, such as laser Doppler anemometry, particle image velocimetry, or hot-wire anemometry.

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