Looking for basic theory on mixing of gases

In summary: Turbulence, and Heat Transfer.In summary, the two gases should be mixed as soon as possible if you want to avoid having a long pipe segment in your CFD simulation.
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random_soldier
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Hi,

In my situation, I am dealing with two ideal gases traveling down a pipe at the same bulk velocities. I am only considering a 1-D treatment at the moment and I would like to find out at which point the two gases should be considered a well mixed, homogeneous mixture. Would anyone know either the particular formulation or even the subject matter to consult to determine the well-mixing of gases?

Thanks and regards.
 
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  • #2
If they are just traveling down a straight pipe, the mixing will be slow. If that is okay for your application and you just want to quantify the (long) distance needed, I'll let others address that.

Instead, would it help your application to on-purpose encourage the mixing of the gasses to happen as soon as possible (as short a run of pipe as possible)? If so, you may be able to leverage some of the concepts for mixing liquids (like 2-part epoxies). See this previous PF thread for more information on that:

https://www.physicsforums.com/threads/mixing-fluids-in-a-flow.973431/

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https://i.ytimg.com/vi/JYW6QDldODk/hqdefault.jpg
 
  • #3
It's to figure out how long I want the pipe segment to be in my CFD simulation so that I don't make a long segment adding unnecessary spatial meshing.

The real world setup the simulation is based on does not have provisions for applying the methods in that thread so no unfortunately. Thanks for the response though.
 
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  • #4
So you have a pipe and at the start of the pipe, the two gases are separated and you want to compute how much time/length it takes for them to mix perfectly?
You could solve the 1D convection-diffusion equation for the transport of species in time. In laminar flows, this can be done analytically. You could even consider the solution of the heat equation
$$C_t=C_{xx}$$
since there is an equivalence between transport of mass and heat. You then solve e.g. on the domain [-1,1] with boundary condition
$$C(x,0)=0, x<0$$
and:
$$C(x,0)=1, x>=0$$
For large t, you expect the concentration to go to ##C(x,\infty)=0.5##. You then compute the time it takes for the concentration to fulfill the condition ##C(x=1,t)=0.501##.

The mixing problem becomes more complicated when the species have large differences in fluid properties or if the problem is turbulent.

As a first guess, you could consider the concentration distribution in an infinitely large medium in time, where the initial mass is concentrated at x=0. The concentration in time is given by

$$C(x,t)=\frac{e^{-x^2/4Dt}}{\sqrt{4 \pi Dt}}$$
##D## is the binary diffusion coefficient of the two species. You can determine how much time it takes for the concentration at x=0 to reduce to 0.01. With the average pipe velocity, you can then determine the pipe length. For confined spaces, the mixing time increases. For instance in the semi-infinite domain ##x>0##, the concentration decay is twice as slow.

For turbulent flow problems, the mixing is much faster.
 
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  • #5
See Transport Phenomena by Bird, Stewart, and Lightfoot: Chapters on Mass Transport
 
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FAQ: Looking for basic theory on mixing of gases

1. What is the basic theory behind mixing of gases?

The basic theory behind mixing of gases is diffusion, which is the movement of molecules from an area of high concentration to an area of low concentration. This process occurs due to the random motion of molecules and can be explained by the laws of thermodynamics.

2. How does temperature affect the mixing of gases?

Temperature plays a crucial role in the mixing of gases. As the temperature increases, the kinetic energy of the molecules also increases, causing them to move faster and thus mix more quickly. On the other hand, a decrease in temperature can slow down the mixing process.

3. What factors influence the rate of gas mixing?

The rate of gas mixing can be influenced by several factors, including temperature, pressure, and the type of gases being mixed. Additionally, the surface area and distance between the gases can also affect the rate of mixing.

4. How can the mixing of gases be controlled?

The mixing of gases can be controlled by adjusting the temperature, pressure, and other factors that influence the rate of mixing. In industrial processes, various techniques such as stirring, agitation, and forced convection can also be used to control the mixing of gases.

5. What are some practical applications of gas mixing?

Gas mixing has numerous practical applications in various industries, including chemical, pharmaceutical, and food processing. It is used to create specific gas mixtures for various purposes, such as welding, gas chromatography, and medical treatments. Gas mixing is also essential in the production of fertilizers, fuels, and other products that require precise gas compositions.

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