Parcel theory -- how can there be buoyancy with miscible gases?

In summary, the parcel theory explains buoyancy in mixtures of miscible gases by considering the behavior of small parcels of gas within a larger gas environment. It accounts for variations in temperature, pressure, and composition, illustrating how these factors influence the density of gas parcels. As a result, buoyant forces arise when lighter parcels ascend through denser gas layers, despite the gases being fully mixed. The theory integrates principles of fluid dynamics and thermodynamics to clarify how buoyancy can occur even when gases are miscible.
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raxp
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TL;DR Summary
Parcel theory holds that the reason hot air rises is that its density is lower than the surrounding cold air, leading to Archimedean buoyancy. While this explanation is perfectly reasonable for a hot air balloon where there is a mechanical interface between the hot and cold gas, for warm and cold regions of an ideal gas, there can be no mechanical interface between the two.
Parcel theory holds that as air is heated, it expands. Its density hence decreases and the hot air "floats" upwards, pushed by the colder, more dense air surrounding it.

It is an experimental fact that hot air rises, but the explanation from buoyancy seems suspect. In a gas, all motions are uncorrelated, and the collision cross-section for each molecule is minuscule. How can there then be a mechanical force exerted between two regions of the same gas, differing only in their temperature? Each single molecule does not "know" to which parcel it belongs and may pass freely between them, unlike the case where there is some mechanical interface (the fabric of a hot air ballon, say) between the two regions.
 
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  • #2
raxp said:
How can there then be a mechanical force exerted between two regions of the same gas, differing only in their temperature?
When the "Mean Free Path" is very short, and the size of the parcel is large, the gasses do not mix rapidly. There is plenty of time for the parcel to rise or fall before it becomes mixed.

At sea level, the parcel dimension is 100 m or more, while the MFP is less than 100 nm. That is a difference of 9 orders of magnitude.
See the equations and table at the bottom of this section.
https://en.wikipedia.org/wiki/Mean_free_path#Kinetic_theory_of_gases
 
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  • #3
Baluncore said:
At sea level, the parcel dimension is 100 m or more, while the MFP is less than 100 nm. That is a difference of 9 orders of magnitude.
Ooh. I had no idea the mean free path for air at sea level was so short!
 
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  • #4
Drakkith said:
Ooh. I had no idea the mean free path for air at sea level was so short!
Not intuitive; I agree. But other numbers count too. There are zillions of molecules involved in diffusion between / within parcels of air. Most of our experiences of what a Science Teacher would call Diffusion (smells that drift around the room) do not involve stationary air.
 
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  • #5
raxp said:
How can there then be a mechanical force exerted between two regions of the same gas, differing only in their temperature?
Two neighboring regions of the same gas at non-zero pressure always exert equal but opposite forces on each-other, even when at the same temperature.

raxp said:
Each single molecule does not "know" to which parcel it belongs and may pass freely between them,
Yes, but that mixing is much slower than the propagation of forces via repeated collisions.
 
  • #6
A.T. said:
Two neighboring regions of the same gas at non-zero pressure always exert equal but opposite forces on each-other, even when at the same temperature.
Caveat here: But an N3 pair doesn't imply equilibrium
 

FAQ: Parcel theory -- how can there be buoyancy with miscible gases?

What is parcel theory in the context of buoyancy and miscible gases?

Parcel theory is a conceptual framework used to describe the behavior of small volumes of fluid, or "parcels," in a larger fluid environment. In meteorology and fluid dynamics, it helps explain how these parcels interact with their surroundings, particularly in terms of buoyancy. When discussing miscible gases, parcel theory examines how the mixing of different gases affects their density and buoyancy, which can lead to complex behaviors in fluid motion.

How does buoyancy occur in a mixture of miscible gases?

Buoyancy in a mixture of miscible gases occurs due to differences in density resulting from temperature and composition variations. Even when gases are miscible, changes in temperature or concentration can create regions of differing density. According to Archimedes' principle, a parcel of gas will experience an upward force if it is less dense than the surrounding fluid, leading to buoyant behavior. The interaction between the temperature and concentration gradients is crucial in determining the overall buoyancy of the gas mixture.

Can buoyancy be observed in a completely mixed gas system?

In a completely mixed gas system, buoyancy may not be as apparent as in systems with distinct density differences. However, buoyancy can still play a role if there are local variations in temperature or pressure that create small density differences. Even in a homogeneous mixture, if one component is heated or cooled, it can lead to buoyant forces that cause movement within the gas, demonstrating that buoyancy can still be present, albeit less pronounced.

What role does temperature play in the buoyancy of miscible gases?

Temperature plays a significant role in the buoyancy of miscible gases because it directly affects the density of the gas mixture. As temperature increases, the density of a gas typically decreases, causing it to rise if surrounded by cooler, denser gas. This temperature-driven buoyancy can lead to convection currents within the gas mixture, contributing to the overall dynamics of the system and influencing how gases mix and move.

How do pressure changes affect the buoyancy of miscible gases?

Pressure changes can affect the buoyancy of miscible gases by altering their densities. An increase in pressure generally increases the density of gases, while a decrease in pressure can reduce density. These changes can create buoyant forces that drive the movement of gas parcels. In systems where pressure varies, such as in the atmosphere or in industrial processes, understanding how pressure influences buoyancy is essential for predicting the behavior of gas mixtures.

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