In a binary mixture, when is one flow negligable?

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SUMMARY

The discussion focuses on identifying a non-dimensional parameter that determines when the flow of one gas in a binary mixture can be considered negligible. The example provided illustrates a scenario where a contaminant is introduced into a river at a low rate, suggesting it does not significantly impact the overall mass or momentum of the flow. The participant expresses difficulty in finding specific literature on this topic, noting that existing fluids textbooks often assume negligible flow without providing a clear parameter. The concept of mass fraction and mass-weighted averages in parts-per-million (ppm) is highlighted as a potential approach for practical applications.

PREREQUISITES
  • Understanding of mass and momentum conservation equations
  • Familiarity with non-dimensional analysis in fluid dynamics
  • Knowledge of mass fraction calculations
  • Experience with parts-per-million (ppm) concentration measurements
NEXT STEPS
  • Research non-dimensional parameters in fluid dynamics, such as the Reynolds number
  • Explore mass fraction calculations in binary mixtures
  • Investigate the impact of contaminants on fluid flow dynamics
  • Study published limits and guidelines for contaminants in environmental engineering
USEFUL FOR

Environmental engineers, fluid dynamics researchers, and professionals involved in pollution control and water quality assessment will benefit from this discussion.

gittenlucky
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I am looking for a non dimensional parameter that will tell me if I can neglect the flow of one of the gases and just consider the mass and momentum conservation equations for the background species. This is not a homework question.

For example: If there is a pipe dumping a contaminant into a river at a rate of a few kilograms per hour, it will not affect the overall mass or momentum of the overall flow.

I am having a lot of trouble finding this parameter. All of my fluids textbooks just say something along the lines of "it will be assumed the flow of the contaminant is negligible and will not affect the overall dynamics". I have a feeling it will have something to do with the mass fraction, but I can not find any specific statement in literature.

Thank you for your assistance.
 
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In practice I would do a mass weighted average in parts-per-million (ppm). Then you may be able to find published limits on the contaminant.
 

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