In a binary mixture, when is one flow negligable?

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In a binary mixture, determining when one gas flow can be neglected involves identifying a non-dimensional parameter related to mass and momentum conservation. The discussion highlights that if a contaminant is introduced at a low rate, such as a few kilograms per hour, it may not significantly impact the overall flow dynamics. The challenge lies in finding specific literature that defines this parameter, as most textbooks assume negligible flow without providing detailed criteria. A suggested practical approach is to use mass-weighted averages in parts-per-million (ppm) to assess the contaminant's impact. Published limits on the contaminant may also provide guidance on when its flow can be considered negligible.
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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