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As we know diffussivity of gas is really slow (e.g. $\require{mhchem}\ce{O2}$ and $\ce{H2O}$ in the air are respectively $0.176$ and $0.282 ~\text{cm}^2/\text{s}$).

here is a example to specify how slow it is, to evaporate water filled in a $1~\text{m}$ testing tube without external heating, one requires almost $50$ years!! (Note that the vapor is saturated at the water-air interface so the energy for phase conversion is not a issue here.)

However, if one farts in a room without sensible air flow, the smell can be noticed by him within $10$ seconds. This is definitely a speed that diffusion can not achieve. Does it mean that the air flow in a 'normal' room can be around $1~\text{m/s}$, or the initial far speed from anus gives a strong momentum which I don't think it could be that strong?

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Living human bodies typically have a thin envelope of air warmed by conduction, and this warm air forms a rising plume. Classic photo: the plume of warm air above a human body, visualized by Schlieren Photography:

Schlieren Photography ALWAYS SILENT, SOMETIMES DEADLY!

Unless your subject is nude, any ejected gas will inflate their clothing and then leak promptly from clothing crevices or slowly through the weave of the cloth. If it forms no jets and cannot escape outside the boundary layer of the rising heat-plume, then the stench will be entrained and become part of the rising plume.

A Titanium chloride smoke marker applied to clothing might demonstrate the "who dealt it, smelt it" phenomenon, and also reveal the location in the closed room of the descending part of the plume.

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According to this website, the diffusion coefficient of methane (which is also produced in farts) is about 20 ${\rm m}^2$/s.

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  • $\begingroup$ that website does not have a correct diffusivity value. for example water vapor should be 22 cm2/s at 0 degree according to diffusivity equation: d=2.12e-5*((t-273.15)/273.15)^1.75 (m2/s) rather than 22m2/s. $\endgroup$ – Chenming Zhang Jul 5 '13 at 0:00
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    $\begingroup$ Methane is odorless though $\endgroup$ – pentane May 8 '15 at 19:21

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