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When you are sitting in a room where there is a source of bad smell, such as somebody smoking or some other source of bad smell, it is often a solution to simply move to another spot where bad smell is not present. Assuming you are not actually the source of the smell, this will work for a while until you notice the smell has somehow migrated to exactly the spot where you are now sitting. Frustrating.

This got me thinking about the fluid mechanics of this problem. Treat bad smell as a gas that is (perhaps continuously) emitted at a certain fixed source. One explanation could be that human breathes and perhaps creates a pressure differential that causes the smell to move around. Is there any truth to this? Please provide a reasoned argument with reference to the relevant thermodynamic and/or fluid quantities in answering the question. Theoretical explanation is desired, but extra kudos if you know of an experiment.

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In a word the answer is diffuion. When the there is a concentration gradient, a certain area in the room has less molecules of the bad smell or perfume, then there is tendency that the concentration of the molecules in the room tend to equalize. Perhaps some one will elaborate with a mathematical explanation – Prathyush Oct 18 '12 at 18:06
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In addition to fluid dynamics, and the answer of tpg2114 is good, you should consider, particularly if the odor is strong, the fact that the olfactory nerves in our nose can be saturated and keep on sending the odor signals. While moving there is sensory distraction but after sitting it will again be noticed. This is particularly true of very unpleasant smells, like those from a cesspool. It takes some minutes for the nose to clear, in my observation. – anna v Oct 19 '12 at 6:32
@annav, it seems like that, like sensitizing, I agree with you. But, once the smell has reached the nose, it most certainly has also reached other parts of the body - hair, fingers, limbs - and become entrained in their motion. The nose is not likely to be the first point on the body the smell has drifted to. – Bobbi Bennett Oct 23 '12 at 5:09

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From a fluid dynamics standpoint, as a body moves through a fluid, a small region of fluid is dragged along with it. This is what forms the boundary layer. In the near-body region, odor will be dragged along with the body.

Likewise, behind a moving person is a turbulent wake and a low pressure region. The low pressure reason will "suck" the odor along with the body, and the turbulence will mix the odor into the air which will also help distribute it.

Turns out there is an experiment, in this paper, that looks at the effect of a stationary body and a moving body (as in human body) in a room with stratified contaminants. The principles discussed therein are along the lines of your question.

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I have backed away from dust spills and seen just this turbulent wake effect. The smoke follows! So, is it better to back away slowly, or quickly? Maybe moving slowly makes less turbulence? – Bobbi Bennett Oct 18 '12 at 21:19
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Slowly will generate less wake and thus less of that suction process. If you look at see.ed.ac.uk/~johnc/teaching/fluidmechanics4/2003-04/fluids14/… and go to the image of the cylinders, you will see what that looks like. If you back away very slowly, that is similar to the Re < 1 case which shows no velocity towards the cylinder on the backside, so nothing follows you. As you move faster, there are bigger regions with velocity pointing towards you, hence more suction (and more drag). – tpg2114 Oct 18 '12 at 21:50
Interesting. In combination with what anna said above in a comment to my question, it explains what I have observed circumstantially. – SMeznaric Oct 19 '12 at 16:10
@tpg2114 What about a combination of boundary layers and the fact that convective acceleration would need the particles/packets of bad odor move with the velocity vector of the person. – drN Oct 21 '12 at 22:24
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This probably isn't primarily a result of fluid dynamics

Toxic particles in cigarette smoke can remain on nearby surfaces, as well as the hair and clothing of the smoker, long after the cigarette has been put out, and small children are susceptible because they are likely to breathe in close proximity, or even lick and suck them

http://news.bbc.co.uk/1/hi/health/7813124.stm

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I agree and disagree. Fluid dynamics certainly plays a role. Because the fluid velocity must match the surface velocity of an object, a body moving through a region of odor (or any set of molecules) will drag them along close to the surface. This dragging along may be a minor contributor compared to the amount that sticks to surfaces, but it's not easy to speculate and I haven't done the math or looked for experiments. – tpg2114 Oct 18 '12 at 18:41
Plus the wake behind the body will be turbulent and low pressure, which will mix the odor considerably and drag it along behind the body. – tpg2114 Oct 18 '12 at 18:43
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Fluid dynamics (more precisely, the gas dynamics) plays of cause, the role, especially if you account also for diffusion of smell agents. The latter are usually organic molecules. In most cases it is diffusion that follows you. However, also the gas flow certainly plays a role, and one cannot say in advance, what is more important.

In principle, a research along the line of your question is quite reasonable. The question is in the applied area: how to best organize ventilation in order to fast remove bad smells, or in a more general statement, to renew the air in some closed room. I did not follow the specific question concerning smells, but people are very active in very closely related problems concerning ventilation of rooms and e.g. car cabins. You may find lots of literature on these subjects.

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