# Differential motion of smoke particles?

1. Nov 17, 2008

### chason

Hi All,

I work in a bio research lab. We are trying to set up a smoke exposure chamber to expose mice to low levels of cigarette smoke. In the contraption we have, a cigarette is burned in a small chamber and the smoke is pumped into the mouse exposure chamber. In my tests so far, the smoke is either too concentrated in the exposure chamber or too concentrated in the cigarette chamber (cigarette burns too slowly). I want to use a second pump to draw off smoke from the cigarette chamber and release it into the fume hood the instrument is in, rather than the exposure chamber. This should reduce the concentration of smoke in both the exposure and cigarette chambers.

My question is, if I have one pump running faster than the other, will smoke particles of different sizes be more likely to be drawn by one pump or the other? Tobacco smoke particles range from 0.01 to 1.0 microns. I am trying to make sure that the mice get exposed to the typical range of smoke particles, not one that is enriched for the lower or higher sizes

2. Nov 17, 2008

### natives

I really dont know how to technically help out but I was seriously interested in the problem and I'd like you to try out these solutions and see if experimentally they apply...Am using knowledge of pressure exerted due to small suspendable particles from A-level thermodynamics physics and university 2nd year primary knowledge in vector calculus and electric flux,surface density,gauss's law and a bit of the divergence theorem....My assumptions on approaching the problem are 1. A constant velocity vector V is associated with each and all smoke particles independent of time and temperature variations[to overcome this assumption plotting and formulating the equation of a vector field V(x,y,z,t=time,T=Temperature) would be a basically good approach.Initially!I cant do that because it requires physical experimentation)...2.the pumps provide constant compression and/or tension pressure at any time t...3.other assumptions would be made automatically under whatever circumstances either by or you..that is there might be other assumptions I've made do not see the importance of listing out,and am expecting you to just know,like no energy losses,perfectly elastic collisions e.t.c!...APPROACH: take an opening to pump 1 have area A1,consider an imaginary plane on top of this opening such that a smoke particle of mass m1 collides with momentum=m1v1=Ft...devide by t<which is very small,just couldnt get the delta sign,but its very small> then devide by area A1 giving pressure P1<on imaginary plane at opening 1>=(m1v1)/tA1...now am thinkin t is time time between collisions on plane so its inversely proportional to number N1 of smoke particles passing through the opening..taking a constant k for proportionality then t=k1/N1 thus pressure P1=(m1v1N1)/k1A1...but v1 in the above equation is the magnitude of the smoke's velocity vector normal to the imaginary plane...mathematically this equal to dot product of vector v_1 of smoke particles and the unit normal vector n_1 to the plane v1=v_1.n_1...thus P1=[m1(v_1.n_1)N1]/k1A1...this is almost it because almost all the quantities above can be experimentally obtained and settin m1 to the typical values of 0.1 and 1 microns..also using Gauss' law,giving analogy of the smoke particles inclosed in a spherical region of radius R as flux enclosed in that spherical region{am not sure if this is correct but it might help!}...then number of particles N=surface closed integral of D.ds where D=smoke number particle density per unit surface=£N/A and ds=small vanishing surface s....where £=summation of!To get £N=total physicall measured mass enclosed in the spherical region/typical mass....to compare wether your question of the 2 pumps would work,take ratios of P1/P2 then compare dependency of the ratio over the other parameters,keeping some constant and others variable as much as you wish...I know this is not very technical but inorder to prove it useful start by experimenting on it...I'd like some feedback if possible through

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Last edited by a moderator: Nov 17, 2008
3. Nov 17, 2008

### natives

In addition...To give a theoretical answer to the question...Using above formulation and ratio,keeping the openings to have the same opening area,the same orientation relative to some x,y,z axes somewhere and with air tight conditions then you can achieve the pressure ratios P1/P2 directly proportional to the number-of-particles ratio N1/N2...with k1=k2...with this then YES theoretically more pump pressure more smoke!

4. Nov 17, 2008

### natives

I would also advise a third pump to provide constant air supply to preven crushing of the smoke chamber due to airtight conditions!