droplet volumes

Eric Van Buren eric.vanburen at wayne.edu
Fri Feb 10 13:02:50 EST 2006

Hello Bill Throndset,

You can calculate the volume of a drop if you know the speed of the
stream. I think I've seen 10 m/s given for pre-SE BD sorters. I
googled and found a site that gives 20 m/s for a 60 psi MoFlo.

Thus, a nozzle with a 70 micrometer diameter circular opening would form a
cylindar of liquid with volume V = h*pi*r^2. What's the height? Set t to one
second: h = (20 m/s) * (1 s) = 20 m.

V = (20 m) * pi * (70E-6 m / 2)^2 = 7.7E-8 m^3

Converting we get

V = (7.7E-8 m^3) * (100 cm/m)^3 * (1 ml/cm^3) = 0.077 ml

Now, in one second 100,000 drops are formed, so the volume per drop, V(d), is

V(d) = (0.077 ml) / (100,000 drops) = 7.7E-7 ml/drop = 0.77 nl/drop

You should be able to measure this empirically as well. Since measuring
mass is easier than measuring volume, you'll need to know the density of
your sheath fluid. Weigh your empty collection tube, put sheath fluid in
your sample tube and sort enough drops to make a sufficient volume (maybe
1E+6 to 5E+6 drops), weigh the collection tube again and then do some math.
(Make sure you're sorting 1-drop packets or else account for your packet

The portion of each drop that comes from the sample stream is dependent
on the sample differential, because this controls the diameter of the
sample (core) stream. You could probably devise an experiment using
a concentrated dye for your sample and then taking aliquots from the
stream at different sample pressures to figure this out. A suspect a
spectrophotometer would come in handy.

Good luck,

>Can anyone tell me the volume of droplets coming out of a jet-in-air nozzle?  I am
usually using a 70 micron nozzle at 60psi and about 100,000 droplets per second.   I'd
also like to know how to calculate this myself.  Also, since the droplets are made up of
sheath and sample, what portion of each droplet is sheath, and what portion is sample? 
> Bill Throndset
> Genencor International
> Palo Alto, CA  

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