# Bacteria sorting?

Howard Shapiro hms at shapirolab.com
Mon Mar 11 19:18:58 EST 2002

```Alice Givan wrote-

>In my comment on calculating the volume of a droplet,  I "guessed" that
>the diameter of
>the drop might be approximately the diameter of the nozzle orifice.  I
>knew this was a
>rough approximation --- as the stream can contract a bit as it leaves the
>orifice and
>then the droplet that forms can have a diameter greater than the diameter
>of the stream.
>Joe Trotter (whom I always trust) says that the droplet diameter is
>approximately 1.89
>times the nozzle diameter. In fact,  I just went and measured the drop and
>the stream
>on my monitor screen and I got about 1.6 (using a bad ruler and a roughed
>up piece
>of paper).  So my approximation that the drop diameter was equal to the
>nozzle orifice
>diameter was, obviously, grossly wrong either way.

I wouldn't have gone that route.

>   Perhaps the best way to calculate
>the volume of a drop is by  Dirk Van Bockstaele's method (calculating the
>volume
>of the  "column" of liquid coming out of the nozzle in one second and then
>dividing
>that volume into however many drops are being generated in one
>second).  However,  in
>order to do this from first principles you need to know the diameter of
>the stream and
>also the velocity of the stream.....possible,  but awkward.

Velocity for a stream-in-air nozzle, in m/sec, should be 3.7 * (sheath
pressure(in psi))^(1/2).   This is from Pinkel and Stovel, also on p. 139
of the 3rd Ed. of PFC.  Page 140 has the "column" volume calculation.

>   I suppose you could also
>do it simply by measuring the volume flowing from the stream in 10 minutes
>and then
>calculating the volume for one second (I might be missing something here
>-- Howard,
>where are you (I know,  he is working on the fourth edition just when I
>need him).

I'm still here, obviously. And you can probably limit the calculation of
stream volume to 1 minute; you'll divide by 60 to get the volume per
second, and you'll get enough volume out in a minute (or two) to get an
accurate enough calculation.

And there's time (but not much) to clear this up in the 4th Edition.  Do
you have a reference to Dirk van Bockstaele's calculation?

-Howard

```

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