Re: [Phys-l] Coalesing drops

[Paul Doherty <dohertypm@gmail.com>]

BC

Check out the new exhibit at the Exploratorium.
At the exhibit there is a 15 cm diameter upward vertical airflow.
Visitors create water drops and drop them into the airflow.

Drops of a certain size, about  5 mm, are at trerminal velocity in  
the airstream and float at a constant altitude.

Squirt a couple of drops and when they collide and coalesce the  
resulting larger drop explodes in a spray of small droplets.

I'll try to get images and  video.

Paul D



On Oct 10, 2010, at 12:13 AM, Bernard Cleyet wrote:

> Bob!
>
> (delayed by trip to birthday dinner a day away, not mine.)
>
> Yes!  You're correct.  I forgot about the buoyant force, which is  
> negligible in this case, and the g force is ~ to the cube of the  
> radius,  while the drag is only prop. to the square.***
>
> http://en.wikipedia.org/wiki/Stokes'_law
>
> doesn't apply.
>
> hyperphysics has done the work for me:
>
> http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html#c5
>
>
> for 2 mm and 5 mm drops their terminal speeds are v. ~ 6.4 and 10.1  
> m/s.
>
> I cheated and found in Eisberg and Lerner (I've seen it elsewhere  
> also.) the formula for the position (time) for v^2 drag.
>
>
> The formulae, as I graphed for two and 5 mm D drops, is on my site.
>
> http://www.cleyet.org/images/Drops%20at%20the%20Exploratorium/
>
> Here's the generic:
>
> X = (1/gamma) (Ln[exp(sqrt(gamma*g)*t )+ exp(sqrt(gamma*g)*t)]/2)
>
> gamma = drag factor / m  =  0.5* density (air) * cross section(Pi *  
> R^2) * coefficient (sphere ~0.5)  /  density * [(4/3) Pi * R^3]
>
> this reduces to ~ 2.25E-4 / r
>
> I pray no error.   The equations for 2 mm and 5 mm diameter are  
> part of the titles of the graphs.   They were generated by the  
> function feature in Kaleidograph.   I extracted the data it created  
> and subtracted the positions.  As one can see if dropped ~ 10 cm  
> apart after v.~ 600 ms the five mm one will catch up.  This is  
> after falling about five feet.
>
>
>
> *** what happens when ones mind's eye model is incomplete.
>
> bc no experience w/ dropping, so doesn't know if practical.
>
>
>
> On 2010, Oct 08, , at 19:25, LaMontagne, Bob wrote:
>
> > Just curious - what do you mean by "The smaller will catch up and  
> > likely coalesce instead of shatter."?  My understanding is that  
> > the fall speed of droplets is proportional to the square root of  
> > their radii. Don't larger drops catch up with smaller ones?
> >
> > Bob at P