Sphlow Java 0.2
About Sphlow Java:
The intended use is for metallurgical processes involving flotation of
inclusions, such as tundishes or electron beam melting hearths. Inclusions
are second-phase particles, such as oxide or nitride impurities, tungsten
carbide tool bit chips left over from machining operations, etc. which
get into metal and must be removed while the metal is molten. A given
tundish or hearth design and operating parameter set will lead to a rough
critical rising/sinking velocity for removal of all inclusions, such that
(nearly) all inclusions rising or sinking faster than that critical velocity
will be removed in that vessel. So, if inclusions are distributed
in size and density (D
), then since velocity
increases with diameter, those particles in the distribution above the
critical velocity contour in the graph on the right will be removed from
the molten metal by floating to the top or sinking to the bottom of the
Of course, you're free to use it for whatever purpose you like (skydiving
and blowing bubbles underwater come to mind).
How to use it:
To draw the first plot, hit return in the velocity field. You may
then use the menus and change the value in any field, just make certain
you press <return> after each entry so that it will register.
To zoom in on a graph, drag the mouse from the top left corner to the bottom
right corner of what you'd like to see. To zoom out, drag the mouse
upward. You can also change the limits in the "D-rho curve controls"
So, type in your fluid viscosity and density, or choose from the liquids
offered. When you give it a critical velocity, Sphlow Java will tell
you the Reynolds number, friction factor and particle diameter and show
you the relevant point for the given particle density in the friction factor-Reynolds
number curve on the left. It will also plot diameters which rise/fall
at the same velocity for a range of particle densities in the curve on
the right. You may plot up to nine such velocity contours by selecting
a new curve number and entering a new velocity. If you change liquid
properties or D-rho graph limits, Sphlow Java will redraw all of
the velocity contours.
The red vertical line on the right indicates the liquid density.
The starting point corresponds to nickel spheres in water.
How it works:
This applet calculates and displays the relationship between size, density
and terminal rising/sinking velocity of a spherical particle in a fluid.
It is based on the relationship between friction factor and Reynolds number
in laminar flow, from Stokes flow where Re
<0.2 to Newton's law
flow for Reynolds numbers from about 103
At each point, it first calculates the ratio f/Re
divided by Reynolds number) given by:
||4 mu g |rhop-rhof|
are the viscosity and gravitational acceleration
and particle densities, and u
the rising or sinking velocity.
It then draws a diagonal line of slope 1 in the graph on the left corresponding
to that value of f/Re
, and the intersection with the red curve gives
the Reynolds number and friction factor. Since
the particle diameter D
This model assumes a quiescent liquid. If there is a lot of vertical
flow, recirculation or turbulence in your problem, particles will be swept
up and down, so it is wise to be conservative in your estimate of critical
use a much
larger velocity than the vessel
height divided by residence time).
The model also assumes constant liquid and particle densities.
If these densities vary strongly with temperature, things will be somewhat
more complicated: if the liquid coefficient of thermal expansion (CTE)
is higher than that of the particle, there will be a range of densities
at which particles will be neutrally buoyant; if the particle CTE is higher
then it will always float or sink. Density also changes in porous
inclusions, e.g. porous titanium nitride in molten titanium, where
dissolving the dense nitride decreases a particle's average density but
filling a pore increases it. (See the paper
of Jean-Pierre Bellot and Alec Mitchell in the 12/1997
issue of Metallurgical
and Materials Transactions for details. Hey, while you're
there, check out my
Finally, the model assumes spherical inclusion particles. For
non-spherical particles, the friction factor will usually be smaller than
that of the smallest sphere containing the particle (always so in the case
of Stokes flow where Re<0.2), so velocity will be higher, and
this model will give a conservative velocity estimate for such particles.
Due to a bug in the ptplot package, the "fill" button will redraw the plot
with limits set to encompass all points that have ever been drawn, not
merely those which are currently active. It should not be necessary
to use this button. Another bug in ptplot limits the minimum size
of the graphs, so a version smaller than 800x500 will not be feasible anytime
soon. Also, some of the velocity contours are not drawn to the top
of the D-rho
graph space; I will fix that soon.
Though Sphlow Java 0.2 has been successfully tested on Netscape 3.01
and 4.05 for Irix and Netscape 3.01 and 4.05 for PowerPC Mac, I have heard
it doesn't work on Sandia Mac Netscape 3. My guess is that this is
because the classes are not signed.
Sphlow Java is based in large part on the ptplot
at UCBerkeley, copyright Regents of the University of California.
I also learned a lot from the Scoop
(where my first applet
and the Lemniscate
among the curves
from the University of St. Andrews
Byte code is due to the SGI JDK 1.1, but it should be JDK 1.0 compliant.
This applet has been tested on Netscape 3.01 and 4.05 for Irix and Netscape
3.01 and 4.05 for PowerPC Mac. The Magic Red Curve in the friction
factor graph on the left is based on principles of fluid flow around a
sphere, and taken from Transport
by Bird, Stewart and Lightfoot. Dynamic HTML is
based on the flower
shop layers example
Get the source
code here (distributed under GPL),
and promote open source software!
Email compliments/complaints/comments, bug reports and suggestions for
new liquids to me.