Sphlow Java 0.2

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A menu with dynamic HTML enhancements: 

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 and rhop), 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 vessel.

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" panel.

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 to 105.  At each point, it first calculates the ratio f/Re (friction factor divided by Reynolds number) given by:
f = 4 mu g |rhop-rhof|
Re rhof2u3
where mu and g are the viscosity and gravitational acceleration respectively, rhof and rhop the fluid 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
Re = rhof u D ,
the particle diameter D follows straightforwardly.


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 velocity (i.e. 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 paper too!)

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.

Known bugs:

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.

JARS-registeredCredits and source:

Sphlow Java is based in large part on the ptplot package at UCBerkeley, copyright Regents of the University of California.  I also learned a lot from the Scoop on Java (where my first applet came from), 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 Phenomena by Bird, Stewart and Lightfoot.  Dynamic HTML is based on the flower shop layers example at Netscape.

Get the source code here (distributed under GPL), and promote open source softwareFree like Mozilla!

Email compliments/complaints/comments, bug reports and suggestions for new liquids to me.