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Author Topic: Calculations for upward current classifier  (Read 2195 times)

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Offline DharmaSoldat

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Re: Calculations for upward current classifier
« Reply #10 on: January 21, 2019, 09:33:45 AM »
Tonofsteel... It's mostly an experiment and a way to save my back from hurting :D

I wanted to be able to take a small and relatively lightweight battery powered unit out into to the field for sample or small-run processing without a lot of heavy panning. Afterwards I might try beefing up the unit to do larger field processing but it's mostly for the former reason.

Offline geezir

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Re: Calculations for upward current classifier
« Reply #11 on: January 21, 2019, 06:05:26 PM »
Over the years I have come up with great new ideas, only to find out that I was reinventing the wheel. Reinventing the wheel in its self is not a bad thing. It is how we get better wheels.  <-wave->

Interesting thread but the answer to it is rather detailed and will take some space and time.

So let's start.
If you have access to a handbook on mineral processing they will start with ore handling and continue with the breaking of the ore into a size to release the desired mineral. Larger particles are separated by screening but particles that are too fine to be sorted by screening are usually sorted in water by wet classification bases on  how the particles fall in the fluid..
At one time the gains actually "fell" but today the most common classifier is the cyclone. The particles are accelerated into the cone and the denser (larger) keep to the wall exit out the base and the lighter particles are drawn into the over-flow.
Where gravity supplies the acceleration in system such as elutriation there are two main formulas used to calculate the particles fall rate.
(From "Mineral Processing Technology" BA Wills)
   1. Newton's Law
If a particle is large (heavy) enough (Mass x Acceleration = Force) the drag force will be largely turbulent resistance.

   2. Stokes' Law
If a particle lacks mass to accelerate the drag force will be due to viscous resistance.

In both cases if the particles have the same density the larger one will have the higher terminal velocity.
In both cases if are the same size the denser particle will have the higher terminal velocity.

The formulas for both cases are available for anyone wishing to look them up. However the formula for calculating the size density ratio would be of interest to anyone using gravity separation methods.

Free Fall Ratio
Two mineral particles have densities Da and Db and diameters da and db and fall in a fluid of Df
From Newton's law
         da/db = Db - Df 
                            Da - Df 
And from stokes law the square root of the above.

For example quartz 2.65 sg and galena 7.5 sg in water
                     7.5 - 1 
                     2.65 -1
6.5/1.65=3.9394 and the square root of that is 1.98479

For larger particles that follow Newton's law a particle of quartz 3.94 larger than galena will fall at the same rate.
For small particles that follow Stokes' law the ratio is 1.99.

Newton's Law is valid for particles over 5mm and Stokes' law is valid for particles under 0.05mm and the size in-between
Are in a transition zone.

More to follow:

Offline geezir

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Re: Calculations for upward current classifier
« Reply #12 on: January 21, 2019, 09:54:46 PM »
A bit more ...
Before talking about elutriation lets discuss particle size.  What happens when a particle increases or decreases in size.

Let's compare a 1mm to 10mm.
1mm cube = 1 cubic mm surface area 1x6 or 6 sq mm
10 mm cube = 1000 cubic mm surface area 100x6 600 sq mm

Our volume increased by 1000 and the surface by 600. (volume = weight or mass) (surface = drag or resistance)

Mass x acceleration = force

With a consistent density and gravity acceleration the force is
 1mm = 1g force  10mm = 1000g force
 Let's compare force to resistance (use total surface area)

1g : 6
1000g : 600 (1g : 0.6)


In reality as a particle increases in size and turbulent drag becomes the main resistance the face size (frontal area) has much more relationship to drag than surface area.

As particle size changes the ratio between volume and surface area changes. An increase in size increases weight to surface area. As a particle decreases in size the reverse is true. A micron sized particle has a huge surface area in relation to its mass. 

The bigger the particle the more horsepower per surface area.

more to follow:

Offline DharmaSoldat

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Re: Calculations for upward current classifier
« Reply #13 on: January 22, 2019, 07:24:35 AM »
I've been using the Ferguson-Church equation to figure out the settling velocity of the various particles... https://hinderedsettling.com/2013/08/09/grain-settling-python/.

It blends the small and large particle size SV together in an analytic equation.

There are other forces to account for of course but as a general starting point I've found it useful.

 


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