calculate density of a powder

[theMan]

Let's say I take a solid piece of pure aluminum, with density ~2.7g/ml, and grind it down into a fine powder, lets say 400 mesh (37µm particle size). How can I figure the density of this powder under STP, i.e. in regular atmospheric conditions with no added pressure? The powder is not compacted in any way, except by its own weight.

also, i want to do this theoretically, as in no weighing.

 

[Paperdoc]

Can't be done by calculation because too many variables are unknown. For example, you suggest the average particle size might be 37 micons. IF they ALL were spherical with 37 microns diameter you could calculate the number of such spheres at the known density of 2.7 g/ml and a known weight of aluminum, then use the spherical packing model to calculate the actual volume of those spheres and get your answer. However, I just said IF they ALL were spheres, and IF they ALL have exactly the same diameter. Neither will happen no matter how you grind the original mass of metal. Even if you assumed they all were spheres but had a known distribution of diameters, I doubt you could get a really good answer, and this is STILL not realistic.

Because the particles produced by the procedure you postulate will be of highly irregular shape and size, you cannot calculate. Moreover, how they pack together is impossible to predict, because irregular protruding pieces on each particle will snag on others. So, for example, if you were to collect all the metal dust into a cylinder and measure the weight and volume of it, you'd get an answer for apparent bulk density, They you shake the cylinder and watch the volume apparently shrink. New answer. Now someone brings in a vibrating platform to put the container on and it shrinks more. But by how much - you cannot predict and calculate! What will happen when you try an ultrasonic probe?

So the answer actually is, first you perform and carefully define the method by which you prepare, collect, pack and measure the dust. Then you weigh and measure volume and calculate density. Then, to assess your process, you repeat 30 times and gather a mean and standard deviation. Now you know with some quantifiable precision the answer based on real-world data, but you cannot calculate from first assumptions. And the result will change if I do the experiment again but using a different procedure.

 

[Cogman]

Can't be done, density can vary dramatically depending on how the particles are distributed. IE shacking a sack of aluminum power will change the volume considerably thus changing the density.

Kind of like how you can pore sand into a container of rocks, but you can't pore rocks into a container of sand, even though the amount of rocks and sand are the same.

Paperdoc's method is the only way to get a fairly reliable and consistent answer.

 

[CycloWizard]

What Paperdoc said. There were some papers in Science about two years ago that indicated that the packing density of uniform spheres is actually a lower limit to packing density. There are methods by which one can approximate what the packing density might be using simulations (e.g. Monte Carlo settling simulations), but setting something like that up would be much more time consuming (and less reliable) than simply testing. The question I have is: why do you need to know the density of a powder? If we know how you plan to use the value, then we could suggest a better method.

 

[MrDudeMan]

Not that it really matters, but this has every identifying mark of a homework problem. There's not much to add to what the three of them said assuming that's true. If it isn't, some more information would be helpful.

 

[soccerballtux]

Originally posted by: MrDudeMan
Not that it really matters, but this has every identifying mark of a homework problem. There's not much to add to what the three of them said assuming that's true. If it isn't, some more information would be helpful.

Lol, yea--

2.7g/ml, and grind it down into a fine powder, lets say 400 mesh (37µm particle size)

hm 2.7g/ml 37 um size that's not specific at all. LOL.

 

[PlasmaBomb]

Theoretically I would look up the MSDS for aluminium powder 400 mesh and it would tell me the correct density...

 

[ShawnD1]

Originally posted by: PlasmaBomb
Theoretically I would look up the MSDS for aluminium powder 400 mesh and it would tell me the correct density...

The thing you're looking for on the sheet will be called "bulk density" as opposed to regular density. It won't be on the MSDS but it should be on the supplier's certificate of analysis.

 

[gururu2]

its very easy to do under your stated conditions and this is what is typically done in the pharmaceutical industry.

1) Obtain a graduated cylinder
2) Place it in a balance.
3) Zero the balance.
4) Fill the graduated cylinder to a desired mark with your powder (say 10 mL)
5) Record the weight.

you have to weigh it. otherwise, if you know the dimensions of the block before grinding and place all of it into a graduated cylinder, you will already know the total mass and can then dervie the density directly by seeing how much volume was occupied.

This will give you g/cc which is the density of the material without any physical manupulation.
Stop overthinking it AT.

 

[PlasmaBomb]

Originally posted by: gururu2
its very easy to do under your stated conditions and this is what is typically done in the pharmaceutical industry.

1) Obtain a graduated cylinder
2) Place it in a balance.
3) Zero the balance.
4) Fill the graduated cylinder to a desired mark with your powder (say 10 mL)
5) Record the weight.

you have to weigh it. otherwise, if you know the dimensions of the block before grinding and place all of it into a graduated cylinder, you will already know the total mass and can then dervie the density directly by seeing how much volume was occupied.

This will give you g/cc which is the density of the material without any physical manupulation.
Stop overthinking it AT.

also, i want to do this theoretically, as in no weighing.

BTW the weighing counts as physical manipulation, since you have to transfer the powder from the box to the cylinder.

 

[gururu2]

if you know the physical dimensions of the aluminum block, all you need is a measuring cup. no balance required

 

[frostedflakes]

He meant that OP wanted to calculate density theoretically, not using quantitative methods.

 

[magomago]

So what he is essentially asking for is how much air did he introduce between the particles?

The best you can do is make assumptions to the shape of the particles...For Ease, I would say take spherical shapes. Now take a cube slice out of it. The density of the spherical shape in that cube slice should stay the same so you can find the mass since you defined the size of the particles. Then find the theoretical volume of air in between the particles as Volume Cube - Volume Particles; go from there and find the mass of air. Now add the two masses and divide by the cube volume. That is the theoretical new density.

But honestly that isn't going to give you very accurate results. As paperdoc said, things are WAY too variable in a situation like that. You can't prove that are the particles in there are of the same size, let alone prove that the spacing between each particle is the same. I did my mse undergrad design project/thesis (well it was just me on the project lol) on cryomilled copper and i'll tell you right now that it isn't perfectly spherical shapes. IMO my biggest concern isn't the particle size (really you are getting an AVERAGE particle size) as much as it is the volume of air between each particle. The theoretical method may get you a ballpark estimate, but you'd really need to weigh the powder for a given volume size to get an answer...and even then its only the density of the sample you weighed; To make things more accurate i'd probably (as suggested) see if it can be vibrated for a while prior to measurement to let everything get nice and snug