Does a shrinking disk grow in the z-direction?

This is not a homework question! I am observing that a thin, flat disk made from a material whose density is gradually increasing, shrinks in the radial direction (of course) but appears to grow very slightly in the z-direction. The change in density is supposed to be isotropic.

Is growth in the z-direction predicted or an artifact of my experiment? I don't know enough continuum mechanics to solve this problem or even how to search for a solution. Is the solution to this problem somewhere in the literature?

sophiecentaur
Gold Member
I'm not clear about your model. How is the density increasing? Is it actually accreting material or is it changing dimensions? Are you thinking of a massive astronomical body?

Actually its a chemical reaction where the product are denser than the reactants. And the size of my disk is about a cm in diameter and a few mm in height. We can detect size differences down to a couple nm.

sophiecentaur
Gold Member
If the material remains isotropic / amorphous then I can't see what could change the ratio of its dimensions.

Is the reaction possibly exothermic and the disc is heating up and expanding in the z direction from the heat?

sophiecentaur
Gold Member
So it's anisotropic then?

The reaction is exothermal, but the disc is kept isothermal. And the material is isotropic. The reaction takes days. It's the geometry that puzzles me. The problem is then a disc that is subjected to constant forces in the radial direction that also has a time changing density. (The internal forces caused by the change is density can be equated to external forces pushing on the disc -- I think.)

If it were a parallelpiped I would agree that the shrinkage would be proportional to the dimensions since the forces would be proportional. But it's the radial shrinkage that puzzles me. Can all the material fit into the shrinking circle, or does some have to pop out into the z-direction, even with the shrinkage forces in the z-direction.

sophiecentaur