Re: How to measure amount of solid during freezing?

Your problem seems to be one of determining the fraction of a liquid sample
that is in the solid state as its temperature is being decreased about its
freezing point.  Apparently in the presence of agitation.

For the case of water, light scattering might work.  This is a complex
technique.  More can be found out about it in the polymer characterization
literature where it is used to determine polymer molecular weights.  Light
scattering may also work for any clear liquid that is being solidified.  The
presence of agitation will increase the complexity of getting good results
with light scattering.

Ice is less dense than water.  So, in this case, perhaps the ice can be
scooped up during the experiment and its quantity determined.  This is an
invasive procedure and may not meet the need.

For other liquids, the problem depends on the difference in physical
properties of the solid and liquid phases.

I recommend that books on physical chemistry, and/or books on the compounds
of interest, be checked.  These might give ideas about how the desired
measurements can be carried out.