Subject: A homogenous aqueous solution is frozen. Does it all melt 'evenly'?

If a homogenous aqueous solution is frozen and then thawed at room temp, 
will the very first liquid that is thawed have the same composition as the 
very last?  Or does the whole sample need to thaw in order to insure that 
any amount of liquid taken from the total solution is going to be of the 
same composition as the original solution?

I am talking mostly of ions in the 10-150 millimolar range.  Does it matter 
if it is a solution of sugars or proteins or other non-ionic molecules?

Re: A homogenous aqueous solution is frozen. Does it all melt 'evenly'?