I want to make a uniform distribution of 2 different phases, both nanoparticles, by using ball-milling by changing the milling time. Will there be any change? Is there any mathematical model to support this?
In theory when you mix two powders using ball milling, you should get a homogeneous mixture. However when there are density differences between the two powders, you may get some non-homogeneity. It is all probabilistic in nature.
The best way is to take samples of he powder after the ball milling is completed and measure the weight of the samples to see if the mixture density remains the same for all samples of slightly different.
Any mathematical model will be essentially fitting a probability distribution for the mixture density with a mean and a standard deviation.
I just want to get a bit more clarification on the answer you gave. By probabilistic in nature you mean to say that if I B-M the sample for the same amount of time in, suppose, two different but identical machine, the outcome will be different?