Kevin,
The reason numerous people have not responded is because this type of question has no simple answer. DOE is always dependent upon, current knowledge or available/past information and resources, how many trials you can afford to run, stability of processing conditions such as tools/wear and numerous factors.
From your description, it seems you have 6 continuous factors, 1 categorical factor (vendor), and one that could be continuous or categorical (particle size). The number of vendors has a big effect on the number of trials.
Most statisticians will recommend a sequential approach to building a model; in other words, smaller designs or definitive screening designs to learn the most important factors. Then analyze the results and revise the experiments and models. Also, some find reasonable operating conditions for a few vendors, then revise the model via offline quality improvement, while running the process; in other words, continuous process improvement.
It is likely there are conditions that make little to no sense to run: maybe high concentration and large particles or low concentration and very small particles would make no sense. This is the engineering and research aspect of design, that can help keep keep cost down. I do not know your industry, but IEEE publications, or if you are in semiconductors, SRC publications can provide some pointers.
If you are working for a company, look for your company's statistician, or find a university professor or grad student (with experience with experimental designs for manufacturing) to work with you.
Of course, you could use JMP to create a Custom Design for interactions, specifying your factors and specifying your model for 2 factor interactions. The resulting design of 70 or more trials would have good efficiency. But the devil is in the details of how to run that experiment and get good results and assure no cross contamination from one trial to the next.
Good Luck!
