If I include a min pressure parameter for the pump when I set up an lc method will it stop the pump if the mobile phase runs out? What value would I use?

Yes, the primary purpose of the low-pressure cutoff is to protect the system in case the mobile phase runs dry or the systems developes a catastrophic leak.

For "run dry" protection, any pressure slightly above 0 should work. For leak protection, any pressure sufficiently below the usual operating pressure should work.

We usually use a value of 100 psi, because we use gradients and if you use a value of 10, then you might have a problem when only one line is empty

Thanks fellow anonymous's for taking the time to answer such a basic question.

Quick word of warning. Depending on your solvents 100 psi may not be low enough to cause a shut off of your instrument. We were running a 40:40:20 of Water:MeOH:ACN, someone forgot to refill the water bottle before leaving for the night because the instrument only had two injections to go, in the morning it was discovered that the instrument was still pumping 12 hours later completely dry Water line and nearly empty MeOH bottle. It took quite awhile to get the bubbles out of the system.

The moral of this story is to check how much your individual solvents affect the pressure changes of your instrument. We have now lowered our cutoff down to 50psi.

I can not see An.Nonymous how decreasing the cutoff down to 50 psi could be of any help in the particular example. What you are describing is that as one of the containers had some remaining solvent, the pumps were not dry off completely so the system was still operating with a residual pressure higher than 100 psi. Decreasing the pressure limit to 50 psi wouldn't have change anything in your example.

Maybe you should consider increasing your cutoff lower limit ;-).

Kostas