There are a number of protocols to achieve a liver flush.
The original flush involved only lemon juice and olive oil.
The Hulda Clark e method adds the use of Magnesium Sulphate, but there are several other well-tried protocols, some of which advocate the use of magnesium citrate. For example, the Dave Frahm protocol.
The magnesium will relax the smooth muscle.
One advantage of magnesium sulphate is that in sufficient concentration, 25mg/100ml on an empty stomach will on its own contract the gallbladder by an average of 30%. This is why it has a good reputation as a cure for gallbladder pain. It isn't effective on a full stomach.