Q. What fraction full of water should jar be, to get max cleaning effect when shake it? Assume you shake the jar on a fixed trajectory and schedule. The jar contains two fluids, "water" and "air," of different densities. We'll model them as incompressible. These fluids each experience forces proportional to acceleration times density-difference times their volume. (To make it simplest you may assume the water density is 1 and air density is 0. And as we said the acceleration is fixed.) The amount of energy that the fluids accumulate as a result of those forces, is proportional to force times distance traveled. The maximum amount of distance the water can travel is proportional to 1-F where F is the water-fraction. This also seems true if "maximum" is replaced by "average, under randomness assumptions." Conclusion: achieved kinetic energy of water = F*(1-F)*constant. If we then guess that the cleaning rate is increasing function of kinetic energy, then max cleaning effect is got by choosing F=1/2.