[math-fun] Cleaning out a jar

What's the optimum amount of water to put in a jar if you want to clean the jar by putting some water in it and shaking it for a bit? I grant that the problem is ill-posed in all kinds of ways, but maybe some not-too-farfetched model gives results in line with experimental data conducted on jars of ordinary shape containing food residues of an ordinary kind. I seem to recall that number theorist David Solomon, back when we were housemates in Berkeley in the 1980s, came up with an idealization of the problem for which the optimum volume of water was 1/e times the volume of the jar. I'll ask him if he remembers any details. Jim Propp