Through laboratory experiments of oil-in-water emulsification, we show that we can construct a high-shear-rate mixer (precession mixer) by using the precession of a cylindrical container without any mixing blades. For high-shear-rate mixing, a container with a larger diameter and its faster spin are preferable so that the wall velocity becomes large enough. Then, the emulsification is most efficient when we set the Poincar\'e number $Po=\Omega_p/\Omega_s$, which is the ratio of the spin and precession rotation speeds, about $0.2$--$0.3$. When $Po$ is smaller than these values, shear rates in the mixer get much lower, though mixing in the bulk of the container is enhanced. On the other hand, when $Po$ is larger, shear rates near the cylindrical wall get higher but mixing in the bulk drastically declines. Through our systematic parameter survey for efficient emulsification by the precession mixer, we have also discovered an experimental law describing the maximum shear rate in the mixer. Since we can use it to appropriately choose the driving conditions of the mixer according to the properties of the materials to be mixed, this experimental law gives useful information for the practical use of the mixer.

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