Herein disclosed is a method, comprising: forming a dispersion under high shear comprising gas bubbles of an oxidant dispersed in a liquid phase, wherein the bubbles have a mean diameter of less than 1.5 micron; and contacting the dispersion with an oxidation catalyst to produce a product stream, wherein the product stream comprises a substance selected from the group consisting of dicarboxylic acid, benzoic acid, 2-methylbenzoic acid, 3-methylbenzoic acid, 4-methylbenzoic acid, and phthalic anhydride. In some cases, forming the dispersion under high shear comprises introducing the oxidant and the liquid phase into a high shear device comprising at least one rotor and at least one complementarily-shaped stator. Herein also disclosed is a system for producing a substance selected from the group consisting of dicarboxylic acid, benzoic acid, 2-methylbenzoic acid, 3-methylbenzoic acid, 4-methylbenzoic acid, and phthalic anhydride.