Process for preparing an alkaline dispersion of aggregated silicon dioxide particles by dividing a preliminary dispersion within a pH of 3 to 5 into at least two streams, placing these streams under a pressure of at least 50 bar and depressurizing them to a collision point, each via one nozzle, in a grinding chamber, and admixing the dispersion that runs off at the bottom, while still in the grinding chamber, with an alkaline substance in an amount such that the dispersion overall has a pH of more than 7.