Which preposition to use with percolation

of Occurrences 4%

A layer of moist clay, about two inches deep, is then placed upon the sugar at the broad end of the cone, and, by the gradual percolation of its thick liquid, carries off the remaining impurities.

through Occurrences 2%

The immediate banks of the river would have, perhaps, been fringed with verdure, but the influence of the irrigation would have extended no farther than the water itself could have reached, by percolation through the sand.

Which preposition to use with  percolation