Abstract: A liquid is filtered with a microsieve. Use is made of a crossflow channel running along a supply surface of the microsieve, and of a drain connected to a drain surface of the microsieve. During a filtering phase, a pressure drop is maintained from a point in the crossflow channel upstream of the microsieve to a point in the drain. The filtering phase is repeatedly interrupted by reducing a flow limitation in the crossflow channel downstream of the microsieve, such that a pressure difference across the microsieve reverses sign. As a result, the pressure reversal coincides with an increase of the flow through the crossflow channel, with a strongly cleaning effect on the microsieve.