According to a first aspect, the present invention is embodied as a method of processing a filtered liquid with a microfluidic device. The method includes positioning a porous filtering medium with respect to the microfluidic device, so as to allow a flow path between the filtering medium and a channel of the microfluidic device. The method further includes introducing a liquid in the porous filtering medium for the liquid to advance along the filtering medium and be filtered by the medium. The method further includes applying compression to the filtering medium to extract a given volume of the filtered liquid from the filtering medium, where the extracted liquid volume reaches said channel via the flow path. The method further includes processing the extracted volume with the microfluidic device.