The invention generally relates to the field of dispensing liquids, and in particular to aerosolizing of fine liquid droplets, for example for delivery of medicinal products to the deeper, peripheral lung. The invention provides perforated membranes with specifically shaped holes, each hole exhibiting two adjacent and preferably coaxially arranged cylindrical longitudinal sections, whose second length is larger than the first length and whose second diameter is larger than the first diameter. Such perforated membranes provide an improved hole diameter precision (± 0.5 µm), lower achievable pitch values and/or higher achievable hole densities in order to allow for the generation of very fine aerosols with droplet sizes preferably below 3 µm at high throughput rates larger than 0.5 ml/min. The invention further provides a process for the preparation of such perforated membranes and their application in inhalation devices, such as vibrating mesh nebulisers, and for inhalation therapies.