A drug delivery apparatus includes a mouthpiece portion having an internal conduit for delivering an aerosol including the drug to the patient. The internal conduit has an inlet end and a mouthpiece end that is structured to be received in the patient's mouth. The mouthpiece portion is structured to operate at a substantially fixed inhalation flow rate when the patient inhales through the mouthpiece end. The apparatus further includes an aerosol generator for generating the aerosol from a drug supply and injecting the aerosol into a first region within the mouthpiece portion located between an outlet of the aerosol generator and the inlet end of the conduit. The mouthpiece portion also includes a flow accelerating mechanism that causes a localized flow rate at the first region to be greater than the inhalation flow rate. A method is also provided that increases the local flow rate within the mouthpiece portion.