In one aspect a drug delivery device may include a reservoir containing a liquid drug formulation and a microneedle assembly in fluid communication with the reservoir. The microneedle assembly may include a plurality of microneedles, with each microneedle defining an open channel for receiving a drug formulation. The open channel may have a normalized hydraulic radius ranging from about 0.1 to about 0.8. The open channel may also have a liquid-to-solid interfacial energy and a liquid-to-vapor interfacial energy when a fixed volume of the drug formulation is received therein. In addition, the drug formulation and a cross-sectional geometry of the open channel may be selected and configured such that the liquid-to-solid energy exceeds the liquid-to-vapor energy as the length of the fixed volume of drug formulation is increased within the open channel.