The shape of the liquid-vapor interface along the length of the adiabatic section of a heat pipe - a passive heat transfer device that relies on capillary pumping - is investigated to identify the mechanisms behind both performance enhancement techniques as well as operational failure. In formulating the associated mathematical model, the liquid flow within the (screen type) wick is described using Darcy’s law while Poiseuille’s equation is applied for the vapor phase. The liquid and vapor phases are coupled together using the Young-Laplace equation with additional closure provided by select thermodynamic relations e.g. to relate the temperature and pressure changes experienced by the vapor. Our model thereby predicts the shape of the liquid-vapor interface and its deflection owing to the variations in the heat load, operating temperature and the wick-surface characteristics. Together, these details can prescribe the parameter space over which the liquid-vapor interface remains mechanically-stable meaning that the heat pipe can function effectively. The possibility of employing a wick with non-uniform wetting characteristics is also explored with comparisons drawn against the uniform wettability case. The comparison in question reveals some of the benefits of the former approach. For instance, a wick exhibiting a contact angle that varies as a function of the axial coordinate allows for better control of (i) the depth to which the interface is recessed within the wires comprising the wick, and, therefore (ii) the entrainment of liquid droplets into the counter-flowing vapor stream. As such, the space of acceptable operating parameters can be suitably expanded.