Evaporating liquid droplets play a crucial role in numerous scientific, engineering, and medical applications. During evaporation, these droplets undergo significant shape changes, transitioning from nearly spherical forms to more elongated shapes. These transformations are pivotal in determining how mass is locally transferred during the evaporation process. Traditionally, models have oversimplified this by assuming a constant droplet shape, along with fixed saturation conditions and fluxes at the droplet interface. This approach, rooted in Maxwell's hypothesis, simplifies the complexities of interfacial dynamics by presuming that the gas near the liquid/gas interface is nearly saturated. However, this simplification falls short as the scale of observation gets smaller. At these scales, the curvature affects the vapor pressure around the droplet, resulting in curved surface exhibiting evaporation rates greater than flat surface. The significance of interface dynamics in evaporation is considered in diffuse-interface models (DIMs), which are grounded in thermodynamics and account for evaporative cooling effects and the topological evolution of the liquid-vapor interface. This theory offers a more granular view by representing the interfacial region through continuous variations in properties such as density, aligning with the microscopic theories of interfaces. Here, the curvature not only shapes the geometrical aspects of the interface but also critically influences the local evaporation characteristics. Our study utilizes the van der Waals square gradient theory within the DIM framework to investigate the curvature’s influence on the local mass flux during the evaporation of deformed droplets. We employ a space-time least-squares spectral element method in two dimensions, capturing the interplay between droplet deformation, evaporative cooling, and the topological evolution of the liquid-vapor interface. This method allows for a detailed examination of the dynamics at play, including the Kelvin effect on equilibrium vapor pressure and its consequent impact on local evaporation fluxes.