Understanding mass transport of photosynthates in the phloem of plants is necessary for predicting plant carbon allocation, productivity, and responses to water and thermal stress. Several hypotheses about optimization of phloem structure and function and limitations of phloem transport under drought have been proposed and tested with models and anatomical data. However, the true impact of radial water exchange of phloem conduits with their surroundings on mass transport of photosynthates has not been addressed. Here, the physics of the Munch mechanism of sugar transport is re-evaluated to include local variations in viscosity resulting from the radial water exchange in two dimensions (axial and radial) using transient flow simulations. Model results show an increase in radial water exchange due to a decrease in sap viscosity leading to increased sugar front speed and axial mass transport across a wide range of phloem conduit lengths. This increase is around 40% for active loaders (e.g. crops) and around 20% for passive loaders (e.g. trees). Thus, sugar transport operates more efficiently than predicted by previous models that ignore these two effects. A faster front speed leads to higher phloem resiliency under drought because more sugar can be transported with a smaller pressure gradient.