A new, fast magnetic resonance imaging (MRI) method is described and applied to map flow fields in systems with internal velocities rapidly varying along the streamlines. While conventional MRI techniques encode the velocity information in a preparatory period prior to the imaging acquisition module, our technique repeatedly refreshes the velocity encoding during a single-shot imaging sequence. In this way, the maximum acceleration responsible for velocity variation of the molecules is increased by up to two orders of magnitude compared to standard procedures. Besides being compatible with high acceleration, this pulse sequence is suited to acquiring in a single scan the multiple velocity images required to construct a full velocity vector map. The power of this new methodology is demonstrated by following the internal dynamics of toluene droplets levitating in a counterflow of water during mass transfer of acetone from the water phase into the drop in the presence of surface-active impurities. The dramatic reduction in measurement time allows visualization for the first time of the important impact of even small concentrations of acetone on accumulation of surfactants at the drop’s surface.