  We report spontaneous motion in a fully bio-compatible system consisting of
pure water droplets in an oil-surfactant medium of squalane and monoolein.
Water from the droplet is solubilized by the reverse micellar solution,
creating a concentration gradient of swollen reverse micelles around each
droplet. The strong advection and weak diffusion conditions allow for the first
experimental realization of spontaneous motion in a system of isotropic
particles at sufficiently large P\'eclet number according to a straightforward
generalization of a recently proposed mechanism. Experiments with a highly
concentrated solution of salt instead of water, and tetradecane instead of
squalane, confirm the above mechanism. The present swimming droplets are able
to carry external bodies such as large colloids, salt crystals, and even cells.
