We report in this paper a particular case of the Marangoni effect - the migration of a squalane droplet in the external water medium, driven by the asymmetric adsorption of the surfactant at one side of the droplet. The specific features of this experiment compared to similar reports on drop motion lies in both the presence of the external liquid and the existence of two "discrete" profile and velocity regimes during the migration of the drop. The amazing dynamic profile of the droplet (cometlike) observed in the earlier stage of the motion was related to the strong transient pinning of the rear side of the drop where adsorption sets in. This strong retention preceding the drop motion was related to the external hydrostatic pressure of the environmental fluid which, under the particular geometry of nonsymmetric diffusion, results in a higher contact angle hysteresis (compared to that in air), before the drop can move. As shown by these results, the whole macroscopic behavior of this drop migration, including the pinning strength, the magnitude and velocity of the motion is governed by the viscosity, the external hydrostatic pressure and the pressure within the thin wetting film on the rear side of the drop. Using a simplified hydrodynamic approach, an estimated average velocity of similar to 1.5 mm/s was found, which compares well to measured ones, especially in the earlier stage of the motion where the drop retains the comet like profile. In addition, some preliminary results are briefly presented, which cleary show how both the velocity and amplitude of the migration, as well as the characteristics of the thin film on the rear side depend on the drop size and viscosity.