  We study self-propelled dynamics of a droplet due to a Marangoni effect and
chemical reactions in a binary fluid with a dilute third component of chemical
product which affects the interfacial energy of a droplet. The equation for the
migration velocity of the center of mass of a droplet is derived in the limit
of an infinitesimally thin inter- face. We found that there is a bifurcation
from a motionless state to a propagating state of droplet by changing the
strength of the Marangoni effect.
