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Spontaneous motion or self-propulsion have been attracting attention in last decades for its potential application to biological problems such as cell motility and wound healing. Recently several model experiments showing spontaneous motion have been proposed. The systems in these works consist of relatively simple ingredients for instance oil drops in water nevertheless the motion is as if the drops are alive. The key questions are why the particle moves without external force and why it breaks symmetry and chooses one direction. The first point has been discussed in hydrodynamics of the Marangoni effect in which a liquid droplet is driven by a gradient of surface tension. The mechanism is that the gradient induces convective flow inside and outside of a drop, which leads to swimming motion of the drop itself. The second point was less discussed, but has been discussed in the field of nonlinear dynamics as drift instability. Thus far there are only few attempts to discuss the spontaneous symmetry breaking from hydrodynamics. In this work, we derive the nonlinear equations exhibiting drift instability. This is of importance because all the coefficients are determined with physical quantities. |
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