Self-propelled motion of a fluid droplet under chemical reaction

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.Comment: 19 pages, 4 figure

A fixed point can hide another one: the nonperturbative behavior of the tetracritical fixed point of the O(NN) models at large NN

We show that at $N=\infty$ and below its upper critical dimension, $d<d_{\rm up}$, the critical and tetracritical behaviors of the O($N$) models are associated with the same renormalization group fixed point (FP) potential. Only their derivatives make them different with the subtleties that taking their $N\to\infty$ limit and deriving them do not commute and that two relevant eigenperturbations show singularities. This invalidates both the $\epsilon-$ and the $1/N-$ expansions. We also show how the Bardeen-Moshe-Bander line of tetracritical FPs at $N=\infty$ and $d=d_{\rm up}$ can be understood from a finite-$N$ analysis.Comment: 8 pages, 11 figure