Propagation Dynamics of a Particle Phase in a Single-File Pore

We study propagation dynamics of a particle phase in a single-file pore connected to a reservoir of particles (bulk liquid phase). We show that the total mass $M(t)$ of particles entering the pore up to time $t$ grows as $M(t) = 2 m(J,\rho_F) \sqrt{D_0 t}$, where $D_0$ is the "bare" diffusion coefficient and the prefactor $m(J,\rho_F)$ is a non-trivial function of the reservoir density $\rho_F$ and the amplitude $J$ of attractive particle-particle interactions. Behavior of the dynamic density profiles is also discussed.