Novel Surface Modes in Spinodal Decomposition

We study the spontaneous phase separation of a binary mixture in the presence of a flat wall, focusing on the early stage of the demixing kinetics. Based on a Ginzburg-Landau type approach, we show the existence of novel unstable concentration waves with wave vectors ${\overrightarrow{k}}_{\parallel }$ parallel to the wall, which are characterized by a surface dispersion relation ${\omega }_s\left(k_{\parallel }\right)$ and amplitudes $\overline{s}$ decaying exponentially into the bulk. The surface modes are superimposed on the laterally averaged concentration profile and are directly observable by experiment, if the wall right after a quench does not favor any of the two components of the mixture.