Dispersion relation around a kink solution in binary fluids undergoing spinodal decomposition

A numerical study is presented of the dispersion relation for the linearized operator about the kink or interfacial wall solution to a model of spinodal decomposition of an incompressible binary fluid. The essential spectrum of the linearized operator does not stay well separated from the Nambu-Goldstone- (NG-) like mode representing purely interfacial motion. For large wave vector k along the interface, the NG-like mode decays as k^3, while for small wave vector it decays as. However, the bottom of the essential spectrum decays like k^2 and at small enough k, it intersects the point spectrum, the NG-like mode. The dispersion relation of the NG-like modes as one varies the viscosity indicates a nonuniversal crossover behavior from k^3 to, due to the interaction between NG-like mode and the essential spectrum.