This study aims to address the key challenge of simultaneously and accurately characterizing the bulk and interfacial rheological properties of complex fluids that possess both bulk and interfacial viscoelasticity. Considering that the non-contact surface light scattering (SLS) technique enables the broadband characterization of interfacial dynamics, this study focuses on constructing and analyzing the dispersion behaviors of surface waves in such viscoelastic systems. Specifically, the bulk complex viscosity and the interfacial complex dilational modulus are respectively described by Maxwell models, leading to a dispersion equation that combines both bulk and interfacial relaxation times. The systematic analyses of the complex-root structure of this equation and the corresponding power spectral characteristics reveal how the coupling between bulk and interfacial relaxations induces the transformation between capillary and elastic modes and drives the evolution of spectral structures. These findings provide a theoretical foundation for accurately extracting bulk and interfacial thermophysical parameters of such systems by using the SLS method.

Viscoelastic interfacial systems generally exhibit multi-timescale stress relaxation. Although multi-mode models can provide a more complete physical description, they often result in mathematically cumbersome dispersion relations that hinder analytical interpretation. Therefore, in this study, a single-mode Maxwell model is employed to characterize both the bulk complex viscosity and the interfacial complex dilational modulus. This simplified physically consistent framework enables the analytical derivation of the surface wave dispersion relation and facilitates a clear examination of the influences of four key dimensionless parameters, that is, the bulk and interfacial relaxation times ( \bar\tau , \bar\tau _\texts ), surface tension ( \bar\sigma ), and surface dilational modulus ( \bar\varepsilon ), on the modal distribution and power spectrum characteristics of surface waves.

The results show that \bar\tau governs the transition between viscous-dominated and elastic-dominated regimes, and the increase of can lead to mode bifurcation and damping reduction. The interfacial relaxation time \bar\tau _\texts controls the appearance and evolution of elastic wave branches, the increase of can enhance the interfacial contribution and promote double peak spectra. The surface tension \bar\sigma determines the characteristic frequency scale of capillary modes, while the surface dilatational modulus \bar\varepsilon adjusts the relative strength and width of spectral peak, reflecting interfacial elasticity and energy dissipation. Parameter variations can induce transitions between overdamped, capillary, and elastic modes.

By combining bulk and interfacial Maxwell models, this study establishes a self-consistent framework that links rheological relaxation parameters to measurable surface-wave spectra. The analysis clarifies the physical roles of \bar\tau , \bar\tau _\texts , \bar\sigma and \bar\varepsilon in governing mode structure and spectral evolution, thereby providing theoretical guidance for explaining SLS data and extracting viscoelastic properties of complex interfacial systems over a wide frequency range.