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The dynamics of membrane undulations inside a viscous solvent is governed bydistinctive, anomalous, power laws. Inside a viscoelastic continuous mediumthese universal behaviors are modified by the specific bulk viscoelasticspectrum. Yet, in structured fluids the continuum limit is reached only beyonda characteristic correlation length. We study the crossover to this asymptoticbulk dynamics. The analysis relies on a recent generalization of thehydrodynamic interaction in structured fluids, which shows a slow spatial decayof the interaction toward the bulk limit. For membranes which are weaklycoupled to the structured medium we find a wide crossover regime characterizedby different, universal, dynamic power laws. We discuss various systems forwhich this behavior is relevant, and delineate the time regime over which itmay be observed.

Membrane undulations in a structured fluid: Universal dynamics at intermediate length and time scales