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Nonlinear fractional waves at elastic interfaces

Julian Kappler1, Shamit Shrivastava2, Matthias F. Schneider3, and Roland R. Netz1

  • 1Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
  • 2Institute of Biomedical Engineering, University of Oxford, Oxford OX3 7DQ, United Kingdom
  • 3Department of Physics, Technische Universität Dortmund, 44227 Dortmund, Germany

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Phys. Rev. Fluids 2, 114804 – Published 20 November, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.114804

Abstract

We derive the nonlinear fractional surface wave equation that governs compression waves at an elastic interface that is coupled to a viscous bulk medium. The fractional character of the differential equation comes from the fact that the effective thickness of the bulk layer that is coupled to the interface is frequency dependent. The nonlinearity arises from the nonlinear dependence of the interface compressibility on the local compression, which is obtained from experimental measurements and reflects a phase transition at the interface. Numerical solutions of our nonlinear fractional theory reproduce several experimental key features of surface waves in phospholipid monolayers at the air-water interface without freely adjustable fitting parameters. In particular, the propagation distance of the surface wave abruptly increases at a threshold excitation amplitude. The wave velocity is found to be of the order of 40 cm/s in both experiments and theory and slightly increases as a function of the excitation amplitude. Nonlinear acoustic switching effects in membranes are thus shown to arise purely based on intrinsic membrane properties, namely, the presence of compressibility nonlinearities that accompany phase transitions at the interface.

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Phys. Rev. Fluids 2, 114804– Published 20 November, 2017
  • Received 12 February 2017

©2017 American Physical Society

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