Effect of size‐distributed bubbles on acoustic properties of an elastic tube with polymeric liquid

Abstract

PurposeThe objective of this study is to model the influence of free gas, in the form of size‐distributed fine bubbles, on sound attenuation and dispersion in a thin‐walled elastic cylindrical tube filled with viscoelastic polymeric liquid.Design/methodology/approachSound wave propagation in the system is described within a three‐phase interaction scheme, based on a quasi‐homogeneous approach to liquid‐gas mixture dynamics in the wave. Coupled equations of tube wall deformations and viscoelastic liquid dynamics in the tube are solved using a long‐wave approximation. The dissipative losses, stemming from flow gradients in the wave, as well as from non‐equilibrium bubble‐liquid interaction, are accounted for. The dispersion equation for the waveguide is obtained and studied numerically.FindingsThe results of the study indicate that bubble‐size distribution in viscoelastic liquid has an essential impact on sound propagation in the tube at sufficiently high frequencies. The frequency range in which the mixture heterogeneity influences the acoustic properties of the system is sensitive to both the distribution parameters and the rheological properties of the liquid. As distinct to polydispersity features, the viscoelastic properties of liquid are also relevant in the low‐frequency range, where they lead to an increase of the wave speed and a decrease of its attenuation.Originality/valueA model of sound wave propagation in a tube filled with a heterogeneous viscoelastic liquid‐bubble mixture is formulated. The study provides a basis for modeling transient processes in tubes filled with polymeric liquids containing free gas, and for acoustic control of certain processes in polymer technologies.