Nonlinear wave propagation in a non-diffusive model of bubbly liquids

@article{Oliveri1990NonlinearWP,
  title={Nonlinear wave propagation in a non-diffusive model of bubbly liquids},
  author={Francesco Oliveri},
  journal={Acta Mechanica},
  year={1990},
  volume={83},
  pages={135-148}
}
  • F. Oliveri
  • Published 1 September 1990
  • Mathematics
  • Acta Mechanica
SummaryIn this paper an “ad hoc” asymptotic approach is employed in order to study nonlinear wave propagation compatible with the non-diffusive version of the model of bubbly liquids introduced by Drumheller and Bedford [13]. A third order transport equation representing a generalization of the usually considered Korteweg-de Vries-Burgers equation and a simplified version of the evolution equation obtained in a previous paper by Fusco and Oliveri [16] for the full model including the diffusion… 
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References

SHOWING 1-10 OF 21 REFERENCES
Wave propagation in bubbly liquids at finite volume fraction
We derive effective equations for wave propagation in a bubbly liquid in a linearized low-frequency regime by a multiple-scale method. The effective equations are valid for finite volume fraction.…
Two-phase flow equations for a dilute dispersion of gas bubbles in liquid
Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the…
Effective equations for wave propagation in bubbly liquids
We derive a system of effective equations for wave propagation in a bubbly liquid. Starting from a microscopic description, we obtain the effective equations by using Foldy's approximation in a…
Propagation of perturbations in a gas-liquid mixture
The present investigation has been performed over a wide range of the dimensionless parameters characterizing the process of propagation of pressure perturbations in a gas-liquid mixture; these are…
A theory of bubbly liquids
A theory of bubbly liquids is developed in which the liquid and the bubbles are treated as separate continua. A variational procedure is used to obtain the equations of motion. The theory is…
On the equations of motion for mixtures of liquid and gas bubbles
On the basis of previous work by the author, equations are derived describing one-dimensional unsteady flow in bubble-fluid mixtures. Attention is subsequently focused on pressure waves of small and…
Bubble Dynamics and Cavitation
The first analysis of a problem in cavitation and bubble dynamics was made by Rayleigh (1917), who solved the problem of the collapse of an empty cavity in a large mass of liquid. Rayleigh also…
A generalization of the Rayleigh–Plesset equation of bubble dynamics
The classical Rayleigh‐Plesset equation of spherical bubble dynamics in an incompressible liquid is generalized to include the non‐Newtonian behavior of the liquid and mass exchange processes at the…
Sound and Shock Waves in Liquids Containing Bubbles
The propagation of infinitesimal sound waves in a liquid containing gas bubbles is considered. Relative motion of gas bubbles and liquid is explicitly allowed for, and it is shown that a significant…
Derivation of a non-linear model equation for wave propagation in bubbly liquids
SommarioMediante l'usa di uno schema asintotico viene dedotta una equazione differenziale alle derivate parziali del quarto ordine, atta a descrivere l'evoluzione di un'onda non lineare propagantesi…
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