Nonlinear acoustic propagation in bubbly liquids: Multiple scattering, softening and hardening phenomena

Shock Propagation in Polydisperse Bubbly Liquids

We investigate the shock dynamics of liquid flows containing small gas bubbles, based on a continuum bubbly flow model. Particular attention is devoted to the effects on shock dynamics of distributed bubble sizes and gas-phase nonlinearity. Ensemble-averaged conservation laws for polydisperse bubbly flows, together with a Rayleigh–Plesset-type model for single bubble dynamics, form the starting...

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 nonlinear setting. We discuss in detail the range of validity of the effective equations as well as some of their properties.

Investigating Acoustic Causality in Highly Dispersive Bubbly Liquids

Solution of Nonlinear Hardening and Softening type Oscillators by Adomian’s Decomposition Method

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

Statistical mechanics of bubbly liquids

The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles’ velocities. The e...