Acoustic lattice Boltzmann model for immiscible binary fluids with a species-dependent impedance

A lattice Boltzmann model is considered for immiscible binary fluids with species-dependent acoustic impedance. Acoustic waves and pulses are simulated within the model, and the reflection and transmission components at the fluid interface are found to compare well with theory. The model is then applied to simulate the acoustic field due to plane-wave propagation through a bubble.

Figure 1

Variation of the density $\rho$ and the order parameter $\mathrm{\Delta }\rho$ across a plane interface at $x=50.5$ for $\kappa =0.001$ and $\kappa =0.0001$.

Figure 2

An acoustic pulse propagating across the plane interface between the binary fluids with $\alpha =0$ and $\kappa =0.001$. The pulse is shown at 260 (solid line), 311 (dashed line), and 365 (dotted line) time steps.

Figure 3

An acoustic pulse propagating across the plane interface between the binary fluids with $\alpha =-0.25$ and $\kappa =0.0001$. The pulse is shown at 260 (solid line), 335 (dashed line), and 385 (dotted line) time steps.

Figure 4

An acoustic pulse propagating across a bubble with $\alpha =-0.25$ and $\kappa =0.0001$. The pulse is shown at 260 (solid line), 365 (dashed line), and 505 (dotted line) time steps

Figure 5

The reflection and transmission coefficients as a function of $\alpha$.

Figure 6

The interaction between an acoustic wave and a bubble.

Figure 7

The density variation inside the bubble in Fig. 6 indicating the presence of a partial standing wave.