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184<br />
Bubble interactions in Acoustic Fields fully accounting for viscous<br />
effects<br />
N. Chatzidai a , J. Tsamopoulos a<br />
The interaction of gas bubbles pulsating in a liquid is a well-known phenomenon,<br />
first analysed by Bjerknes: If the driving frequency lies between the two linear<br />
pulsation frequencies of the individual bubbles, they will repel each other; otherwise<br />
an attractive force arises. We have studied (a) the nonlinear interactions of two<br />
deforming bubbles subject to changes in the far-field pressure, ignoring viscous<br />
effects 1,2 and (b) the formation of acoustic streamers when viscous effects are small<br />
and the bubbles remain spherical 3. In order to fully account for viscous effects and<br />
large bubble deformations, we have now developed a new Numerical method and<br />
solved the NS equations by a finite element/Galerkin method coupled with implicit<br />
Euler for time integration. The highly deforming interfaces are accurately computed<br />
by a block-structured mesh, which closely follows their surfaces. In every block we<br />
solve a set of partial, elliptic differential equations for the mesh nodes. At each time<br />
step, the flow equations are solved along with the mesh equations using Picard<br />
iterations. It is shown that the bubbles deform less, when viscous effects are properly<br />
accounted for. The attraction or repulsion of two gas bubbles depends on their<br />
relative size, their distance, the Re number and the pressure amplitude. Increasing the<br />
viscosity of the liquid increases the time required for two equal bubbles, subjected to a<br />
step change in the far-field pressure, to approach each other.<br />
a Laboratory of Computational Fluid Dynamics, Dep. Chem. Engin., University of Patras, Greece 26500<br />
1 Pelekasis and Tsamopoulos, J. Fluid Mech. 254, 467 (1993).<br />
2 Pelekasis and Tsamopoulos, J. Fluid Mech. 254, 501 (1993).<br />
3 Pelekasis, Gaki, Doinikov and Tsamopoulos, J. Fluid Mech., 500 (2004)<br />
Center of mass<br />
2<br />
1<br />
0<br />
-1<br />
-2<br />
Re=50<br />
Re=100<br />
Time<br />
0 10 20 30 40 50 60 70 80 90<br />
Figure 1: Evolution of center of mass of two bubbles with equal radius R1=R2=1, at<br />
an initial dimensionless distance D=5, and a step change of the dimensionless<br />
pressure at the far-field P=2.
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