## 5aAO2. Bubble distribution measurements---Theoretical aspects.

### Session: Friday Morning, December 6

### Time: 8:35

**Author: Frank S. Henyey**

**Location: Appl. Phys. Lab., Univ. of Washington, Seattle, WA 98105**

**Abstract:**

Two theoretical topics in support of bubble cloud measurements are
presented: (1) Corrections to Foldy's effective medium theory. A very large
class of multiple scattering contributions are summed to give a correction to
Foldy's formula for the index of refraction of a random collection of small
scatterers. The result has a simple theoretical interpretation, and is a much
smaller correction than that obtained by [Z. Ye and L. Ding, J. Acoust. Soc. Am.
98, 1629--1636 (1995)] due to cancellations between their multiple scattering
contributions and others. The probable effect of neglected contributions is
discussed, and contrasted to a claim that Foldy's model gives infinite results
[A. S. Sangani, J. Fluid Mech. 232, 221--284 (1991)]. The finiteness is due to a
cancellation between multiple scattering terms. (2) The Kramers--Kronig
integrals are applied to resonator data. (This work is done in collaboration
with R. Goodman, D. Farmer, and S. Vagle.) The real and imaginary parts of the
index of refraction are measured, and the Kramers--Kronig integrals give a
prediction for each in terms of the other. Discrepancies between the measured
and predicted functions indicate inaccuracies of the measurements, if enough
bandwidth and fine enough sampling are included.

ASA 132nd meeting - Hawaii, December 1996