We propose a model for concentrated emulsions based on the speculation
that a macroscopic shear strain does not produce an affine deformatio
n in the randomly close-packed droplet structure. The model yields an
anomalous contribution to the complex dynamic shear modulus that varie
s as the square root of frequency. We test this prediction using a nov
el light scattering technique to measure the dynamic shear modulus, an
d directly observe the predicted behavior over six decades of frequenc
y and a wide range of volume fractions.