THERMAL FLUCTUATIONS OF THE SHAPES OF DROPLETS IN DENSE AND COMPRESSED EMULSIONS

We generalize the theory of diffusing-wave spectroscopy (DWS) to inclu de the effects of fluctuations of the amplitudes of the scattered fiel ds. Thus DWS can be used to probe the internal dynamics of flexible pa rticles. We study the thermally induced shape fluctuations of monodisp erse emulsion droplets as a function of the droplet volume fraction ph i. We find that a droplet's mean-squared deviation from spherical shap e increases with phi, while the characteristic rate of relaxation of t he shape deformations decreases with phi. Our generalization of the th eory of DWS allows us to measure the autocorrelation function of the f luctuating amplitude of the field scattered from a droplet. We use flu id dynamics and scattering theory to calculate this autocorrelation fu nction theoretically for an isolated droplet. The significant contribu tion of many independent modes of deformation results in a distinctly nonexponential relaxation. The measured behavior agrees with the theor y as phi approaches zero. At higher values of phi throughout the range of colloidal liquids we find a surprising scaling behavior, which imp lies that particle interactions bring about the enhancement and slowin g down of shape fluctuations without altering the spectrum of excited deformation modes. We relate the form of the scaling function to the p article radial distribution function. In ''compressed'' emulsions with phi as high as 0.8, shape fluctuations may be the only dynamical beha vior that can occur. We suggest that in these systems the amplitude of the shape fluctuations is related to the emulsion's elastic modulus.