Thermal fluctuations of the shapes of droplets in dense and compressed emulsions

Abstract

We generalize the theory of diffusing-wave spectroscopy (DWS) to include the effects of fluctuations of the amplitudes of the scattered fields. Thus DWS can be used to probe the internal dynamics of flexible particles. We study the thermally induced shape fluctuations of monodisperse emulsion droplets as a function of the droplet volume fraction \ensuremath{\varphi}. We find that a droplet's mean-squared deviation from spherical shape increases with \ensuremath{\varphi}, while the characteristic rate of relaxation of the shape deformations decreases with \ensuremath{\varphi}. Our generalization of the theory of DWS allows us to measure the autocorrelation function of the fluctuating amplitude of the field scattered from a droplet. We use fluid dynamics and scattering theory to calculate this autocorrelation function theoretically for an isolated droplet. The significant contribution of many independent modes of deformation results in a distinctly nonexponential relaxation. The measured behavior agrees with the theory as \ensuremath{\varphi} approaches zero. At higher values of \ensuremath{\varphi} throughout the range of colloidal liquids we find a surprising scaling behavior, which implies that particle interactions bring about the enhancement and slowing down of shape fluctuations without altering the spectrum of excited deformation modes. We relate the form of the scaling function to the particle radial distribution function. In ``compressed'' emulsions with \ensuremath{\varphi} as high as 0.8, shape fluctuations may be the only dynamical behavior that can occur. We suggest that in these systems the amplitude of the shape fluctuations is related to the emulsion's elastic modulus. (c) 1995 The American Physical Society