Decoupling the rheological responses of a soft solid emulsion with liquid inclusions

Soft solid emulsions are liquid droplets encapsulated in a soft solid material. Typical of dispersed systems, they can combine properties from both the liquid inclusions and the soft solids. The relative importance of the two phases in the rheological response is captured through the elastocapillary number, which compares capillary forces in the liquid inclusions to the matrix rigidity. We work with solid emulsions formed of poly(ethylene glycol) droplets in a poly(dimethylsiloxane) (PDMS) continuous phase. We create three families of emulsions with varying elastocapillary numbers, and range of inclusion volume fractions from 0 to 0.5. Through oscillatory rheology we probe both the elastic response and the dissipative effects of liquid droplets. In the case of a dominant response from the continuous phase or the drops, the results can be described with Palierne's model. However, for the intermediate elastocapillary series we show that the evolution of the storage and loss moduli decouple with dispersed phase volume fraction. We attribute the increase of loss factor with volume fraction to the high polydispersity in droplet size. We can further modulate the response of the materials by cooling to freeze the droplets. This approach allows us to compare these soft solid emulsions with theories related to solid dispersions.