The rheological properties of emulsions are of considerable importance in a diverse range of scenarios. Here we describe a superposition of the effects of droplet elasticity and volume fraction on the dynamics of emulsions. The superposition is governed by physical interactions between droplets, and provides a new mechanism for modifying the flow behavior of emulsions, by controlling the elasticity of the dispersed phase. We investigate the properties of suspensions of emulsified wormlike micelles (WLM). Dense suspensions of the emulsified WLM droplets exhibit thermally responsive properties in which the viscoelastic moduli decrease by an order of magnitude over a temperature range of 0 $^circ$C to 25 $^circ$C. Surprisingly, the fragility (i.e. the volume-fraction dependence of the modulus) of the emulsions does not change with temperature. Instead, the emulsion modulus scales as a power-law with volume fraction with a constant exponent across all temperatures even as the droplet properties change from elastic to viscous. Nevertheless, the underlying droplet dynamics depend strongly on temperature. From stress relaxation experiments, we quantify droplet dynamics across the cage breaking time scale below which the droplets are locally caged by neighbors and above which the droplets escape their cages to fully relax. For elastic droplets and high volume fractions, droplets relax less stress through cage rattling and the terminal relaxations are slower than for viscous droplets and lower volume fractions. The cage rattling and cage breaking dynamics are highly correlated for variations in both temperature and emulsion concentration, suggesting that thermal and volume fraction effects represent independent parameters to control emulsion properties.
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