Rheological behaviour of suspensions of bubbles in yield stress fluids

• We study the rheology of suspensions of monodisperse bubbles in yield stress fluids.
• Experiments are made on model systems of bubble suspension in concentrated emulsions.
• Capillary numbers quantify the importance of surface tension effects in suspensions.
• The suspensions’ behaviour is ruled by the capillary numbers and the volume fraction.
• All results are in good agreement with micro-mechanical estimates.

The rheological properties of suspensions of bubbles in yield stress fluids are investigated through experiments on model systems made of monodisperse bubbles dispersed in concentrated emulsions. Thanks to this highly tunable system, the bubble size and the rheological properties of the suspending yield stress fluid are varied over a wide range. We show that the macroscopic response under shear of the suspensions depends on the gas volume fraction and the bubble stiffness in the suspending fluid. This relative stiffness can be quantified through capillary numbers comparing the capillary pressure to stress scales associated with the rheological properties of the suspending fluid. We demonstrate that those capillary numbers govern the decrease of the elastic and loss moduli, the absence of variation of the yield stress and the increase of the consistency with the gas volume fraction, for the investigated range of capillary numbers. Micro-mechanical estimates are consistent with the experimental data and provide insight on the experimental results.