Turbulence drag modulation by dispersed droplets in Taylor-Couette flow: the effects of the dispersed phase viscosity

The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, $\zeta$, ranging from $0.53$ to $8.02$. The droplet volume fraction, $\phi$, is varied from 0\% to 10\% with a spacing of 2\%. The global transport quantity, quantified by the normalized friction coefficient $c_{f,\phi}/c_{f,\phi=0}$, shows a weak dependence on the turbulent intensity due to the vanishing finite-size effect of the droplets. The interesting fact is that, with increasing $\zeta$, the $c_{f,\phi}/c_{f,\phi=0}$ first increases and then saturates to a plateau value which is similar to that of the rigid particle suspension. By performing image analysis, this drag modification is interpreted from the aspect of droplet deformability, which is responsible for the breakup and coalescence effect of the droplets. The statistics of the droplet size distribution show that, with increasing $\zeta$, the stabilizing effect induced by interfacial tension comes to be substantial and the pure inertial breakup process becomes dominant. The measurement of the droplet distribution along the radial direction of the system shows a bulk-clustering effect, which can be attributed to the non-negligible coalescence effect of the droplet. It is found that the droplet coalescence effect could be suppressed as the $\zeta$ increases, thereby affecting the contribution of interfacial tension to the total stress, and accounting for the observed emulsion rheology.