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We now focus on the thermochemical equilibration efficiency, which we characterize with an equilibration time $t_{1/2}$ corresponding to the time at which the mean scalar field in the metal phase $\langle \chi_1 \rangle$ is half its initial value. Figure \[fig:drop\_t12\]a shows the equilibration time $t_{1/2}$ normalized by the free-fall time $t_g$ obtained from numerical simulations as a function of the Péclet number in the inner phase $\mathrm{Pe_1}$, for various values of Re$_1$ and Bo.

At $\mathrm{Pe_1}\lesssim 10^2$, we find that $t_{1/2}/t_g \sim \mathrm{Pe_1}$, irrespectively of Re$_1$ and Bo. This implies $t_{1/2} \sim t_\kappa$, which means that equilibration is controlled by diffusion. Increasing Pe$_{1}$ above $\sim 10^{2}$ results in faster equilibration than in the diffusion regime. At Pe$_{1}\gtrsim 10^{2}$ the equilibration time depends on the deformation regime of the drop, and hence on Re$_{1}$ and Bo, with the stirring regime being the most efficient at improving equilibration: we find $t_{1/2}/t_g \sim \mathrm{Pe_1}^{0.77}$ in the high Pe spherical regime (circles), while in the stirring regime, $t_{1/2}/t_g$ shows a weak dependency on Pe$_1$ (diamonds) with $t_{1/2}/t_g=0.53\,\mathrm{ln(Pe_1)}$ (the logarithmic Pe$_{1}$ dependency will be explained in section \[sec:stirring\]). The effect of the deformation regime can also be seen from figure \[fig:drop\_t12\]b which shows the 