Multiscale control of active emulsion dynamics

We numerically study the energy transfer in a multicomponent two-dimensional film made of an active polar gel and a passive isotropic fluid in presence of surfactant favoring emulsification. We show that by confining the active behavior into the localized component, the typical scale where chemical energy is transformed in mechanical energy can be substantially controlled. Quantitative analysis of kinetic energy spectra and fluxes shows the presence of a multiscale dynamics due to the existence of a flux induced by the active stress only, without the presence of a turbulent cascade. An increase in the intensity of active doping induces drag reduction due to the competition of elastic and dissipative stresses against active forces. Furthermore we show that a nonhomogeneous activity pattern induces localized response, including a modulation of the slip length, opening the way toward the control of active flows by external variation of the actvity level.

Figure 1

Contour plot of concentration field $\varphi$, where the active component is red and the passive one is blue showing late-time configurations of active fluids at different intensities of active doping $\zeta$. Velocity streamlines are plotted in black for the case at $\zeta =0.050$. Last panel: $pdf$ of the concentration field; notice the transition to mixing for $\zeta >0.020$ characterized by the presence of a single peak.

Figure 2

Left: Log-log plot of time-averaged energy spectra varying activity $\left(\zeta =0.013,0.015,0.02,0.03,0.04,0.05\right)$. Right: Total amount of energy injected in the system by active agents. Vertical black dashed lines mark the wave number $k_v,k_d$, and $k_a$, respectively (see text), for the case at $\zeta =0.05$.

Figure 3

Time-averaged components of the total energy flux at $\zeta =0.013$ (left) and $\zeta =0.050$ (right). Notice the different $y$ range in the two graphs.

Figure 4

Drag factor versus activity. Inset shows time evolution of kinetic energy $E_{\mathrm{tot}}$ and power terms ${\epsilon }^{\left(i\right)}\left(t\right)$ defined in the same way as ${\epsilon }^{\mathrm{act}}\left(t\right)$, while rising activity from $\zeta =0.010$ to $\zeta =0.030$ at time $t_1$ and reducing it to its previous value at time $t_2$, denoted by vertical dashed lines.

Figure 5

Contour plot of concentration of active and passive phases in an externally controlled active emulsion subject to Poiseuille flow in a $512\times 256$ channel (color legend is the same as in Fig. 1). Velocity streamlines are plotted in black, showing effective reduction of the channel width. Activity $\zeta$ is modulated in the flow direction as shown in the central color bar [beige corresponds to $\zeta =0.010$, while $\zeta \left(x_0\right)=0.03]$. Time-averaged profiles of ${\mathit{v}}_x$ are shown in the last panel. Notice that profiles close to $x_0$ exhibit a non-null (negative) slip length.