Figure 7
Active droplets in an external gradient. (A, B) Snapshots of two-dimensional projections of the three-dimensional system at times indicated above the frame, showing droplets drift up the gradient (black arrow). White circles denote droplets while color indicates the volume fraction in the background field. (C) Droplet radius R as a function of time t indicating that all droplets reach \(\overline{R}_\mathrm{3D}\) (dashed line); compare to Fig. 6. (A–C) Four droplets with radii chosen uniformly from \([0.8 R_0, 1.2 R_0]\) were placed in a cubic Cartesian domain of size \([-\frac{L}{2}, \frac{L}{2}]^3\) with boundary conditions \(\phi _\mathrm{out}(x = -\frac{L}{2}) = 0\) and \(\phi _\mathrm{out}(x = \frac{L}{2}) = 0.1\) to impose the gradient and no-flux boundary conditions at the remaining system boundaries. Model parameters are \(L = 10^3 w\), \(\Delta x\approx \ell \approx \Delta s \approx R_0 {= \,} 40 w\), \(s(\phi )= k_\mathrm{f}(1 - \phi ) - k_\mathrm{b}\phi\), \(\phi _\mathrm{out}(t=0) = k_\mathrm{f}/(k_\mathrm{f}+ k_\mathrm{b})\), \(k_\mathrm{f}= 10^{-5} \tau ^{-1}\) and \(k_\mathrm{b}= 10^{-4} \tau ^{-1}\). Remaining parameters are specified in Fig. 2.
