Spontaneous Division and Motility in Active Nematic Droplets

We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.

Figure 1

The three behaviors of an active nematic droplet for fixed surface tension $\mathrm{\Sigma }=2.6$ and varying activity obtained from a numerical solution of Eq. (2). (a)–(c) For small activity the droplet stretches under the effect of the quadrupolar straining flow generated by the pair of $+1/2$ disclinations. (d)–(f) For $\alpha =16$, the uniformly oriented director field in the interior of the droplet is unstable to splay and the droplet deforms. Following the deformation of the droplet, the backflow is no longer axially symmetric and this causes the droplet to move. (g)–(i) For very large activity ($\alpha =36$), the capillary forces are no longer sufficient to balance the initial straining flow and the droplet divides. Movies displaying the time evolution of each state are included as Supplementary Material [34].

Figure 2

(a) Extension of the droplet versus activity for various $\mathrm{\Sigma }$ values. The data collapse on the same master curve when rescaled with respect to the active capillary number ${\mathrm{Ca}}_{\alpha }=\alpha R/\mathrm{\Sigma }$ (inset). (b) The velocity of a motile droplet versus activity for various $\mathrm{\Sigma }$ value. When rescaled with respect to ${\mathrm{Ca}}_{\alpha }$, the data intersect at the critical capillary number ${\mathrm{Ca}}_{\alpha }^{\text{mot}}\approx 4.5$ (inset). The solid lines show the typical square-root law and are obtained from a fit.

Figure 3

Phase diagram showing the three classes of behavior exhibited by contractile active droplets for different $\alpha$ (activity) and $\mathrm{\Sigma }$ (surface tension). For low activity, the quadrupolar straining flow generated by the pair of $+1/2$ disclinations leads to a stationary elongated shape. When the activity is very strong, the active backflow causes the droplet to spontaneously divide. For intermediate activity and sufficiently large surface tension the director spontaneously splays and the droplet moves as a consequence of the associated backflow.