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Description
An oil droplet suspended in a surfactant solution can undergo micellar solubilization at its interface when the surfactant concentration exceeds the critical micelle concentration, thereby enabling autonomous propulsion; such droplets are referred to as chemically active droplets. The self-propulsion of an active droplet is governed by the nonlinear coupling among chemical transport in the bulk, surfactant consumption at the droplet surface, and fluid flow driven by self-generated Marangoni stresses. To quantify the underlying hydrodynamics, we investigate the swimming motion of a two-dimensional active droplet. By varying the Peclet number, $Pe$, we distinguish four droplet behaviors: stationary, steady, periodic, and chaotic. We perform a weakly nonlinear analysis to predict the onset of instability associated with the spontaneous transition from a stationary state to steady self-propulsion. Near this instability threshold $Pe_{1c}$, the droplet undergoes a supercritical bifurcation with velocity $U \sim \sqrt{Pe - Pe_{1c}}$. Subsequently, we conduct a global linear stability analysis to identify the onset of the second instability, which induces the transition from steady to periodic motion. Stresslet calculations show that the droplet behaves as a puller in the steady regime but periodically switches between pusher and puller behavior in the periodic regime.
| Country | China |
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