Active droplet driven by collective chemotaxis

Abstract

Surfactant-laden fluid interfaces of soft colloids, such as bubbles and droplets, are ubiquitously seen in various natural phenomena and industrial settings. In canonical systems where microparticles are driven in hydrodynamic flows, convection of the surfactant changes local surface tension. Subsequently, the interplay of Marangoni and hydrodynamic stresses leads to rich interfacial dynamics that directly impact the particle motions. Here we introduce a new mechanism for self-propelled droplets, driven by a thin layer of chemically active microparticles situated at the interface of a suspended droplet, which is a direct extension of the planar collective surfing model by Masoud and Shelley (H. Masoud and M. J. Shelley, Phys. Rev. Lett., 2014, 112, 128304). These particles can generate chemicals locally, leading to spontaneous Marangoni flows that drive the self-aggregation of microparticles. This process, in turn, creates a polarized surfactant distribution, which induces collective chemotaxis and dipolar bulk flows, ultimately breaking the symmetry. By assuming the local surfactant production to be either proportional to particle density or saturated at a high particle density, we observe that the system can be chemotactically diverging or approach a steady state with constant migration velocity. The system is studied analytically in the linear region for the initial transient dynamics, yielding critical numbers and familiar patterns, as well as numerically for larger amplitudes and over a long time using spectral methods.