Weakly nonlinear dynamics of self-propelling active droplets

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• Gunnar Peng, Imperial College London
• Thursday 22 June 2023, 13:00-14:00
• MR12, Centre for Mathematical Sciences, Wilberforce Road, Cambridge.

If you have a question about this talk, please contact Marco Vona.

An active droplet emitting or consuming a chemical that affects its surface tension can exhibit spontaneous motion, by driving a symmetry-breaking Marangoni flow. We derive a reduced-order model for the slow dynamics of the droplet near the threshold for spontaneous motion using a weakly nonlinear expansion, which involves matching a quasi-steady droplet-scale solution to an unsteady diffusive remote region. The resulting amplitude equation for the droplet velocity includes a term representing the interaction of the droplet with its own wake in the remote region, which can be expressed as a time integral over the history of the droplet motion. This allows theoretical analysis and efficient numerical simulation of fully three-dimensional problems for one or more droplets in various settings.

This talk is part of the DAMTP BioLunch series.

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