The many behaviors of deformable active droplets

Y. -N. Young; Michael J. Shelley; David B. Stein; Y. -N. Young; Michael J. Shelley; David B. Stein

doi:10.3934/mbe.2021145

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 3: 2849-2881. doi: 10.3934/mbe.2021145

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The many behaviors of deformable active droplets

1.
Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA
2.
Center for Computational Biology, Flatiron Institute, New York, New York 10010, USA
3.
Courant Institute, New York University, New York, New York 10012, USA

Received: 01 January 2021 Accepted: 08 March 2021 Published: 25 March 2021

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.
- active fluids,
- confinement,
- swimming,
- surface tension effects,
- flow instability
Citation: Y. -N. Young, Michael J. Shelley, David B. Stein. The many behaviors of deformable active droplets[J]. Mathematical Biosciences and Engineering, 2021, 18(3): 2849-2881. doi: 10.3934/mbe.2021145

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Abstract

Active fluids consume fuel at the microscopic scale, converting this energy into forces that can drive macroscopic motions over scales far larger than their microscopic constituents. In some cases, the mechanisms that give rise to this phenomenon have been well characterized, and can explain experimentally observed behaviors in both bulk fluids and those confined in simple stationary geometries. More recently, active fluids have been encapsulated in viscous drops or elastic shells so as to interact with an outer environment or a deformable boundary. Such systems are not as well understood. In this work, we examine the behavior of droplets of an active nematic fluid. We study their linear stability about the isotropic equilibrium over a wide range of parameters, identifying regions in which different modes of instability dominate. Simulations of their full dynamics are used to identify their nonlinear behavior within each region. When a single mode dominates, the droplets behave simply: as rotors, swimmers, or extensors. When parameters are tuned so that multiple modes have nearly the same growth rate, a pantheon of modes appears, including zigzaggers, washing machines, wanderers, and pulsators.

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