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Stability of co-annular active and passive confined fluids

Tanumoy Dhar1, Michael J. Shelley2,3, and David Saintillan1,2,*

  • *Contact author: dstn@ucsd.edu
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Phys. Rev. Fluids 10, 083103 – Published 21 August, 2025

DOI: https://doi.org/10.1103/m5ck-v2q3

Abstract

The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned active nematic in the limit of strong elastic relaxation in two dimensions. Using an active liquid crystal model, we employ the Lorentz reciprocal theorem for Stokes flow to study the growth of interfacial perturbations as a result of both active and elastic stresses. Instabilities are uncovered in both extensile and contractile systems, for which growth rates are calculated and presented in terms of the dimensionless ratios of active, elastic, and capillary stresses, as well as the viscosity ratio between the two fluids. We also extend our theory to analyze the inverse scenario, namely, the stability of an active nematic droplet surrounded by a passive viscous layer. Our results highlight the subtle interplay of capillary, active, elastic, and viscous stresses in governing droplet stability. The instabilities uncovered here may be relevant to a plethora of biological active systems, from the dynamics of passive droplets in bacterial suspensions to the organization of subcellular compartments inside the cell and the cell nucleus.

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Phys. Rev. Fluids 10, 083103– Published 21 August, 2025
  • Received 9 January 2025
  • Accepted 25 July 2025
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