Adjoint-based interfacial control of viscous drops

Alexandru Fikl, Daniel J. Bodony

Research output: Contribution to journalArticlepeer-review


We develop a continuous adjoint formulation for controlling the deformation of clean, neutrally buoyant droplets in Stokes flow. The focus is on surface tension-driven flows where the interface is deformed by the local fluid velocity. We apply results from shape optimization to rigorously derive the optimality conditions for a range of interfacial problems. In the cases of interest, we make use of boundary integral methods as a natural choice for the numerical discretization of the flow variables. In the static case, our methodology is tested on a tracking-type cost functional and corresponds to classic shape optimization problems. We show agreement with black-box finite difference-based gradients and accurate minimization of the cost functionals. Finally, we demonstrate the methodology on the control of unsteady droplet deformation through external forcing.

Original languageEnglish (US)
Article numberA39
JournalJournal of Fluid Mechanics
StatePublished - 2021


  • boundary integral methods
  • capillary flows
  • control theory

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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