Sinking motion of microdroplets in an immiscible liquid layer of variable depth

  • Yunze Liu

Student thesis: Master of Science by Research


In this thesis, we study the motion of a microdroplet sinking into an immiscible viscous liquid layer with a constant depth gradient. The droplet sinks because the air-droplet surface tension is too large to enable a Neumann equilibrium. As sinking, it also moves away from the contact line of the liquid layer into the deeper region. We find that the motion of the droplet is governed by two regimes: the distance of the droplet from the contact line exhibits a square root of time behaviour at early times; the distance tends towards a constant value with an exponential dependence at late times. We propose an argument for these behaviours. While sinking, the droplet is deformed as it is squeezed onto the inclined rigid boundary. The droplet adopts different curvatures on either side, generating a capillary pressure difference which drives it towards the deeper region. The motion is dominantly resisted by viscous forces in the lubrication layer between the droplet and the rigid boundary at early times and viscous forces in the bulk at late times. We investigate the influence of the initial position of the droplet, the viscosity of the liquid layer and the depth gradient on the motion of the droplet in the light of our physical interpretation. We find that our explanation is consistent with the effects of initial position and viscosity for the lower viscosity oils (1,000 cSt and 12,500 cSt). However, the motion is slower than expected on higher viscosity oils (60,000 cSt and 100,000 cSt). These findings will serve as a baseline for future studies of the motion of microdroplets deposited on an ultra-soft yielding viscoelastic substrate of variable depth
Date of Award1 Aug 2020
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorAnne Juel (Supervisor) & Draga Pihler-Puzovic (Supervisor)


  • Laplace pressure
  • microdroplet
  • viscoelastic

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