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Post-pinch-off relaxation of two-dimensional droplets in a Hele-Shaw cell

Dhirendra Tiwari1,2,3,*, Lionel Mercury1, Marcel Dijkstra4, Himanshu Chaudhary5, and José Federico Hernández-Sánchez6,7

  • 1Institut des sciences de la Terre d'Orléans, UMR 7327 Université d'Orléans, CNRS, BRGM, 1A rue de la Férollerie, 45071 Orléans, France
  • 2Mesoscale Chemical Systems Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 3The BIOS Lab-on-a-Chip Group, MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 4Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS), University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
  • 5School of Engineering Sciences in Chemistry, Biotechnology and Health, Dept. Chemistry, Division of Applied Physical Chemistry, KTH Royal Institute of Technology, SE-10044 Stockholm, Sweden
  • 6Instituto de Ciencias Aplicadas y Tecnología, Universidad Nacional Autónoma de México, Circuito Exterior S/N, Ciudad Universitaria, A.P. 70-186, Delegación Coyoacán, C.P. 04510, Ciudad de México, México
  • 7Physics of Fluids group, MESA+ Institute for Nanotechnology, J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

  • *Corresponding author: dhirendra.tiwari@cnrs-orleans.fr
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Phys. Rev. Fluids 3, 124202 – Published 18 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.124202

Abstract

We report on the shape relaxation of two-dimensional (2D) droplets, formed right after the spontaneous pinch-off of a capillary bridge droplet confined within a Hele-Shaw cell. An array of bridge droplets confined within a microchip device first undergoes neck thinning due to the evaporation-driven volume change. Subsequently, an abrupt topological change transforms each bridge droplet into a small central satellite droplet and the twin droplets pinned at the edges of the cell. We monitor the shape relaxation with high-temporal-resolution optical microscopy. Capillary action drives the 2D shape relaxation, while the viscous dissipation in the film retards it. As a result, the tip of the twin droplets exhibits a self-similar parabolic shape evolution. Based on these observations, the lubrication-approximation model accurately predicts the internal pressure evolution and the droplet tip displacement. The geometrical confinement substantially slows down the dynamics, facilitating visualization of the capillary-viscous regime, even for low-viscosity liquids. The characteristic relaxation timescale shows an explicit dependence on the confinement ratio (width/gap) and the capillary velocity of liquid. We verify the broad applicability of the model using different liquids.

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Phys. Rev. Fluids 3, 124202– Published 18 December, 2018
  • Received 8 January 2018
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