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Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study
New Journal of Physics (2009)
  • Rajneesh Bhardwaj, Columbia University
  • Xiaohua Fang, Columbia University
  • Daniel Attinger, Columbia University
An efficient way to precisely pattern particles on solid surfaces is to dispense and evaporate colloidal drops, as for bioassays. The dried deposits often exhibit complex structures exemplified by the coffee ring pattern, where most particles have accumulated at the periphery of the deposit. In this work, the formation of deposits during the drying of nanoliter colloidal drops on a flat substrate is investigated numerically and experimentally. A finite-element numerical model is developed that solves the Navier–Stokes, heat and mass transport equations in a Lagrangian framework. The diffusion of vapor in the atmosphere is solved numerically, providing an exact boundary condition for the evaporative flux at the droplet–air interface. Laplace stresses and thermal Marangoni stresses are accounted for. The particle concentration is tracked by solving a continuum advection–diffusion equation. Wetting line motion and the interaction of the free surface of the drop with the growing deposit are modeled based on criteria on wetting angles. Numerical results for evaporation times and flow field are in very good agreement with published experimental and theoretical results. We also performed transient visualization experiments of water and isopropanol drops loaded with polystyrene microspheres evaporating on glass and polydimethylsiloxane substrates, respectively. Measured evaporation times, deposit shapes and sizes and flow fields are in very good agreement with the numerical results. Different flow patterns caused by the competition of Marangoni loops and radial flow are shown to determine the deposit shape to be either a ring-like pattern or a homogeneous bump.
  • coffee ring pattern,
  • colloidal drops,
  • Marangoni stresses,
  • Lagrangian framework
Publication Date
July, 2009
Publisher Statement
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citation Information
Rajneesh Bhardwaj, Xiaohua Fang and Daniel Attinger. "Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study" New Journal of Physics Vol. 11 Iss. 075020 (2009)
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