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Contact: Rajneesh Bhardwaj
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 microsphere evaporating on respectively glass and polydimethylsiloxane substrates. Measured evaporation times, deposit shape 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.

A multiplicity of deposits can be obtained after the drying of a colloidal drop: (a) ring-like pattern from an aqueous drop containing 60 nm polystyrene spheres on titanium substrate (Sommer et al. 2004) (b) central bump obtained after the drying of a 38 nL isopropanol drop on PDMS at ambient temperature (Bhardwaj et al. 2009) (c) multiple rings from a microliter water drop containing 1 mm polystyrene microspheres on glass (our work); (d) fingering at wetting line obtained from a mL isopropanol drop with 1mm polystyrene microspheres on glass (our work); (e) uniform deposition pattern of 60 nm hydroxyapatite particles from aqueous drop on titanium disk (Sommer 2004) (f)hexagonal cells from surfactant-laden aqueous drop containing polystyrene microspheres on hydrophobic OctadecylTricholoroSilane (OTS) substrate (Truskett and Stebe, 2003)
Funding: NSF grant Coupling the High Resolution of Laser Measurements and Finite-Element Simulations to Understand Transport Phenomena during Microdroplet Deposition


  • Bhardwaj R., Fang X. and Attinger D., Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study, New Journal of Physics, Vol 11, pp 075020, 2009
  • Bhardwaj, R., Fang X, Somasundaran P and Attinger, D, Self-assembly of particles from evaporating colloidal droplets: role of the pH and proposition of a phase diagram, Langmuir, to be submitted, 2009