Pattern formation during the evaporation of a colloidal nanoliter drop: a numerical and experimental study

Abstract

An efficient way to precisely pattern particles on solid surfaces is to\ndispense and evaporate colloidal drops, as for bioassays. The dried deposits\noften exhibit complex structures exemplified by the coffee ring pattern, where\nmost particles have accumulated at the periphery of the deposit. In this work,\nthe formation of deposits during the drying of nanoliter colloidal drops on a\nflat substrate is investigated numerically and experimentally. A finite-element\nnumerical model is developed that solves the Navier-Stokes, heat and mass\ntransport equations in a Lagrangian framework. The diffusion of vapor in the\natmosphere is solved numerically, providing an exact boundary condition for the\nevaporative flux at the droplet-air interface. Laplace stresses and thermal\nMarangoni stresses are accounted for. The particle concentration is tracked by\nsolving a continuum advection-diffusion equation. Wetting line motion and the\ninteraction of the free surface of the drop with the growing deposit are\nmodeled based on criteria on wetting angles. Numerical results for evaporation\ntimes and flow field are in very good agreement with published experimental and\ntheoretical results. We also performed transient visualization experiments of\nwater and isopropanol drops loaded with polystyrene microsphere evaporating on\nrespectively glass and polydimethylsiloxane substrates. Measured evaporation\ntimes, deposit shape and sizes, and flow fields are in very good agreement with\nthe numerical results. Different flow patterns caused by the competition of\nMarangoni loops and radial flow are shown to determine the deposit shape to be\neither a ring-like pattern or a homogeneous bump.\n