A simple method for simulating the coffee stain effect

Inkjet printing of structures like microscopic electronic circuit paths on thin substrates includes drop wise application and drying of particulate suspensions. The drying of these drops can leave behind a multiplicity of structures of sediment deposit, which to control is a major subject of investigation in the design of the process. In this work we present a simple and efficient simulation method for predicting the three dimensional structure of sediment deposits based on a one way coupled scheme of Brownian dynamics and analytic modeling of the fluid flow inside a drying colloidal drop under presence of Marangoni flow. Aiming for micrometer sized drops with high particle concentrations (up to 20 vol.%), our method takes into account particle diffusion and convection, particle collisions as well as particle staggering at the contact line. The method is validated by experimental results and applied to predict the behavior of a new setup. We find from our simulations that DLVO forces may be neglected for a well stabilized suspension and that the model works well in predicting coffee stain formation.