Coating Simulation Insights: Evaporation Effects at Contact Lines
The "coffee-ring" problem
When liquid droplets containing dispersed solid material dry on a solid surface they leave the solid material as a deposit. The pattern of this deposit has important implications for many printing, cleaning and coating processes. A classic example of one type of deposit is the "coffee-ring" problem in which a ring stain is formed along the perimeter of a patch of spilled coffee (see the photo on the left). This type of ring deposit develops as a consequence of surface-tension driven flows resulting from evaporation of liquid, particularly at the drop’s perimeter (Deegan, R.D., et al, Nature 389, 827, 1997).
3-D Drying Simulations in FLOW-3D
FLOW-3D's evaporation residue model
simulates a 3D view of residue formed
from toluene after drying (magnified 30x)
Drying is a critical part of the coating process; a well-applied coating can be completely undone by drying defects. During drying, temperature and solute gradients can drive flow within the coating due to density and surface tension gradients, which can potentially destroy the coating quality. FLOW-3D's evaporation residue model allows users to simulate drying-induced flows and reduces time spent on costly physical experimentation.
Modeling Ring Formation
Simulation of flow generated at a contact line by evaporation. Marker particles pile up at
contact line where the evaporation is greatest. Only every third flow vector is plotted
near the contact line to reduce clutter.
A requirement for ring formation is that the contact line at the edge of a drop must be pinned. In the figure above a FLOW-3D simulation shows that edge pinning occurs because of deposition at a contact line where evaporation is greatest. In this example, the fluid makes a 15° static contact angle with the bottom plate. The liquid is water initially at 20°C and evaporation takes place at the liquid surface under the assumption that the surrounding air has a saturation temperature of 4°C. The vertical height of the simulation is 15μm. Evaporation cools the liquid because of heat loss due to evaporization (color indicates temperature). At the same time the solid surface heats the liquid by conduction. Evaporation is greatest in the vicinity of the contact line causing liquid to flow towards the contact line to reestablish static conditions. The net result is a deposition of suspended solid at the liquid edge where the liquid is completely evaporating.
Simulation of drop impingement. Courtesy of UC Berkely. Dan Soltman
and Vivek Subramanian, Inkjet-Printed Line Morphologies and Temperature
Control of the Coffee Ring Effect, Langmuir; 2008; ASAP Web Release Date:
16-Jan-2008; (Research Article) DOI: 10.1021/la7026847