Crater defects caused by surfactants in a drying paint layer

Overview | Example | Animations | References


Paints are a complex mixture of many components, including surfactants and solvents. Surfactants, whether from within an applied paint layer or from contamination during drying, cause surface tension gradients on the paint surface which can drive flows leading to defects. During drying, solvent is evaporated leaving only a very viscous resin. This effectively halts further flow, ``freezing'' defects in place. One type of defect, known as a crater or fish-eye, is a deep, round indentation a few millimeters across, and is believed to be due to surface tension gradients.

initial bolus We have developed a model for defects of this type. An initial non-uniform distribution of surfactant, due to contamination of the paint surface, causes surface tension gradients. These gradients drive a flow which carries paint away from the contamination, creating the crater. The model uses lubrication theory to describe this flow. Meanwhile, as the paint dries its viscosity increases, until no further flow is possible. At this point, the defect has become permanent. The model requires the solution of three coupled non-linear partial differential equations for

  1. film thickness,
  2. surfactant concentration, and
  3. resin concentration.

ensuing crater These equations are solved numerically.

Numerical simulations are being used to provide useful insights into how these craters develop and what measures may be successful in preventing or minimizing them. Using our simulations we can easily vary properties, such as paint drying rate, surfactant diffusivity and the viscosity increase during drying, to study their effects on the final crater shape.


Development of a crater caused by an initial concentrated surfactant.
output at three times

These rendered cut-away views show three stages (from top to bottom) of the simulation:

  • The paint layer begins flat, with a localized concentration of surfactant (shown in red).
  • A crater develops, which spreads outwards and increases in depth.
  • Once the paint is dry, the film appears thinner and the shape of the crater is preserved in the paint.

(The thickness of the film has been exaggerated here.)

[surfactant colour bar] [resin concentration colour bar]

low <   > high


wet <   > dry



A typical simulation of a bolus-driven crater...

Warning: these animated GIF files may take some time to download!

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Pete Evans, Dept. of Mechanical Engineering University of Delaware