# Difference between revisions of "Hydrodynamics of Writing with Ink"

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==Physics of Writing== | ==Physics of Writing== | ||

The spreading force caused by the energetic gain of wetting the surface has to be balanced with the viscous shear force holding it back. Letting <math>f</math> be the roughness (total surface area over projected area, <math>f >= 1</math>), the difference in surface energies reduces to | The spreading force caused by the energetic gain of wetting the surface has to be balanced with the viscous shear force holding it back. Letting <math>f</math> be the roughness (total surface area over projected area, <math>f >= 1</math>), the difference in surface energies reduces to | ||

− | <math>r ~ (\phi \frac{\gamma}{\mu}h)^ | + | <math>r ~ (\phi \frac{\gamma}{\mu}h)^(1/2)t^(1/2)</math> |

− | + | ||

==Experimental Results== | ==Experimental Results== |

## Revision as of 15:45, 17 October 2012

Original entry: Tamas Szalay (APPHY225 2012)

"Hydrodynamics of Writing with Ink"

Jungchul Kim, Myoung-Woon Moon, Kwang-Ryeol Lee, L. Mahadevan, and Ho-Young Kim

Phys. Rev. Lett., 107, 264501 (2011)

## Summary

In this paper, the authors examine the hydrodynamics of writing with ink on paper with a capillary source, eg. a fountain pen. The experiment is performed with a model system of superhydrophilic silicon micropillars to create the rough surface, and a simple glass capillary tube with various solutions inside to simulate the pen. In this model system, they calculate the expected rate of spreading for a stationary pen, and use this to derive the line width for a moving pen, which they then compare to experimental results. The analysis is then extended to a system using actual ink and paper.

## Soft matter keywords

Wetting, Laplace pressure, surface tension, spreading, capillary

## Physics of Writing

The spreading force caused by the energetic gain of wetting the surface has to be balanced with the viscous shear force holding it back. Letting <math>f</math> be the roughness (total surface area over projected area, <math>f >= 1</math>), the difference in surface energies reduces to <math>r ~ (\phi \frac{\gamma}{\mu}h)^(1/2)t^(1/2)</math>