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Hydrodynamics of Writing with Ink

Jungchul Kim, Myoung-Woon Moon, Kwang-Ryeol Lee, L. Mahadevan, and Ho-Young Kim
Phys. Rev. Lett. 107, 264501 – Published 20 December 2011
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Abstract

Writing with ink involves the supply of liquid from a pen onto a porous hydrophilic solid surface, paper. The resulting linewidth depends on the pen speed and the physicochemical properties of the ink and paper. Here we quantify the dynamics of this process using a combination of experiment and theory. Our experiments are carried out using a minimal pen, a long narrow tube that serves as a reservoir of liquid, which can write on a model of paper, a hydrophilic micropillar array. A minimal theory for the rate of wicking or spreading of the liquid is given by balancing the capillary force that drives the liquid flow and the resistance associated with flow through the porous substrate. This allows us to predict the shape of the front and the width of the line laid out by the pen, with results that are corroborated by our experiments.

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  • Received 3 May 2011

DOI:https://doi.org/10.1103/PhysRevLett.107.264501

© 2011 American Physical Society

Authors & Affiliations

Jungchul Kim1, Myoung-Woon Moon2, Kwang-Ryeol Lee2, L. Mahadevan3, and Ho-Young Kim1,*

  • 1School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
  • 2Interdisciplinary and Fusion Technology Division, KIST, Seoul 136-791, Korea
  • 3School of Engineering and Applied Sciences, Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

  • *hyk@snu.ac.kr

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Issue

Vol. 107, Iss. 26 — 23 December 2011

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