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Moving contact-line mobility measured

Published online by Cambridge University Press:  01 March 2018

Yi Xia Open the ORCID record for Yi Xia [Opens in a new window]  and
Paul H. Steen Open the ORCID record for Paul H. Steen [Opens in a new window]
Yi Xia*
Affiliation:
School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
Paul H. Steen*
Affiliation:
School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email addresses for correspondence: yx264@cornell.edu, phs7@cornell.edu
†Email addresses for correspondence: yx264@cornell.edu, phs7@cornell.edu
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Abstract

Contact-line mobility characterizes how fast a liquid can wet or unwet a solid support by relating the contact angle $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ to the contact-line speed $U_{CL}$. The contact angle changes dynamically with contact-line speeds during rapid movement of liquid across a solid. Speeds beyond the region of stick–slip are the focus of this experimental paper. For these speeds, liquid inertia and surface tension compete while damping is weak. The mobility parameter $M$ is defined empirically as the proportionality, when it exists, between $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ and $U_{CL}$, $M\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}=U_{CL}$. We discover that $M$ exists and measure it. The experimental approach is to drive the contact line of a sessile drop by a plane-normal oscillation of the drop’s support. Contact angles, displacements and speeds of the contact line are measured. To unmask the mobility away from stick–slip, the diagram of $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ against $U_{CL}$, the traditional diagram, is remapped to a new diagram by rescaling with displacement. This new diagram reveals a regime where $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FC}$ is proportional to $U_{CL}$ and the slope yields the mobility $M$. The experimental approach reported introduces the cyclically dynamic contact angle goniometer. The concept and method of the goniometer are illustrated with data mappings for water on a low-hysteresis non-wetting substrate.

JFM classification

Interfacial Flows (free surface): Capillary flows Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 841 , 25 April 2018 , pp. 767 - 783
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Copyright
© 2018 Cambridge University Press 

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