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Energy dissipation and the contact-line region of a spreading bridge

Published online by Cambridge University Press:  07 June 2012

H. B. van Lengerich  and
P. H. Steen
H. B. van Lengerich*
Affiliation:
School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
P. H. Steen
Affiliation:
School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

A drop on a circular support spontaneously spreads upon contact with a substrate. The motion is driven by a loss of surface energy. The loss of recoverable energy can be expressed alternatively as work done at the liquid–gas interface or dissipation through viscosity and sliding friction. In this paper we require consistency with the energy lost by dissipation in order to infer details of the contact-line region through simulations. Simulations with the boundary integral method are used to compute the flow field of a corresponding experiment where polydimethylsiloxane spreads on a relatively hydrophobic surface. The flow field is used to calculate the energy dissipation, from which slip lengths for local slip and Navier slip boundary conditions are found. Velocities, shear rates and pressures along the interface as well as interface shapes in the microscopic region of the contact line are also reported. Angles, slip length and viscous bending length scale allow a test of the Voinov–Hocking–Cox model without free parameters.

JFM classification

Low-Reynolds-number flows: Boundary integral methods Interfacial Flows (free surface): Contact lines Drops and Bubbles: Drops and Bubbles
Type
Papers
Information
Journal of Fluid Mechanics , Volume 703 , 25 July 2012 , pp. 111 - 141
Copyright
Copyright © Cambridge University Press 2012

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