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Viscous drag force model for dynamic Wilhelmy plate experiments

Peter Zhang

Kamran Mohseni*

  • Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA

  • Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32611, USA and Department of Electrical and Computer Engineering, University of Florida, Gainesville, Florida 32611, USA

  • *mohseni@ufl.edu
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Phys. Rev. Fluids 4, 084004 – Published 21 August, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.084004

Abstract

In this work we revisit the dynamic Wilhelmy plate method for measuring dynamic contact angles with a specific focus on the viscous drag force which acts along the submerged surface of the plate. Particle image velocimetry shows that the viscous drag force can induce significant contact angle measurement errors if ignored. Preexisting models are found to underestimate the viscous drag force at moderate to high Capillary numbers, in finite-sized fluid domains, and for curved interfaces. Therefore, we propose a new model for the shear stress along a Wilhelmy plate by combining the dominant terms from a moving contact line flow, a Stokes flow past the leading edge of a flat plate, and a Couette-Poiseuille flow. This new model accounts for the shape of the fluid interface, the finite length of the plate, and the finite-size of the fluid container. Good agreement is obtained in comparisons with particle image velocimetry measurements over a Capillary number range from 0.001 to 0.3. This viscous drag model is applied to a dynamic Wilhelmy plate experiment and we obtain dynamic microscopic contact angle measurements and unbalanced Young's forces that are consistent with hydrodynamic theories of the moving contact line.

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Phys. Rev. Fluids 4, 084004– Published 21 August, 2019
  • Received 2 May 2019
Article part of CHORUS
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