Viscous drag force model for dynamic Wilhelmy plate experiments

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.

Robust and durable liquid-repellent surfaces

“…138,139 Furthermore, Zhang et al found that the viscous drag forces acting on the submerged plate surface during a dynamic Wilhelmy plate experiment could be of the same order of magnitude as surface tension forces, which were always highly underestimated due to the ignorance of the interface curvature, the tip of the plate, or the flow formed between the plate and liquid container. 140 They further proposed a new viscous drag force model that incorporated the effects of the moving contact line, the leading edge of a flat plate and a Couette–Poiseuille flow to measure CA by the Wilhelmy plate method, and the results of their demonstrative example showed that CA values of glycerin advancing on glass plate increased by 20° while the capillary number varied from 10 −3 to 10 −1 .…”

Evaluation of Viscosity Dependence of the Critical Meniscus Height with Optical Fiber Sensors

“…The use of fiber instead of a plate gives considerable advantages. For example, steady-state measurements are possible with high viscosity liquids, which is a challenge at present [23]. The meniscus height rapidly settles at equilibrium on small diameter and stationary fiber, resulting in high accuracy of results [24].…”