Stood-up drop to measure receding contact angles

TL;DR

The paper introduces the stood-up drop (SUD) technique as a fast, needle-free method to measure receding contact angles by depositing a nano-to-microliter drop via a short liquid jet that spreads into a pancake and retracts into a stationary spherical-cap. Through experiments and Volume-of-Fluid simulations, it shows that the measured $\theta_{\mathrm{SUD}}$ closely approximates the traditional receding angle $\theta_r$ across hydrophilic to hydrophobic surfaces, while addressing needle-induced distortions and user-dependence inherent to goniometry. It maps the viability of SUD in the $Oh$–$\Gamma$ parameter space, deriving scaling criteria and highlighting limitations such as potential detachment on highly hydrophobic or textured surfaces and volume-related resolution issues. The approach offers a rapid, low-volume, and automation-friendly alternative for robust wetting characterization, with potential extensions to non-Newtonian fluids and dynamic surface-tension studies.

Abstract

The wetting behavior of drops on natural and industrial surfaces is determined by the advancing and receding contact angles. They are commonly measured by the sessile drop technique, also called goniometry, which doses liquid through a solid needle. Consequently, this method requires substantial drop volumes, long contact times, tends to be user-dependent, and is difficult to automate. Here, we propose the stood-up drop (SUD) technique as an alternative to measure receding contact angles. The method consists of depositing a liquid drop on a surface by a short liquid jet, at which it spreads radially forming a pancake-shaped film. Then the liquid retracts, forming a spherical cap drop shape (stood-up drop). At this quasi-equilibrium state, the contact angle ($θ_\text{SUD}$) closely resembles the receding contact angle measured by goniometry. Our method is suitable for a wide variety of surfaces from hydrophilic to hydrophobic, overcoming typical complications of goniometry such as needle-induced distortion of the drop shape, and it reduces user dependence. We delineate when the receding contact angle can be obtained by the stood-up method using Volume-of-Fluid (VoF) simulations that systematically vary viscosity, contact angle, and deposited drop volume. Finally, we provide simple scaling criteria to predict when the stood-up drop technique works.

Figures (6)

• Figure 1: (a) Experimental setup for SUD technique. A liquid jet is generated at certain applied pressure $P_{app}$ for a very short jetting time $\tau$. Once the liquid impacts the sample surface, it spreads radially and then retracts. During the first retraction phase the drop can vibrate, before the contact line smoothly recedes. The liquid forms a drop with a spherical-cap shape, whose contact angle is ($\theta_\text{SUD}$). The drop profile in the first column represents the initial configuration of the drop for the numerical simulations. The configuration resembles a pancake shape, similar to that observed in experiments post-impact. The second to fourth columns sketch the retraction of the drop from an initial (lighter shade) to the quasi-equilibrium state (darker shade) as time progresses. (b) Experimental snapshots of a liquid jet impacting on a Si wafer surface at $P_{app} = 350 \;\text{mbar}$ and jetting time $\tau = 5 \;\text{ms}$. See also Video 1.
• Figure 2: The initial configuration of the drop for the numerical simulations. The configuration resembles a pancake shape, similar to that observed in experiments post-impact.
• Figure 3: (a) Snapshots of a simulated drop with static contact angle $\theta_s = 27^{\circ}$ and volume of $0.5 \mu L$. The arrows represent the velocity profile inside the drop to visualize whether the drop is in the retracting or advancing phase. The dashed red line represents the height at which the contact angles are measured, in line with experimental conditions. (b) Comparison of measured contact angle from numerical simulations and experiments, as a function of time for the simulation shown in (a). $\tau = 1 \; \text{ms}$.
• Figure 4: Top view snapshots of the impacting liquid jet on a PMMA surface. Frame rate: $4000$ fps. No pinning points are observed. Pressure: $350$ mbar. Jetting time: $\tau = 1 \; \text{ms}$. Scale bar represents $0.5$ mm. White dots correspond to specular reflections.
• Figure 5: Comparison between the receding $\left(\theta_{r} \right)$ and advancing $\left(\theta_{a} \right)$ contact angles measured by goniometry technique (dark blue and white rectangles) and the stood-up contact angles (light blue rectangles) $\left(\theta_{\text{SUD}}\right)$. Values of $\left(\theta_{r} \right)$ and $\left(\theta_{\text{SUD}}\right)$ are very close, apart from a few samples. For the following samples: PDMS/PFOTS on Si wafer and glass, Teflon on ITO, and Si wafer, $\theta_{\text{SUD}}$ was measured by the tangent fitting method described in Section 2.3, while the rest of the surfaces by the Young-Laplace fit provided by the goniometer software.