An Investigation of Flow and Interface Dynamics Near a Moving Contact Line at Obtuse Contact Angles

TL;DR

The paper tackles the problem of flow and interface dynamics near a moving contact line at obtuse dynamic angles ($\theta_d>90^\circ$) in low to moderate $Re$, combining high-resolution PIV experiments, theoretical models (HS71, DRG, GLM, MWS), and VoF-based Basilisk simulations. It shows that curvature corrections (MWS) and composite interface-shape theories (DRG) can predict interface geometry and flow fields away from the contact line, while dynamic-angle boundary conditions improve GLM’s accuracy near the wall; a pronounced, finite interfacial-speed deceleration near the contact line emerges in both experiments and simulations, offering a physically plausible resolution to the classical moving-contact-line singularity. The work validates a unified experimental–theoretical–numerical framework for obtuse-angle regimes and provides boundary-condition data and insights crucial for extending models to 3D, unsteady, and hysteretic wetting phenomena. Overall, the findings clarify how inertia, wettability, and curvature interact to shape near-wall dynamics and establish a robust platform for future multimodal studies of moving contact lines.

Abstract

The flow near a moving contact line is primarily governed by three key parameters: viscosity ratio, dynamic contact angle, and inertia. While the behavior of dynamic contact angles has been extensively studied in earlier experimental and theoretical works, quantitative characterization of flow configurations remains limited. The present study reports detailed measurements of flow fields, interface shapes, and interfacial speeds in the low to moderate Reynolds number ($Re$) regimes using particle image velocimetry (PIV) and high-resolution image analysis. The investigation is restricted to dynamic contact angles greater than $90^{\circ}$. In the low-$Re$ regime, excellent agreement is observed between measured streamfunction contours and the modified viscous theory of Huh \& Scriven \cite{huh1971hydrodynamic} that accounts for a curved interface. Theoretical models such as the DRG formulation, using a single fitting parameter, accurately predict interface shapes even at finite $Re$. The interfacial speed away from the contact line compares favorably with theoretical predictions, whereas a pronounced deceleration is observed close to the contact line. Complementary Volume-of-Fluid (VoF) based numerical simulations were performed using identical geometric and material parameters to validate and extend the experimental observations. The simulations successfully reproduce the interface topology, flow structure, and the deceleration of the interfacial velocity near the contact line, providing strong support to the experimental findings. We argue that this rapid reduction in speed, observed both in experiments and simulations, is critical to the resolution of the long-standing moving contact line singularity.

Figures (17)

• Figure 1: An illustration of the experimental setup. (i) A transparent acrylic tank filled with liquid (ii) A glass plate traversing into the liquid bath (iii) A linear traversing system (iv) A combination of laser and lens for forming a thin laser sheet (v) High-speed camera. The inset provides a magnified view of the field of interest, showing the fluid phase B forming an obtuse contact angle with the solid surface.
• Figure 2: A streakline image illustrates the flow pattern in the vicinity of a moving contact line at $Re= 3.03$ and $Ca = 1.24\times 10^{-5}$. As the solid surface, depicted by a grey slab, descends into the liquid, the material points at the interface migrate toward the contact line and subsequently align with the solid surface. The red arrow indicates the flow direction, and the yellow solid curve indicates the air and water interface.
• Figure 3: A schematic diagram of the problem geometry and the flow patterns emerged near the contact line. (a) A solid surface, represented by a black-edged slab, descends into the liquid bath in phase B. The system is characterized by $\hat{r}-\hat{\theta}$ cylindrical coordinate system, where $\hat{r}$ and $\hat{\theta}$ represent the radial and angular coordinates, respectively, with the contact point serving as the origin. An interface between phase A and phase B is depicted by a solid black line at $\theta=\phi$. (b) Considering the advancing motion of the solid, kinematically consistent flow patterns are shown in both phases: split-streamline motion in phase A and rolling motion in phase B.
• Figure 4: (a) The cartoon depicts three regions as proposed by the study of Cox cox1986dynamics. (b) The schematic indicates the problem geometry with the curved interface where the angle $\beta$ represents the interface angle shown for an arbitrary point on the interface. The angle $\alpha$ represents a local interface slope measured from the vertical direction.
• Figure 5: (a) A schematic represents two interfaces: one with the equilibrium contact angle $\theta_e$ at the wall and the other with $\omega_0$ angle at the wall. The latter interface represents the static interface dictated by the outer solution $h_s(x)$ with the contact point as the origin at the wall. The contact angle $\omega_0$ is obtained by matching the inner to the outer region as mentioned in rame1991identifying. (b) depicts an interface that forms an equilibrium angle ($\theta_e$) at the contact line while becoming flat in the far field. The interface is dictated by $h(s)$ at any arbitrary arc length $s$ from the origin where contact line is at origin. $\alpha(s)$ denotes a local slope at that arbitrary arc length.