Dendritic Pattern Formation and Contact Line Forces during Dewetting of Dilute Polymer Solutions on a Hydrophobic Surface

The micro-scale morphology of the receding contact line of dilute polyethylene oxide solution drops (c ∼ 100 ppm) after impact and inertial spreading on a fluorinated hydrophobic surface is investigated. One can observe the formation of transient liquid filaments and dendritic structures that evolve into a bead-on-a-string structure similar to the well-known capillary breakup mechanism of dilute polymer solutions, which confirm the interaction between stetched polymer coils and the receding three-phase contact line. The estimation of the average polymer force per unit contact line lenght provides a quantitative explanation for the reduction of the contact line retraction velocity reduction observed experimentally.

On the receding contact between a graded and a homogeneous layer due to a flat-ended indenter

This paper solves the frictionless receding contact problem between a graded and a homogeneous elastic layer due to a flat-ended rigid indenter. Although its Poisson’s ratio is kept as a constant, the shear modulus in the graded layer is assumed to exponentially vary along the thickness direction. The primary goal of this study is to investigate the functional dependence of both contact pressures and the extent of receding contact on the mechanical and geometric properties. For verification and validation purposes, both theoretical analysis and finite element modelings are conducted. In the analytical formulation, governing equations and boundary conditions of the double contact problem are converted into dual singular integral equations of Cauchy type with the help of Fourier integral transforms. In view of the drastically different singularity behavior of the stationary and receding contact pressures, Gauss–Chebyshev quadratures and collocations of both the first and the second kinds have to be jointly used to transform the dual singular integral equations into an algebraic system. As the resultant algebraic equations are nonlinear with respect to the extent of receding contact, an iterative algorithm based on the method of steepest descent is further developed. The semianalytical results are extensively verified and validated with those obtained from the graded finite element method, whose implementation details are also given for easy reference. Results from both approaches reveal that the property gradation, indenter width, and thickness ratio all play significant roles in the determination of both contact pressures and the receding contact extent. An appropriate combination of these parameters is able to tailor the double contact properties as desired.

Time Resolved PIV of the Flow Field Underneath an Accelerating Meniscus

We present an experimental analysis of the flow field near an accelerating contact line using time-resolved Particle Image Velocimetry (TR-PIV). Both advancing and receding contact lines are investigated. The analyzed configuration consists of a liquid column that moves along a vertical 2D channel, open to the atmosphere and driven by a controlled pressure head. Large counter-rotating vortices were observed and analyzed in terms of the maximum intensity of the Q-field. To compute smooth spatial derivatives and improve the measurement resolution in the post-processing stage, we propose a combination of Proper Orthogonal Decomposition (POD) and Radial Basis Functions (RBF). The RBFs are used to regress the spatial and temporal structures of the leading POD modes, so that “high-resolution” modes are obtained. These can then be combined to reconstruct high-resolution fields that are smooth and robust against measurement noise and amenable to analytic differentiation. The results show significant differences in the flow topology between the advancing and the receding cases despite velocity and acceleration of contact lines are comparable in absolute values. This suggests that the flow dynamics are tightly linked to the shape of the interface, which significantly differs in the two cases.

Which Is the Motion State of a Droplet on an Inclined Hydrophilic Rough Surface in Gravity: Pinned or Sliding?

The motion state of a droplet on an inclined, hydrophilic rough surface in gravity, pinned or sliding, is governed by the balance between the driving and the pinned forces. It can be judged by the droplet’s shape on the inclined hydrophilic rough surface and the droplet’s contact angle hysteresis. In this paper, we used the minimum energy theory, the minimum energy dissipation theory, and the nonlinear numerical optimization algorithm to establish Models 1–3 to calculate out the advancing/receding contact angles (θa/θr), the initial front/rear contact angles (θ1−0/θ2−0) and the dynamic front/rear contact angles (θ1−*/θ2−*) for a droplet on a rough surface. Also, we predicted the motion state of the droplet on an inclined hydrophilic rough surface in gravity by comparing θ1−0(θ2−0) and θ1−*(θ2−*) with θa(θr). Experiments were done to verify the predictions. They showed that the predictions were in good agreement with the experimental results. These models are promising as novel design approaches of hydrophilic functional rough surfaces, which are frequently applied to manipulate droplets in microfluidic chips.