Dynamic contact angles in CFD simulations

Dynamic wetting characteristics during droplet formation in a microfluidic T-junction

Evaporation of fluid from a pinned drop placed on solid surface proceeds via constant contact radius (CCR) mode, with a continuous reduction in the contact angle. The reduction of contact angle leads to an imbalance of interfacial tensions at the three-phase contact line. When the unbalanced force is sufficiently strong, the drop slips from the pinned contact line and slides inward. Depinning of the drop alters the mode of evaporation to constant contact angle (CCA) mode till it repins onto the surface. The change in evaporation mode from CCR to CCA is usually achieved by tuning the pinning energy barrier by controlling the surface properties of the substrate. Here, we demonstrate that the evaporation mode can be controlled by solely tailoring the surface tension of the drop, which is achieved in microgel particle-laden sessile drops that show spontaneous adsorption of microgels to the air/water interface, leading to a decrease in the interfacial tension. We show that droplets containing a sufficient number of microgels evaporate predominantly in CCR mode even on a hydrophobic surface, and the contact line remains pinned throughout the evaporation of the drop. Interestingly, the contact line dynamics can be controlled by tuning the softness of the microgels and the particle concentration in the drops.

Force based dynamic contact angles and wetting kinetics on a Wilhelmy plate

Mathematical model of dynamic imbibition in nanoporous reservoirs

Static nanodroplets and dynamic contact line (CL) movements were visualized by an in situ transmission electron microscope (TEM) liquid cell technique at nanometer spatial resolution. Crawling and sliding movements of nanoscale CL were observed. The crawling happened at a capillary number (Ca) range of ∼10-9 to ∼10-8, and the sliding happened at a Ca range of ∼10-8 to ∼10-7. Three dimensional (3D) image construction had been employed to study static and dynamic contact angles (CAs) at nanoscale. CA hysteresis at nanoscale was observed in the sliding but not in the crawling. The energies associated with sliding were analyzed to investigate the CA hysteresis. An empirical model of the relationship between nanoscale CAs and Ca was developed. Both the experimental observation and the empirical analysis suggested that the competition among substrate defect, CL elastic, and molecular activation energies dictated different CL movements at nanoscale.

The debate on the dependence of apparent contact angles on drop contact area or three-phase contact line: A review

The experimental results of Xia and Steen for the contact line dynamics of a drop placed on a vertically oscillating surface are analyzed by numerical phase field simulations. The concept of contact line mobility or friction is discussed, and an angle-dependent model is formulated. The results of numerical simulations based on this model are compared to the detailed experimental results of Xia and Steen with good general agreement. The total energy input in terms of work done by the oscillating support, and the dissipation at the contact line, are calculated from the simulated results. It is found that the contact line dissipation is almost entirely responsible for the dissipation that sets the amplitude of the response. It is argued that angle-dependent line friction may be a fruitful interpretation of the relations between contact line speed and dynamic contact angle that are often used in practical computational fluid dynamics.

In this paper, the surface evaporation of a sessile water droplet on hydrophobic solid substrates was numerically and experimentally investigated. The droplet evaporation is governed by multi-dimensional heat and mass transport and interfacial processes of three (gas, liquid, and solid) phases. A Computational Fluid Dynamics (CFD) simulation was performed to analyze the simultaneous heat and mass transfer in the surface evaporation of a sessile water droplet by considering the Marangoni and/or free convection. The results from the CFD simulation were validated using experimental results for the water droplet evaporation on a hydrophobic-coated silicon substrate. It was found that the droplet evaporation rate is greatly increased by a thermocapillary-driven flow (Marangoni convection) in the droplet with small liquid volumes of less than 2.4 μL on the hydrophobic substrate, while the contribution of the free convection is negligible. The peak mass flux of droplet evaporation was always observed along the three-phase contact line.

For several decades, evaporation phenomena have been intensively investigated for a broad range of applications. However, the dynamics of contact line depinning during droplet evaporation has only been inductively inferred on the basis of experimental data and remains unclear. This study focuses on the dynamics of contact line depinning during droplet evaporation based on thermodynamics. Considering the decrease in the Gibbs free energy of a system with different evaporation modes, a theoretical model was developed to estimate the receding contact angle during contact line depinning as a function of surface conditions. Comparison of experimentally measured and theoretically modeled receding contact angles indicated that the dynamics of contact line depinning during droplet evaporation was caused by the most favorable thermodynamic process encountered during constant contact radius (CCR mode) and constant contact angle (CCA mode) evaporation to rapidly reach an equilibrium state during droplet evaporation.

Knowledge of bubble-particle interaction is important in many industrial processes such as in flotation. While the collision (first interaction sub-process) between bubbles and particles is influenced only by hydrodynamic forces, the bubble behaviour during the attachment (second sub-process) is influenced both by hydrodynamic and surface forces. This work is focused on the study of the three-phase contact (TPC) line expansion during bubble adhesion on hydrophobic surface and on its experimental and mathematical description. The experiments were carried out in pure water where mobile bubble surface is expected. The rising bubble was studied in dynamic arrangement, whereas the stationary bubble was analysed in static arrangement. The attachment process was recorded using a high-speed digital camera and evaluated using image analysis. The diameter of the expanding TPC line as well as the dynamic contact angle was determined. Two approaches - the hydrodynamic and the molecular-kinetic - were used for mathematical description of the TPC line expansion. According to our results, the hydrodynamic model is suitable for the description of the initial fast phase of the expansion. The molecular-kinetic model was assessed as appropriate for almost whole range of TPC expansion. Parameters of the model were evaluated and compared for both types of arrangement.

Spontaneous imbibition in microchannels is a critical phenomenon in various industrial applications, such as enhanced oil recovery and microfluidic systems. One of the key factors influencing the imbibition process is the dynamic wetting effect, which governs the interaction between the liquid and solid surfaces. This paper improves the original pseudopotential model for interfluid forces by coupling it with the Peng-Robinson equation of state. The model's accuracy is verified through thermodynamic consistency checks, simulations of gas-liquid interfacial tensions, and testing of static equilibrium contact angles. Following model validation, we use it to simulate spontaneous gas-liquid imbibition in microchannels and investigate dynamic contact angle evolution during the process. The results demonstrate that (1) as the microchannel width increases, inertia forces become more significant during the initial imbibition stages, leading to a greater difference between the dynamic and static contact angles. (2) A decrease in fluid-solid interaction strength results in a larger gap between dynamic and static contact angles. (3) Higher interfacial tension strengthens the capillary forces, accelerating the imbibition rate and enlarging the difference between the dynamic and static contact angles. Furthermore, the dynamic contact angle data obtained from our simulations can be used to correct the traditional Lucas-Washburn equation. The corrected equation predicts imbibition distances that closely match the simulation results.

Wetting dynamics and surface energy components of single carbon fibers

The dynamic contact angle, the angle between the surfaces of the liquid and the solid at a moving contact line, is one of the primary conditions for the dynamics of the liquid surface confined by solid wall. It has been commonly modeled as a function of the velocity of the contact line relative to the solid surface under steady state condition. Some situations, such as the impact of a drop on a solid surface or sudden release of a contact line stuck on an edge of solid, however, involve a transient motion of the contact line, which would lead to a deviation of the dynamic contact angle from the steady one. In this study, dynamic contact angle for an accelerating or decelerating contact line advancing on glass surface is measured in two experimental systems different with other, i.e. one with a rapid meniscus formation after contact of a descending rod with the liquid surface, and the other with accelerating advance of liquid column in a circular tube. The experimental results revealed that the contact angle is increased with the (positive) acceleration of the contact line relative to the solid and vice versa. The critical condition for the appearance of the deviation of the contact angle brought with the acceleration is also discussed.

The phenomena and characteristics of droplets impacting and spreading on a horizontal solid surface are key scientific issues in microfluidic technology and surface physics. The movement regularity and mechanism of the three-phase contact line (TCL) of DNA microdroplets spreading on a hydrophilic PMMA smooth surface without splashing or rebounding are investigated by high-speed camera technology. Some significant results are achieved, for example: based on the changes in droplet morphology, the changes of DNA droplet TCL are divided into eight stages, i.e., expanding, pinning, retracting, repinning, microexpanding, micro-oscillating, stabilizing, and retraction drying, which are helpful to understand the deposition of DNA molecules on the substrate surface. Among them, the TCL moves intensely in the stages of expanding and retracting, respectively, following the cubic function and quadratic function; then, TCL remains virtually unchanged since entering the repinning stage until the stabilizing stage, and DNA molecules are deposited on the surface of PMMA, accumulating to form crystals. Furthermore, the relationship between three correlated damped-like oscillations, i.e., droplet top height (htop), TCL position, and dynamic contact angle (DCA) size, is systematically investigated; the htop oscillates first, then the TCL and DCA oscillate after a delay of 5 ms, and the oscillation period increases sequentially, which is 7.55, 7.90, and 8.40 ms, respectively. Finally, the effects of dynamic characteristics and crystallization of DNA molecules on TCL movement and DCA size are expounded. This research provides detailed experimental data and proposes a theoretical model for understanding the dynamic mechanism of DNA droplet spreading on solid surfaces and has been helpful for designing DNA chips and developing micro-/nano-fluidic sensors.

While designing the power requirements of a ship, the most important factor to be considered is the ship resistance, or the sea drag forces acting on the ship. It is important to have an estimate of the ship resistance while designing the propulsion system since the power required to overcome the sea drag forces contribute to ‘losses’ in the propulsion system. There are three main methods to calculate ship resistance: Statistical methods like the Holtrop-Mennen (HM) method, numerical analysis or CFD (Computational Fluid Dynamics) simulations, and model testing, i.e. scaled model tests in towing tanks. At the start of the design stage, when only basic ship parameters are available, only statistical models like the HM method can be used. Numerical analysis/ CFD simulations and model tests can be performed only when the complete 3D design of the ship is completed. The present paper aims at predicting the calm water ship resistance using CFD simulations, using the Flow-3D software package. A case study of a roll-on/roll-off passenger (RoPax) ferry was investigated. Ship resistance was calculated at various ship speeds. Since the mesh affects the results in any CFD simulation, multiple meshes were used to check the mesh sensitivity. The results from the simulations were compared with the estimate from the HM method. The results from simulations agreed well with the HM method for low ship speeds. The difference in the results was considerably high compared to the HM method for higher ship speeds. The capability of Flow-3D to perform ship resistance analysis was demonstrated.