Dynamic Contact Angle Hysteresis Research Articles

Numerical Study of Heat Transfer and Fluid Flow Characteristics of a Hydrogen Pulsating Heat Pipe with Medium Filling Ratio

Benefiting from its high thermal conductivity, simple structure, and light weight, the pulsating heat pipe (PHP) can meet the requirements for high efficiency, flexibility, and low cost in industrial heat transfer applications such as aerospace detector cooling and vehicle thermal management. Compared to a PHP working at room temperature, the mechanism of a PHP with hydrogen as the working fluid differs significantly due to the unique thermal properties of hydrogen. In this paper, a two-dimensional model of a hydrogen PHP with a filling ratio of 51% was established to study the flow characteristics and thermal performance. The volume of fluid (VOF) method was used to capture the phase distribution and interface dynamics, and the Lee model was employed to account for phase change. To validate the model, a comparison was conducted between the simulation results and experimental data obtained in our laboratory. The simulation results show that the pressure and temperature errors were within 25% and 5%, respectively. Throughout a pressure oscillation cycle, the occurrence of uniform flow velocity, acceleration, and flow reversal can be attributed to the changes in the vapor–liquid phase distribution resulting from the effect of condensation and evaporation. In addition, when the fluid velocity was greater than 0.6 m/s, dynamic contact angle hysteresis was observed in the condenser. The results contribute to a deeper understanding of the flow and heat transfer mechanism of the hydrogen PHPs, which have not been yet achieved through visualization experiments.

Multiscale Analysis for Dynamic Contact Angle Hysteresis on Rough Surfaces

Dynamic contact angle hysteresis is of critical importance for many two-phase flow problems with moving contact lines. It is induced by inhomogeneity or roughness of the substrates. In this paper, we present theoretical studies on the time averaging of a reduced model for wetting on rough surfaces and also the analysis on the effect of stochastic thermal forces. We derive equations for the averaged dynamics and show that the apparent contact angle depends on the harmonic averaging of the geometric and chemical properties of the substrates as well as the contact line velocity. The contact angle hysteresis can be determined quantitatively by the equations. The averaging results are proved rigorously by multi-scale analysis and verified by some numerical examples.

Contact Angle Measurement on Curved Wetting Surfaces in Multiphase Lattice Boltzmann Method.

Contact angle is an essential physical quantity that characterizes the wettability of a substrate. Although it is widely used in the studies of surface wetting, capillary phenomena, and moving contact lines, the contact angle measurements in simulations and experiments are still complicated and time-consuming. In this paper, we present an efficient scheme for the measurement of contact angle on curved wetting surfaces in lattice Boltzmann simulations. The measuring results are in excellent agreement with the theoretical predictions without considering the gravity effect. A series of simulations with various drop sizes and surface curvatures confirm that the present scheme is grid-independent. Then, the scheme is verified in gravitational environments by simulating the deformations of sessile and pendent droplets on the curved wetting surface. The numerical results are highly consistent with experimental observations and support the theoretical analysis that the microscopic contact angle is independent of gravity. Furthermore, the method utilizes only the microscopic geometry of the contact angle and does not depend on the droplet profile; therefore, it can be applied to nonaxisymmetric shapes or moving contact lines. The scheme is applied to capture the dynamic contact angle hysteresis on homogeneous or chemically heterogeneous curved surfaces. Importantly, the accurate contact angle measurement enables the dynamic mechanical analysis of moving contact lines. The present measurement is simple and efficient and can be extended to implementations in various multiphase lattice Boltzmann models.

Improved contact angle measurement in multiphase lattice Boltzmann

Contact angle is an essential parameter to characterize substrate wettability. The measurement of contact angle in experiment and simulation is a complex and time-consuming task. In this paper, an improved method of measuring contact angle in multiphase lattice Boltzmann simulations is proposed, which can accurately obtain the real-time contact angle at a low temperature and larger density ratio. The three-phase contact point is determined by an extrapolation, and its position is not affected by the local deformation of flow field in the three-phase contact region. A series of simulations confirms that the present method has high accuracy and gird-independence. The contact angle keeps an excellent linear relationship with the chemical potential of the surface, so that it is very convenient to specify the wettability of a surface. The real-time contact angle measurement enables us to obtain the dynamic contact angle hysteresis on chemically heterogeneous surface, while the mechanical analyses can be effectively implemented at the moving contact line.

Effective boundary conditions for dynamic contact angle hysteresis on chemically inhomogeneous surfaces

Recent experiments (Guan et al., Phys. Rev. Lett., vol. 116, issue 6, 2016a, p. 066102; Guan et al., Phys. Rev. E, vol. 94, issue 4, 2016b, p. 042802) showed many interesting phenomena on dynamic contact angle hysteresis while there is still a lack of complete theoretical interpretation. In this work, we study the time averaging of the apparent advancing and receding contact angles on surfaces with periodic chemical patterns. We first derive a new Cox-type boundary condition for the apparent dynamic contact angle on homogeneous surfaces using the Onsager variational principle. Based on this condition, we propose a reduced model for some typical moving contact line problems on chemically inhomogeneous surfaces in two dimensions. Multiscale expansion and averaging techniques are employed to approximate the model for asymptotically small chemical patterns. We obtain a quantitative formula for the averaged dynamic contact angles. It describes explicitly how the advancing and receding contact angles depend on the velocity and the chemical inhomogeneity of the substrate. The formula is a coarse-graining version of the Cox-type boundary condition on inhomogeneous surfaces. Numerical simulations are presented to validate the analytical results. The numerical results also show that the formula characterizes well the complicated behaviour of dynamic contact angle hysteresis observed in the experiments.

Superhydrophobic behavior of cylinder dual-scale hierarchical nanostructured surfaces

Many surfaces in nature possessing superhydrophobicity have hierarchical (nano- and micro- scale) structures. A three-dimensional (3-D) model of cylindrical hierarchical nanostructured is established to describe the superhydrophobicity of solid surface. Based on thermodynamic analysis, the expressions of free energy (FE) and free energy barrier (FEB) for four precisely different wetting states are established and theoretically discussed. This approach provides theoretical guidance for predicting the dynamic contact angle (CA), static CA and CA hysteresis (CAH). Additionally, the actual three-phase contact line with droplet motion has been simulated, and the process of droplet advancing and receding is closely linked with the movement of contact line. To a great extent, the transition between different wetting states go hand in hand with that of the cylinder height and base spacing of nanostructure. Under the existing geometric parameters, when the nano-cylinders height reaches 1.5 × 10 −7 m, 2.36 × 10 −7 m, 2.56 × 10 −7 m, or when the nano-cylinders base spacing reaches 2.4 × 10 −7 m, 2.65 × 10 −7 m, 3.2 × 10 −7 m, the system will have a transition between different wetting states. Combined with the existing literature data and our experimental results support the correctness of the theoretical research, which are helpful for designing dual-scale hierarchical structure surfaces for researching the wetting behavior of advanced superhydrophobic materials. • A three-dimensional micro/nano model of hierarchical cylindrical structure is proposed and analyzed for the first time. • The single and synergistic effects of the uniform geometric parameters of micron and nanometer on the wettability of the system are discussed. • The critical expressions (Nanometer cylinder height and base spacing) of transition between any two wetting states (existence) are given. • The final stable wetting state of the system can be accurately predicted. • By controlling the micro/nano parameters, the stable wetting state of the hierarchical structure system can be predicted.

Tunable wettability of polymer films by partial engulfment of nanoparticles

A series of poly(methyl methacrylate) (PMMA) surfaces decorated by Cu nanoparticles (NP) with gradually varied morphology were prepared by high-pressure ${\mathrm{CO}}_{2}$ treatment at various time spans. Combining the characterizations of transmission electron microscopy (TEM) and atomic force microscopy (AFM), an accurate three-dimensional view of the morphology of the surfaces was presented. Subsequently, the wettability of the surfaces decreases near linearly with the increase of the apparent height of the decorating NPs in both static (static contact angle) and dynamic (contact angle hysteresis) aspects. The observed tendency contradicts to the Wenzel or Cassie-Baxter model and is explained by the contribution of nanomeniscus formed between the decorating NP and the flat substrate. The capillary pressure from this meniscus is negative and results in the increase of the contact angle with the apparent height $({H}_{N})$ of the Cu NPs decorating the PMMA surface. In addition, the effect of the coverage $({C}_{N})$ by NPs on the wettability can be explained on the same basis. Our experiment demonstrates the important influence of the nanomeniscus on the wettability, which is usually not taken into account. The results in this work provide a comprehensive understanding of how nanostructure affects the wettability of the decorated surfaces and shed light on how to obtain certain wettability through nanostructuring of the surface morphology.

Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces

A dynamic wetting problem is studied for a moving thin fiber inserted in fluid and with a chemically inhomogeneous surface. A reduced model is derived for contact angle hysteresis by using the Onsager principle as an approximation tool. The model is simple and captures the essential dynamics of the contact angle. From this model, we derive an upper bound of the advancing contact angle and a lower bound of the receding angle, which are verified by numerical simulations. The results are consistent with the quasi-static results. The model can also be used to understand the asymmetric dependence of the advancing and receding contact angles on the fiber velocity, which was observed recently in the physical experiments reported in the work of Guan et al. [“Asymmetric and speed-dependent capillary force hysteresis and relaxation of a suddenly stopped moving contact line,” Phys. Rev. Lett. 116, 066102 (2016)].

A fully 3D simulation of fluid-structure interaction with dynamic wetting and contact angle hysteresis

In this paper, we propose a three-dimensional diffuse-interface immersed-boundary (3D DIIB) method for the simulations of fluid-structure interaction (FSI) with dynamic wetting, complex geometry and contact angle hysteresis. In particular, the movement of rigid solid objects is allowed to have six degrees of freedom. In the method, the complex solid boundaries are represented by a set of Lagrangian patches that cover the whole surface of the solid objects, while the flows are solved on a staggered Cartesian grid. The couplings between the object movement and surrounding fluid flows are performed using an immersed boundary method. A simple model of contact angle hysteresis is used to ensure pinned contact lines if local contact angle is within the window of contact angle hysteresis. To relieve the stress singularity at moving contact lines, a characteristic moving contact line model [1] is adopted at 3D curved solid surfaces, after the geometrical information of interface is constructed in the vicinity of the contact line. For 3D simulations of FSI with dynamic wetting, it is crucial but difficult to estimate capillary force, of which the process consists of locating the moving contact line on complex solid surfaces, discretizing it into line segment, and determining the local tangent to the interface at the contact lines. Special consideration is given to the modeling of the capillary force and associated torque, in order to have accurate approximations. The performance of the 3D DIIB method is systematically examined through a series of numerical experiments, of which the results are either verified against theoretical predictions or compared with experimental data. Finally, we simulate the collision process of raindrops with 3D mosquito body, to show the potential of the 3D DIIB method in practical applications.

Dynamic characteristics of water spreading over laser-textured aluminum alloy surfaces

Laser texturing has great potential for controlling wetting properties as well as spreading dynamics of liquid small volumes on technological metal surfaces. In this work, nanosecond pulse laser was used to create some ordered and anisotropic textures on aluminum alloy surfaces. The dynamic characteristics and contact angle hysteresis were obtained by increasing and decreasing the droplet volume. In this wetting/dewetting cycle, we recorded fluctuational movements of the three-phase contact line over the surfaces with an ordered texture when the capillary number tends to zero. These movements are caused by activity of forces leading to fluid circulation in the droplet, as well as inertia and gravity. To determine the contact angle hysteresis when the three-phase contact line fluctuates, we developed a new approach. We showed that the contact angle hysteresis depends on the droplet state (the presence of air cushions in the cavities in a thin near-surface layer) largely than on the roughness. We found the influence of repeated wetting cycles (multiple advancing and receding liquid movement) on the dynamic characteristics of water spreading over the laser-textured aluminum alloy surfaces. The molecular-kinetic and hydrodynamic models were used to interpret the liquid movement over the surfaces with ordered and anisotropic textures.

Investigation of wettability on performance of pulsating heat pipe

A three-dimensional closed-loop pulsating heat pipe (CLPHP), with different wettability and charged with deionized water is numerically investigated in present work. The thermal performance and bubble dynamics of CLPHP are obtained under the condition of various input heat loads. It's found that the performance of CLPHP is affected by both surface wettability and input heat load. Under lower input heat load, CLPHP with hydrophobic surface (including superhydrophobic surface) has lower thermal resistance than that with hydrophilic surface. Conversely, CLPHP with hydrophilic surface starts up earlier, and has better thermal performance under higher input heat load. Specially, compared with the CLPHP with superhydrophobic surface, the thermal resistance of CLPHP with superhydrophilic reduces by 10.8% under the input heat load of 20 W. Moreover, the reversal of flow direction is observed in CLPHP with hydrophobic surface, while the stable directional circulation is always maintained in CLPHP with hydrophilic surface. The results indicate that the difference between advancing and receding angles (dynamic contact angle hysteresis) leads to various capillary resistance. Furthermore, due to lower flow resistance and the effect of liquid film, CLPHP with hydrophilic surface can effectively raise the dry-out input heat load.

Adaptive Wetting-Adaptation in Wetting.

Many surfaces reversibly change their structure and interfacial energy upon being in contact with a liquid. Such surfaces adapt to a specific liquid. We propose the first order kinetic model to describe dynamic contact angles of such adaptive surfaces. The model is general and does not refer to a particular adaptation process. The aim of the proposed model is to provide a quantitative description of adaptive wetting and to link changes in contact angles to microscopic adaptation processes. By introducing exponentially relaxing interfacial energies and applying Young's equation locally, we predict a change of advancing and receding contact angles depending on the velocity of the contact line. Even for perfectly homogeneous and smooth surfaces, a dynamic contact angle hysteresis is obtained. As possible adaptations, we discuss changes and reconstruction of polymer surfaces or monolayers, diffusion and swelling, adsorption of surfactants, replacement of contaminants, reorientation of liquid molecules, or formation of an electric double layer.

Contact angle measurement in lattice Boltzmann method

Contact angle is an essential characteristic in wetting, capillarity and moving contact line; however, although contact angle phenomena are effectively simulated, an accurate and real-time measurement for contact angle has not been well studied in computational fluid dynamics, especially in dynamic environments. Here, we design a geometry-based mesoscopic scheme for on-the-spot measurement of the contact angle in the lattice Boltzmann method. The measuring results without gravity effect are in good agreement with the benchmarks from the spherical cap method. The performances of the scheme are further verified in gravitational environments by simulating sessile and pendent droplets on smooth solid surfaces and dynamic contact angle hysteresis on chemically heterogeneous surfaces. This scheme is simple and computationally efficient. It requires only the local data and is independent of multiphase models.

Dynamic contact angle hysteresis in liquid bridges

This work presents an experimental study of dynamic contact angle hysteresis using liquid bridges under cyclic compression and stretching between two identical plates. Under various loading rates, contact angle hystereses for three different liquids were measured by examination of advancing and receding liquid bridges, and the capillary forces were recorded. It is found that for a given liquid, the hysteretic behaviour of the contact angle is more pronounced at higher loading rates. By unifying the behaviour of the three liquids, power-law correlations were proposed to describe the relationship between the dynamic contact angle and the capillary number for advancing and receding cases. It is found that the exponents of obtained power-law correlations differ from those derived through earlier methods (e.g., capillary rise), due to the different kinematics of the contact line. The various hysteretic loops of capillary force in liquid bridges under varied cyclic loading rates were also observed, which can be captured quantitatively by the prediction of our developed model incorporating the dynamic contact angle hysteresis. These results illustrate the importance of varying contact line geometries during dynamic wetting and dewetting processes, and warrant an improved modelling approach for higher level phenomena involving these processes, e.g., multiphase flow in porous media and liquid transfer between surfaces with moving contact lines.

Correlating contact line capillarity and dynamic contact angle hysteresis in surfactant-nanoparticle based complex fluids

Dynamic wettability and contact angle hysteresis can be correlated to shed insight onto any solid-liquid interaction. Complex fluids are capable of altering the expected hysteresis and dynamic wetting behavior due to interfacial interactions. We report the effect of capillary number on the dynamic advancing and receding contact angles of surfactant-based nanocolloidal solutions on hydrophilic, near hydrophobic, and superhydrophobic surfaces by performing forced wetting and de-wetting experiments by employing the embedded needle method. A segregated study is performed to infer the contributing effects of the constituents and effects of particle morphology. The static contact angle hysteresis is found to be a function of particle and surfactant concentrations and greatly depends on the nature of the morphology of the particles. An order of estimate of line energy and a dynamic flow parameter called spreading factor and the transient variations of these parameters are explored which sheds light on the dynamics of contact line movement and response to perturbation of three-phase contact. The Cox-Voinov-Tanner law was found to hold for hydrophilic and a weak dependency on superhydrophobic surfaces with capillary number, and even for the complex fluids, with a varying degree of dependency for different fluids.

Numerical simulation of droplet sliding on an inclined surface using moving particle semi-implicit method

Two novel boundary models for the moving particle semi-implicit method are proposed in this paper. These models precisely reproduce the dynamic behavior of a droplet on an inclined surface using a polygon wall model. The existing polygon wall model assumes that the surface is smooth and therefore cannot reproduce the dynamic contact angle correctly. In addition, droplet retention on a surface inclined at a low angle has not been reproduced in the literature. The proposed models take into account forces acting on droplets from surface features of the wall. These models are developed to reproduce the dynamic and static contact angle hysteresis in droplet sliding behavior that have been observed in experiments. Two-dimensional calculations of a droplet sliding down an inclined surface are performed. The proposed models are evaluated by comparing numerical results with experimental observations of droplets sliding on an inclined surface. This comparison confirms that the dynamic contact angle and sliding velocity can be simulated precisely. In addition, we found that our numerical results agree well with the Cox–Voinov law, which is used widely to evaluate dynamic contact angles.

Contact Angle and Adhesion Dynamics and Hysteresis on Molecularly Smooth Chemically Homogeneous Surfaces.

Measuring truly equilibrium adhesion energies or contact angles to obtain the thermodynamic values is experimentally difficult because it requires loading/unloading or advancing/receding boundaries to be measured at rates that can be slower than 1 nm/s. We have measured advancing-receding contact angles and loading-unloading adhesion energies for various systems and geometries involving molecularly smooth and chemically homogeneous surfaces moving at different but steady velocities in both directions, ±V, focusing on the thermodynamic limit of ±V → 0. We have used the Bell Theory (1978) to derive expressions for the dynamic (velocity-dependent) adhesion energies and contact angles suitable for both (i) dynamic adhesion measurements using the classic Johnson-Kendall-Roberts (JKR, 1971) theory of "contact mechanics" and (ii) dynamic contact angle hysteresis measurements of both rolling droplets and syringe-controlled (sessile) droplets on various surfaces. We present our results for systems that exhibited both steady and varying velocities from V ≈ 10 mm/s to 1 nm/s, where in all cases but one, the advancing (V > 0) and receding (V < 0) adhesion energies and/or contact angles converged toward the same theoretical (thermodynamic) values as V → 0. Our equations for the dynamic contact angles are similar to the classic equations of Blake & Haynes (1969) and fitted the experimental adhesion data equally well over the range of velocities studied, although with somewhat different fitting parameters for the characteristic molecular length/dimension or area and characteristic bond formation/rupture lifetime or velocity. Our theoretical and experimental methods and results unify previous kinetic theories of adhesion and contact angle hysteresis and offer new experimental methods for testing kinetic models in the thermodynamic, quasi-static, limit. Our analyses are limited to kinetic effects only, and we conclude that hydrodynamic, i.e., viscous, and inertial effects do not play a role at the interfacial velocities of our experiments, i.e., V < (1-10) mm/s (for water and hexadecane, but for viscous polymers it may be different), consistent with previously reported studies.

Thermo-hydrodynamic transport phenomena in partially wetting liquid plugs moving inside micro-channels

Single-phase as well as two-phase fluid flows inside mini/micro-channels and capillary tubes are of practical importance in many miniaturized engineering systems. While several issues related to single-phase transport are fairly well understood, two-phase systems still pose challenges for engineering design. The presence of gas–liquid interfaces, dominance of surface forces, moving contact lines, wettability, dynamic contact angle hysteresis and flow in confined geometries are some of the unique features of two-phase systems, which manifest into complex transport phenomena. While Taylor plug/bubble flow is a fairly common flow pattern in several micro-fluidic devices operating at low Bond number, the ensuing transport characteristics are complex and still not fully discerned. This review paper aims at highlighting the nuances and features of a unit cell of a Taylor plug flow, especially focusing on partially wetting systems, which are more common in engineering applications. Emphasis is given to a ‘unit cell’ flow system consisting of an isolated liquid Taylor plug with adjacent gas phase, confined in a capillary tube. Such a seemingly simple flow condition poses considerable challenges for discerning and modelling local thermo-hydrodynamic transport coefficients. Relevant background information and fundamentals are carefully scrutinized while summarizing the state-of-the-art. The role of wettability and dissipation near the contact line is highlighted via available experimental and simulation results. Local momentum and heat transfer exchange processes during the motion of an isolated plug of partially wetting liquid moving inside a capillary tube are delineated.

Phase-field modeling of interfacial dynamics in emulsion flows: Nonequilibrium surface tension

A weakly nonlocal phase-field model is used to define the surface tension in liquid binary mixtures in terms of the composition gradient in the interfacial region so that, at equilibrium, it depends linearly on the characteristic length that defines the interfacial width. Contrary to previous works suggesting that the surface tension in a phase-field model is fixed, we define the surface tension for a curved interface and far-from-equilibrium conditions as the integral of the free energy excess (i.e., above the thermodynamic component of the free energy) across the interface profile in a direction parallel to the composition gradient. Consequently, the nonequilibrium surface tension can be widely different from its equilibrium value under dynamic conditions, while it reduces to its thermodynamic value for a flat interface at local equilibrium. In nonequilibrium conditions, the surface tension changes with time: during mixing, it decreases as the inverse square root of time, while in the linear regime of spinodal decomposition, it increases exponentially to its equilibrium value, as nonlinear effects saturate the exponential growth. In addition, since temperature gradients modify the steepness of the concentration profile in the interfacial region, they induce gradients in the nonequilibrium surface tension, leading to the Marangoni thermocapillary migration of an isolated drop. Similarly, Marangoni stresses are induced in a composition gradient, leading to diffusiophoresis. We also review results on the nonequilibrium surface tension for a wall-bound pendant drop near detachment, which help to explain a discrepancy between our numerically determined static contact angle dependence of the critical Bond number and its sharp-interface counterpart from a static stability analysis of equilibrium shapes after numerical integration of the Young-Laplace equation. Finally, we present new results from phase-field simulations of the motion of an isolated droplet down an incline in gravity, showing that dynamic contact angle hysteresis can be explained in terms of the nonequilibrium surface tension.

Droplet Departure Characteristics and Dropwise Condensation Heat Transfer at Low Steam Pressure

Dropwise condensation has received significant attention due to its great potential to enhance heat transfer by the rapid droplet removal. In this work, droplet departure characteristics on a vertical surface, especially the droplet departure retention at low steam pressure and its effect on the heat transfer performance are investigated experimentally. The energy dissipation increases during droplet movement due to the increased viscosity at low pressure. Droplet oscillation caused by excess kinetic energy weakens and the dynamic contact angle (CA) hysteresis becomes apparent, which is not beneficial to droplet departure. Condensed droplets grow larger and fall more slowly at low pressure compared to that at atmospheric pressure. The droplet moves smoothly downward once it grows to departure size at atmospheric pressure while the droplet exhibits an intermittent motion at low pressure. Based on the droplet departure characteristics, a unified heat transfer model for dropwise condensation is developed by introducing the pressure-dependent departure velocity. The modified model very well predicts heat transfer performances at various pressures and the nonlinearity of heat flux varying with surface subcooling is quantitatively explained. This work provides insights into the heat transfer mechanism of dropwise condensation and offers a new avenue to further enhance heat transfer at low steam pressure.