Wetting Boundary Research Articles

Thermohydrodynamics of boiling in binary compressible fluids.

We numerically study the thermohydrodynamics of boiling for a CO(2) + ethanol mixture on lyophilic and lyophobic surfaces in both closed and open systems, based on a diffuse interface model for a two-component system. The corresponding wetting boundary conditions for an isothermal system are proposed and verified in this paper. New phenomena due to the addition of another component, mainly the preferential evaporation of the more volatile component, are observed. In the open system and the closed system, the physical process shows very different characteristics. In the open system, except for the movement of the contact line, the qualitative features are rather similar for lyophobic and lyophilic surfaces. In the closed system, the vortices that are observed on a lyophobic surface are not seen on a lyophilic surface. More sophisticated wetting boundary conditions for nonisothermal, two-component systems might need to be further developed, taking into account the variations of density, temperature, and surface tension near the wall, while numerical results show that the boundary conditions proposed here also work well even in boiling, where the temperature is nonuniform.

Climatic Zones of Sri Lanka under Changing Climate

Climate change is the major phenomenon and fundamental human development challenge of the 21st century. It is well known that all climatic regions in Sri Lanka have been experienced with severe climatic changes. As a result, entire flora and fauna including humans are vulnerable to these adverse consequences. In general, it is believed that nations would mitigate the climate change or adapt to the changing environments. For employment of such measures, it is necessary to understand the macro-climatic region and their behavior under the changing global climate. Based on the annual rainfall received, the country is divided mainly into four climatic zones: wet, intermediate, dry and arid. The climate of the country depends largely on the monsoon wind patterns and series of temperature. Therefore, it is necessary to understand the climatic zones and their behavior to identify each climatic zone‟s minor and major climate changes. The main objective of this study was to study on macro-climatic regions of Sri Lanka under changing climate. Therefore, the present study was carried out on macro-climatic regions of the island to find out the potential variation of temperature and rainfall patterns. Climatic data for the 30 year period were collected from randomly selected metrological stations in each climatic zone and average temperature and rainfall data were analysed using least significant difference (LSD) test. The results showed that average temperature of the country has increased 0.4° C from the year 1869 to 1980. Kandy (intermediate zone) region shows the higher temperature after the year of 1886 named as colonial era which was prevalent for deforestation and tea cultivation. A significantly increasing trend of temperature and decreasing trend of rainfall could be observed entirely within wet zone, dry zone and intermediate zone in 20th century than 19th century. Findings reveal that the wet zone boundary has squeezed in and dry zone boundary has expanded in recent time. Such boundary movements of the zones are significantly important on reclassification of the dry zone and intermediate zone. Therefore, further studies on climate regions of Sri Lanka under changing climate is needed to examine the relationship between the vegetation cover distribution changes within the boundary of the climatic zones. Hence researchers could identify wet and intermediate zones as a “micro-climatic zones” while dry zone could be identified as a “macro-climatic zone” instead of traditionally generalised term in future. Keywords: Changing climate, Climatic zones, Macro-climatic region, Zone boundary movement, Colonial era

Lattice Boltzmann modeling of contact angle and its hysteresis in two-phase flow with large viscosity difference.

Contact angle hysteresis is an important physical phenomenon omnipresent in nature and various industrial processes, but its effects are not considered in many existing multiphase flow simulations due to modeling complexity. In this work, a multiphase lattice Boltzmann method (LBM) is developed to simulate the contact-line dynamics with consideration of the contact angle hysteresis for a broad range of kinematic viscosity ratios. In this method, the immiscible two-phase flow is described by a color-fluid model, in which the multiple-relaxation-time collision operator is adopted to increase numerical stability and suppress unphysical spurious currents at the contact line. The contact angle hysteresis is introduced using the strategy proposed by Ding and Spelt [Ding and Spelt, J. Fluid Mech. 599, 341 (2008)JFLSA70022-112010.1017/S0022112008000190], and the geometrical wetting boundary condition is enforced to obtain the desired contact angle. This method is first validated by simulations of static contact angle and dynamic capillary intrusion process on ideal (smooth) surfaces. It is then used to simulate the dynamic behavior of a droplet on a nonideal (inhomogeneous) surface subject to a simple shear flow. When the droplet remains pinned on the surface due to hysteresis, the steady interface shapes of the droplet quantitatively agree well with the previous numerical results. Four typical motion modes of contact points, as observed in a recent study, are qualitatively reproduced with varying advancing and receding contact angles. The viscosity ratio is found to have a notable impact on the droplet deformation, breakup, and hysteresis behavior. Finally, this method is extended to simulate the droplet breakup in a microfluidic T junction, with one half of the wall surface ideal and the other half nonideal. Due to the contact angle hysteresis, the droplet asymmetrically breaks up into two daughter droplets with the smaller one in the nonideal branch channel, and the behavior of daughter droplets is significantly different in both branch channels. Also, it is found that the contact angle hysteresis is strengthened with decreasing the viscosity ratio, leading to an earlier droplet breakup and a decrease in the maximum length that the droplet can reach before the breakup. These simulation results manifest that the present multiphase LBM can be a useful substitute to Ba etal. [Phys. Rev. E 88, 043306 (2013)PLEEE81539-375510.1103/PhysRevE.88.043306] for modeling the contact angle hysteresis, and it can be easily implemented with higher computational efficiency.

Parallel embedded boundary methods for fluid and rigid-body interaction

The implementations of an updated body-fitted and a non body-fitted method to deal with the interaction of a fluid and a rigid body are described. The physics of the fluid is modeled by the incompressible Navier–Stokes equations. A parallel fluid solver based on the VMS (Variational Multiscale) Finite Element method serves as the basis for the implementation. For the rigid body movement, the Newton–Euler equations are solved numerically. To account for the interaction, the force that the fluid exerts on the rigid body is determined, on the one hand. On the other hand, the velocity of the rigid body is imposed as a Dirichlet boundary condition on the fluid. A fixed Eulerian mesh discretizes the fluid domain, except for nodes in the vicinity of the rigid body boundary for the case of the updated body-fitted approach. The wet boundary of the rigid body is embedded in the fluid mesh and tracked by a moving surface mesh. It is a distinctive characteristic of the updated body-fitted strategy that, in order to impose velocities on the interface, some of the nodes near the body surface are moved by using a local r-adaptivity algorithm to conform with this surface. By contrast, the non body-fitted approach uses kriging interpolation for velocity prescription over the fluid on the interface. Given that fluid nodes can become solid nodes and vice versa due to the rigid body movement, we have adopted the FMALE approach, a variation of the ALE method to keep the fluid mesh fixed. Algorithms to ensure high performance, like skd-trees to determine if a given spatial point is currently inside the solid, are also used. All these ingredients constitute two approaches that are both computationally efficient and accurate. Numerical experiments are presented to assess their performance comparatively.

From wetting to melting along grain boundaries using phase field and sharp interface methods

We investigate the ability of a multi-order parameter phase field model with obstacle potentials to describe grain boundary premelting in equilibrium situations. In agreement with an energetic picture we find that the transition between dry and wet grain boundaries at the bulk melting point is given by the threshold 2σsl=σgb, with σsl being the solid-melt interfacial energy and σgb the energy of a dry grain boundary. The predictions for premelting are confirmed by simulations using the phase field package OpenPhase. For the prediction of the kinetics of melting along grain boundaries in pure materials, taking into account the short ranged interactions which are responsible for the grain boundary premelting, a sharp interface theory is developed. It confirms that for overheated grain boundaries the melting velocity is reduced (increased) for non-wetting (wetting) grain boundaries. Numerical steady state predictions are in agreement with a fully analytical solution in a subset of the parameter space. Phase field simulations confirm the predictions of the sharp interface theory.

Numerical modelling of moisture transfers with hysteresis within cementitious materials: Verification and investigation of the effects of repeated wetting–drying boundary conditions

In natural environment, the cover layer of reinforced concrete structures is affected by periodic variations of external relative humidity (RH). However, most moisture transport models in the literature only focus on drying of materials. In this study, a method coupling a moisture transport model with any kind of hysteresis modelling is presented. Two hysteresis models (conceptual and empirical) have been implemented and compared. The scope of the study is limited to cyclic variations of RH with no direct contact with liquid water during the wetting steps. Experimental data verifications show that the conceptual approach yields better results than the empirical one. Comparisons of non-hysteresis and hysteresis modellings have been carried out for different cycle durations, RH amplitudes and initial moisture states. All comparisons and investigations enhance the necessity of considering hysteresis to quantify moisture transport under repeated drying–wetting boundary conditions.

Modelling thermocapillary migration of a microfluidic droplet on a solid surface

A multiphase lattice Boltzmann model is developed to simulate immiscible thermocapillary flows with the presence of fluid–surface interactions. In this model, interfacial tension force and Marangoni stress are included by introducing a body force term based on the concept of continuum surface force, and phase segregation is achieved using the recolouring algorithm proposed by Latva-Kokko and Rothman. At a solid surface, fluid–surface interactions are modelled by a partial wetting boundary condition that uses a geometric formulation to specify the contact angle, and a colour-conserving boundary closure scheme to improve the numerical accuracy and suppress spurious velocities at the contact line. An additional convection–diffusion equation is solved by the passive scalar approach to obtain the temperature field, which is coupled to the hydrodynamic equations through an equation of state. This model is first validated by simulations of static contact angle and dynamic capillary intrusion process when a constant interfacial tension is considered. It is then used to simulate the thermocapillary migration of a microfluidic droplet on a horizontal solid surface subject to a uniform temperature gradient. We for the first time demonstrate numerically that the droplet motion undergoes two different states depending on the surface wettability: the droplet migrates towards the cooler regions on hydrophilic surfaces but reverses on hydrophobic surfaces. Decreasing the viscosity ratio can enhance the intensity of thermocapillary vortices, leading to an increase in migration velocity. The contact angle hysteresis, i.e., the difference between the advancing and receding contact angles, is always positive regardless of the contact angle and viscosity ratio. The contact angle hysteresis and the migration velocity both first decrease and then increase with the contact angle, and their minimum values occur at the contact angle of 90 degrees.

High-Precision Structured Finite Volume Model for Numerical Simulation of Dam-and Dyke-Breach Flow

A high precision structured-based finite volume model for numerical simulation of dam-and dyke-breach flow was proposed. The model regarded the fully two-dimensional shallow water equations as the governing equations, and used the Godunov-type finite volume shock-capturing schemes HLLC to calculate flow flux. Its spatial and temporal accuracy were improved to two order accuracy using the slop limiter and predict-correct method, and the slope source terms and friction source terms were treated with central difference scheme and fully implicit method respectively. And then a robust procedure was adapted in the model to efficiently and accurately simulate the movement of wet and dry boundary and a method of high calculation efficiency was applied in the treatment of complex boundary. A popular example was used to validate the capability of the model. The result shows that the model can capture flow processes over irregular boundary accurately and shows good stability and accuracy.

Numerical study of drop motion on a surface with stepwise wettability gradient and contact angle hysteresis

In this work, the motion of a two-dimensional drop on a surface with stepwise wettability gradient (WG) is studied numerically by a hybrid lattice-Boltzmann finite-difference method. We incorporate the geometric wetting boundary condition that allows accurate implementation of a contact angle hysteresis (CAH) model. The method is first validated through a series of tests that check different constituents of the numerical model. Then, simulations of a drop on a wall with given stepwise WG are performed under different conditions. The effects of the Reynolds number, the viscosity ratio, the WG, as well as the CAH on the drop motion are investigated in detail. It was discovered that the shape of the drop in steady motion may be fitted by two arcs that give two apparent contact angles, which are related to the respective contact line velocities and the relevant contact angles (that specify the WG and CAH) through the relation derived by Cox [“The dynamics of the spreading of liquids on a solid surface. Part 1. viscous flow,” J. Fluid Mech. 168, 169–194 (1986)] if the slip length in simulation is defined according to Yue et al. [“Sharp-interface limit of the Cahn-Hilliard model for moving contact lines,” J. Fluid Mech. 645, 279–294 (2010)]. It was also found that the steady capillary number of the drop is significantly affected by the viscosity ratio, the magnitudes of the WG, and the CAH, whereas it almost shows no dependence on the Reynolds number.

Tear film dynamics with evaporation, wetting, and time-dependent flux boundary condition on an eye-shaped domain.

We study tear film dynamics with evaporation on a wettable eye-shaped ocular surface using a lubrication model. The mathematical model has a time-dependent flux boundary condition that models the cycles of tear fluid supply and drainage; it mimics blinks on a stationary eye-shaped domain. We generate computational grids and solve the nonlinear governing equations using the OVERTURE computational framework. In vivo experimental results using fluorescent imaging are used to visualize the influx and redistribution of tears for an open eye. Results from the numerical simulations are compared with the experiment. The model captures the flow around the meniscus and other dynamic features of human tear film observed in vivo.

Simulation of Droplet Resting on Micro-structured Surface by Lattice Boltzmann Method

Three-dimensional liquid droplet resting on micro-structured pillar surface is simulated with lattice Boltzmann method incorporat- ing the Cahn-Hilliard equation. This is based on the two-phase model of Zheng et al. [14] combined with partial wetting boundary condition of Briant et al. [12]. Two Simulations are conducted with the same area fractions but different pillar heights, i.e. surface roughness, which is shown to have minor influence on the apparent contact angles at the Cassie state investigated. The predicted apparent contact angles are contrasted with measurements. Predictions show lower apparent contact angles and the deviations are around 10%. This might be due to the inadequate treatment of wetting boundary condition of the pillar surface, and this is deserved to be further studied.

Color-gradient lattice Boltzmann model for simulating droplet motion with contact-angle hysteresis

Lattice Boltzmann method (LBM) is an effective tool for simulating the contact-line motion due to the nature of its microscopic dynamics. In contact-line motion, contact-angle hysteresis is an inherent phenomenon, but it is neglected in most existing color-gradient based LBMs. In this paper, a color-gradient based multiphase LBM is developed to simulate the contact-line motion, particularly with the hysteresis of contact angle involved. In this model, the perturbation operator based on the continuum surface force concept is introduced to model the interfacial tension, and the recoloring operator proposed by Latva-Kokko and Rothman is used to produce phase segregation and resolve the lattice pinning problem. At the solid surface, the color-conserving wetting boundary condition [Hollis et al., IMA J. Appl. Math. 76, 726 (2011)] is applied to improve the accuracy of simulations and suppress spurious currents at the contact line. In particular, we present a numerical algorithm to allow for the effect of the contact-angle hysteresis, in which an iterative procedure is used to determine the dynamic contact angle. Numerical simulations are conducted to verify the developed model, including the droplet partial wetting process and droplet dynamical behavior in a simple shear flow. The obtained results are compared with theoretical solutions and experimental data, indicating that the model is able to predict the equilibrium droplet shape as well as the dynamic process of partial wetting and thus permits accurate prediction of contact-line motion with the consideration of contact-angle hysteresis.

Local Heat Transfer Dependency on Thermal Boundary Condition in Ribbed Cooling Channel Geometries

The present study is geared toward quantifying the effects of imposed thermal boundary condition in cooling channel applications. In this regard, tests are conducted in a generic passage, with evenly distributed rib type perturbators at 90 deg, with a 30% passage blockage ratio and pitch-to-height ratio of 10. Uniform heat-flux is imposed on the external side of the slab which provides Biot number and solid-to-fluid thermal conductivity ratio around 1 and 600, respectively. Through infrared thermometry measurements over the wetted surface and via an energy balance within the solid, conjugate heat transfer coefficients are calculated over a single rib-pitch. The local heat extraction is demonstrated to be a strong function of the conduction effects, observed more dominantly in the rib vicinity. Moreover, the aero-thermal effects are investigated by comparing the findings with analogous aerodynamic literature, enabling heat transfer distributions to be associated with distinct flow structures. Furthermore, the results are contrasted with the iso-heat-flux wetted boundary condition test case. Neglecting the thermal boundary condition dependence, and thus the true thermal history of the boundary layer, is demonstrated to produce large errors in heat transfer predictions.

Investigation of Lattice Boltzmann wetting boundary conditions for capillaries with irregular polygonal cross-section

We have investigated the performance of an alternative wetting boundary condition for complex geometries in a phase field Lattice Boltzmann scheme, which is an alternative to the commonly used formulation by Yeomans and coworkers. Though our boundary condition is much simpler in its implementation, all investigated schemes show proper droplet spreading behaviour following the Cox–Voinov law. Still, numerical artefacts like spurious velocities or chequer board effects in the pressure field can be significantly reduced by the use of a two-relaxation-time (TRT) scheme, likewise recent studies by the Yeomans group. The outstanding property of our implementation is the presence of an (artificial) thin wetting layer, which influences the relation between the saturation (Sw) and capillary pressure pcap in channels with irregular polygonal cross section. The pcap(Sw) relation from our simulation follows the shifted-Young–Laplace (sYL) law, showing that the physics of this wetting layer is similar to precursor films due to Van der Waals forces. With the knowledge of the thickness of the wetting layer, simulation results can be translated back to realistic pore configurations with thinner wetting layers.

Pore-Scale Simulations of Gas Displacing Liquid in a Homogeneous Pore Network Using the Lattice Boltzmann Method

A lattice Boltzmann high-density-ratio model, which uses diffuse interface theory to describe the interfacial dynamics and was proposed originally by Lee and Liu (J Comput Phys 229:8045–8063, 2010), is extended to simulate immiscible multiphase flows in porous media. A wetting boundary treatment is proposed for concave and convex corners. The capability and accuracy of this model is first validated by simulations of equilibrium contact angle, injection of a non-wetting gas into two parallel capillary tubes, and dynamic capillary intrusion. The model is then used to simulate gas displacement of liquid in a homogenous two-dimensional pore network consisting of uniformly spaced square obstructions. The influence of capillary number (Ca), viscosity ratio (\(M\)), surface wettability, and Bond number (Bo) is studied systematically. In the drainage displacement, we have identified three different regimes, namely stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number, viscosity ratio, and Bond number. Gas saturation generally increases with an increase in capillary number at breakthrough, whereas a slight decrease occurs when Ca is increased from \(8.66\times 10^{-4}\) to \(4.33\times 10^{-3}\), which is associated with the viscous instability at high Ca. Increasing the viscosity ratio can enhance stability during displacement, leading to an increase in gas saturation. In the two-dimensional phase diagram, our results show that the viscous fingering regime occupies a zone markedly different from those obtained in previous numerical and experimental studies. When the surface wettability is taken into account, the residual liquid blob decreases in size with the affinity of the displacing gas to the solid surface. Increasing Bo can increase the gas saturation, and stable displacement is observed for \(Bo>1\) because the applied gravity has a stabilizing influence on the drainage process.

Friction and Wear Mechanism between Rubber and Nickel for Water Lubricated Bearings

Water lubricated rubber bearing is one of the most appropriate bearings widely used in submerged pump for drainage. The water lubricated rubber bearings sometimes worked in absent-water conditions especially at the machine start or brake. The friction and wear characteristics of the water lubricated rubber/Nickel coating pair were tested under dry, wet and water lubrication conditions respectively on the high-speed ring-block friction and wear testing machine. The effect of load and speed on the friction coefficient was examined in the experiment. The friction and wear mechanism of the rubber/Nickel coating pair under different conditions was analyzed with the help of SEM in the paper. The results show that the adhesive wear mainly occurs under dry condition, the grain abrasion occurs under wet condition and boundary lubrication occurs under water lubrication.

Antarctic ice depthsounding radar instrumentation for the NASA DC-8

Prediction of the polar ice sheets' contribution to sea-level change has prompted an intensive glacial characterization with fine spatial and temporal resolution. To provide key metrics required by predictive mass balance models including surface topography, ice thickness, and basal conditions (topography, roughness, frozen or wet boundary conditions, grounding-line position), an expanding series of data collection campaigns have been conducted over the last two decades involving ground-based, airborne, and spaceborne instruments.

A Lattice Boltzmann Simulation of Contact Line Motion and Internal Fluid Flows in an Evaporating Droplet on Homogenous Substrates

A two-dimensional lattice Boltzmann model is constructed to simulate the evaporation of a single droplet on a homogenous wetting substrate. An evaporation model is used in the simulation to describe the mass loss from the surface of the evaporating droplet. In addition, a partial wetting boundary condition is imposed on the lattice sites on the substrate surface to determine the wettability of the substrate. The evaporation of a single droplet in ambient vapor shows a linear decrease in the square of the droplet radius, which agrees well with the d2 law for an evaporating droplet. During the evaporation of a droplet on a hydrophobic substrate, the wetting diameter decreases while the contact angle remains constant. During the evaporation of a droplet on a hydrophilic substrate, the wetting diameter decreases while the contact angle remains almost constant when a partial wetting boundary condition is imposed. However, three stages of contact line motion are observed when the partial wetting boundary condition is modified to describe the dynamical change in the contact angle, and this observation agrees well with a previous study by other investigtors. In addition, internal fluid flows towards the contact line of the droplet in the pinning stage of the evaporation are discussed.

2D and 3D numerical models on compositionally buoyant diapirs in the mantle wedge

We present 2D and 3D numerical model calculations that focus on the physics of compositionally buoyant diapirs rising within a mantle wedge corner flow. Compositional buoyancy is assumed to arise from slab dehydration during which water-rich volatiles enter the mantle wedge and form a wet, less dense boundary layer on top of the slab. Slab dehydration is prescribed to occur in the 80–180 km deep slab interval, and the water transport is treated as a diffusion-like process. In this study, the mantle's rheology is modeled as being isoviscous for the benefit of easier-to-interpret feedbacks between water migration and buoyant viscous flow of the mantle. We use a simple subduction geometry that does not change during the numerical calculation. In a large set of 2D calculations we have identified that five different flow regimes can form, in which the position, number, and formation time of the diapirs vary as a function of four parameters: subduction angle, subduction rate, water diffusivity (mobility), and mantle viscosity. Using the same numerical method and numerical resolution we also conducted a suite of 3D calculations for 16 selected parameter combinations. Comparing the 2D and 3D results for the same model parameters reveals that the 2D models can only give limited insights into the inherently 3D problem of mantle wedge diapirism. While often correctly predicting the position and onset time of the first diapir(s), the 2D models fail to capture the dynamics of diapir ascent as well as the formation of secondary diapirs that result from boundary layer perturbations caused by previous diapirs. Of greatest importance for physically correct results is the numerical resolution in the region where diapirs nucleate, which must be high enough to accurately capture the growth of the thin wet boundary layer on top of the slab and, subsequently, the formation, morphology, and ascent of diapirs. Here 2D models can be very useful to quantify the required resolution, which we find for a 10 19 Pa · s mantle wedge to be about 1 km node spacing for quadratic-order velocity elements.

Lattice Boltzmann simulations of incompressible liquid–gas systems on partial wetting surfaces

A three-dimensional Lattice Boltzmann two-phase model capable of dealing with large liquid and gas density ratios and with a partial wetting surface is introduced. This is based on a high density ratio model combined with a partial wetting boundary method. The predicted three-dimensional droplets at different partial wetting conditions at equilibrium are in good agreement with analytical solutions. Despite the large density ratio, the spurious velocity around the interface is not substantial, and is rather insensitive to the examined liquid and gas density and viscosity ratios. The influence of the gravitational force on the droplet shape is also examined through the variations of the Bond number, where the droplet shape migrates from spherical to flattened interface in tandem with the increase of the Bond number. The predicted interfaces under constant Bond number are also validated against measurements with good agreements.