Wetting Boundary Research Articles

Stress-constrained level set topology optimization for design-dependent pressure load problems

This work presents a level set framework to solve topology optimization problems subject to local stress constraints considering design-dependent pressure loads. Two technical difficulties are related to this problem. The first one is the local nature of stresses. To deal with this issue, stress constraints are included to the problem by means of an Augmented Lagrangian scheme. The second is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction–diffusion equation substitutes the classical Hamilton–Jacobi equation to control the level set evolution. This choice has the advantage of allowing the nucleation of holes inside the domain and the elimination of the undesirable level set reinitializations. In addition, the optimization algorithm allows the rupture of loading boundaries, that is, the crossing of the pressured (wet) boundary with the traction free boundary is not avoided. This gives more freedom to the algorithm for topological changes. In order to validate the proposed scheme against stress concentrations, all numerical examples are performed on constrained domains containing singularities. Moreover, optimized designs obtained from stress-constrained and compliance problems are compared.

Droplets Tracing in a T-junction Microchannel

Emulsions consist of small liquid droplets immersed in another liquid, typically either a mix of oil in water or water in oil. Emulsions have wide applications in the production of pharmaceutical products, food and cosmetics. The properties and quality of an emulsion typically depend on the size and the distribution of the droplets. Thus, the objective of this study was to investigate in detail the formation and behaviour of droplets in a T-junction microchannel. By setting up a model and applying a laminar two-phase flow in ANSYS© simulation, the particle droplets distribution was observed. The model used the predefined wetted wall boundary condition at the solid walls, with a contact angle of 135°. In this study, the behaviour and flow pattern of the particles along the T-junction microchannel were observed with regard to the effect of the initial particle concentration, the flow rate of the particles, and the initial velocity feed through the inlets of the microchannel. From the results, the effects of the velocity, mixing time and flow rate of the particles on the particle distribution and mixing were studied. It was shown that the optimization process was achieved at a flow rate of 0.025 mL/s, with the mixing process occurring within 1.6 seconds and the velocity feed at the two inlets being VA = 0.02 m/s and VB = 0.04 m/s, where the particles experienced less lift shear and compressive forces near the outlet, which caused the mixing process to become efficient.

Direct Numerical Simulation of Flow on Pore-Scale Images Using the Phase-Field Method

SummaryAdvances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible. In this paper, we describe a two-phase-flow simulator that solves mass- and momentum-balance equations valid at the pore scale (i.e., at scales where the Darcy velocity homogenization starts to break down). The simulator is one of the key components of a molecule-to-reservoir truly multiscale modeling work flow.A Helmholtz free-energy-driven, thermodynamically based diffuse-interface/phase-field method is used for the effective simulation of numerous advecting interfaces, while honoring the interfacial tension (IFT). The advective Cahn-Hilliard (CH) (mass-balance, energy dissipation) and Navier-Stokes (NS) (momentum-balance, incompressibility) equations are coupled to each other within the phase-field framework. Wettability on rock/fluid interfaces is accounted for by means of an energy-penalty-based wetting (contact-angle) boundary condition. Individual balance equations are discretized by use of a flexible discontinuous Galerkin (DG) method. The discretization of the mass-balance equation is semi-implicit in time using a convex/concave splitting of the energy term. The momentum-balance equation is split from the incompressibility constraint by a projection method and linearized with a Picard splitting. Mass- and momentum-balance equations are coupled to each other by means of operator splitting, and are solved sequentially.We discuss the mathematical model and its DG discretization, and briefly introduce nonlinear and linear solution strategies. Numerical-validation tests show optimal convergence rates for the DG discretization, indicating the correctness of the numerical scheme and its implementation. Physical-validation tests demonstrate the consistency of the phase distribution and velocity fields simulated within our framework. Finally, two-phase-flow simulations on two real pore-scale images demonstrate the usefulness of the pore-scale simulator. The direct pore-scale numerical-simulation methodology rigorously considers the flow physics by directly acting on pore-scale images of rocks without remeshing. The proposed method is accurate, numerically robust, and exhibits the potential for tackling realistic problems.

Level set topology optimization for design‐dependent pressure load problems

SummaryThis work presents a level set framework to solve the compliance topology optimization problem considering design‐dependent pressure loads. One of the major technical difficulties related to this class of problem is the adequate association between the moving boundary and the pressure acting on it. This difficulty is easily overcome by the level set method that allows for a clear tracking of the boundary along the optimization process. In the present approach, a reaction‐diffusion equation substitutes the classical Hamilton‐Jacobi equation to control the level set evolution. This choice has the advantages of allowing the nucleation of holes inside the domain and the elimination of the undesirable reinitialization steps. Moreover, the proposed algorithm allows merging pressurized (wet) boundaries with traction‐free boundaries during level set movements. This last property, allied to the simplicity of the level set representation and successful combination with the reaction‐diffusion based evolution applied to a design‐dependent pressure load problem, represents the main contribution of this paper. Numerical examples provide successful results, many of which comparable with others found in the literature and solved with different techniques.

Wetting boundary condition for the color-gradient lattice Boltzmann method: Validation with analytical and experimental data

Abstract In the color gradient lattice Boltzmann model (CG-LBM), a fictitious-density wetting boundary condition has been widely used because of its ease of implementation. However, as we show, this may lead to inaccurate results in some cases. In this paper, a new scheme for the wetting boundary condition is proposed which can handle complicated 3D geometries. The validity of our method for static problems is demonstrated by comparing the simulated results to analytical solutions in 2D and 3D geometries with curved boundaries. Then, capillary rise simulations are performed to study dynamic problems where the three-phase contact line moves. The results are compared to experimental results in the literature (Heshmati and Piri, 2014). If a constant contact angle is assumed, the simulations agree with the analytical solution based on the Lucas–Washburn equation. However, to match the experiments, we need to implement a dynamic contact angle that varies with the flow rate.

Adhesives and Adhesion Technologies: A Critical Review

The article critically reviews about adhesives and their various adhesion phenomenons along with their categorization and functions. Benefit and drawbacks of adhesives joining was explained. Requirements for excellent bonding which includes, appropriate selection of adhesive, superior design for joining, surface cleansing, wetting were defined. The review clearly indicates the various theories involved in adhesion are namely mechanical interlocking, electrostatic, diffusion, wetting, chemical bonding, and weak boundary layer. Bond failure modes and their mechanism were elaborated briefly.

Color-gradient lattice Boltzmann modeling of immiscible two-phase flows on partially wetting surfaces

A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

Modelling the influence of velocity on wet friction-element friction in clutches

PurposeThis study aims to establish a friction coefficient model relative to the rotation speed of a wet clutch engagement, which can predict friction coefficient under different stages of slipping velocity and different load pressures. In particular, the model has been improved by accounting the speed effect for the perdition of wet friction-element boundary friction, which is significant for understanding the friction mechanisms and for supporting the development of more efficient and related products.Design/methodology/approachThis research investigated the mechanism of wet friction in a wet clutch engagement. A mixed friction model is established based on the asperity model and Newton’s law of viscosity. To obtain a friction coefficient computed by the model, the normal load shared by both asperities and lubrication fluid needs to be determined. Therefore, rough surface contact mechanism is analysed; a surface topography model is established; and surface parameters are obtained by means of surface topography measurement and reconstruction. Finally, verification of the mixed friction model is achieved.FindingsFriction will be generated by both the asperity contact and the lubrication film shear relative to the rotation speed. And, the higher the relative speed, the larger the shearing power of lubrication film. It is caused by decrease in contact area of asperity. Surface morphology of a sintered bronze friction disk was obtained by a Laser-Micro-Test. The predicted results by the established model show that the total friction coefficient slightly reduced and then increased suddenly with speed. The surface topography model is responsible for the nonlinear behaviour of the asperity friction. Results of the simulation model are in agreement with those of the wet clutch engagement experiments.Originality/valueThis research is original and it is supported by the national defence project. The wet friction element which is applied on tracked vehicles is analysed for the first time. Through the model, the trend of the friction coefficient can be more accurately predicted. The problem of the wet friction plate modelling difficult is solved by using the mixed friction model.

Smoothed profile-lattice Boltzmann method for non-penetration and wetting boundary conditions in two and three dimensions

In this study, the smoothed profile-lattice Boltzmann method (SP-LBM) is proposed to determine the contact line dynamics on a hydrophobic or a hydrophilic curved wall. Two types of smoothed indicator functions are introduced, namely a function that identifies the solid domain for non-slip and non-penetration conditions and a function that denotes the boundary layer for no mass-flux and the wetting boundary conditions. In order to prevent fluid penetration into the solid boundary, the fluid-solid interaction force is computed based on the definition of the fluid velocity as proposed by Guo et al. [1]. In order to implement the Neumann boundary conditions for the order parameter and the chemical potential, the fluxes from the solid surfaces are distributed to relevant physical valuables through a smoothed profile. Several two-dimensional and three-dimensional numerical investigations including those determining the Couette flows, flow around a circular cylinder, transition layer on a wetting boundary, and dynamic behavior of a droplet on a flat or curved plate demonstrate the efficiency of the present method in calculating the contact angle of a droplet on curved surfaces with wall impermeability. The present model provides a simple algorithm to compute the surface normal vector and contact line dynamics on an arbitrarily shaped boundary by using a smoothed-profile.

Numerical modeling of the tidal wave run-up and the eelgrass habitat at the Laizhou Bay

In this paper, a modern lattice Boltzmann method is used to study the change of hydrodynamics and environmental factors of the intertidal zone in the Laizhou Bay between 1989 and 2013. In order to simulate the change of the shorelines caused by the tidal wave run-up, we use a high-order dry–wet boundary condition based on lattice Boltzmann model for shallow water equations. The hydrodynamic conditions including the intertidal area and the water depth on the eelgrass habitat are evaluated. As a result, the relationship among the reclamation area, the flow fields and the loss of intertidal wetland between 1989 and 2013 was established respectively. According to the interaction between the eelgrass in the intertidal zone and the hydrodynamic conditions, the area suitable for eelgrass growth will be revealed, which will provide scientific basis for wetland protection and theoretical support to marine ecological environment restoration.

Connections, Transactions and Rock Art within and beyond the Wet Tropics of North Queensland

This paper explores past connections of Aboriginal people within what is now known as the Wet Tropics, a coastal strip of tropical rainforest in northeast Australia. As a result of historical and ethnographic descriptions the rainforest is often defined as a ‘cultural zone’. The proclamation of the Wet Tropics World Heritage Area, based on environmental parameters, has exaggerated the idea of the rainforest as a cultural boundary. We propose that in the past, Aboriginal connections were multifaceted, multifunctional and multidirectional, extending beyond the Wet Tropics boundaries. We use rock art to illustrate connections within and beyond the rainforest. For example, decorated shields, an iconic item of rainforest material culture, are depicted in rock art assemblages south of the rainforest boundary. Are the shield paintings out-of-place or do they illustrate networks of connection? We examine rock art motifs found in rainforest areas and compare them with those found in other rock art regions in North Queensland. We identify, for example, that sites located in the eastern rainforest are dominated by painted anthropomorphs (people) and zoomorphs (animals) in the silhouette style similar to figurative rock art of southeast Cape York Peninsula. We suggest that, like other areas, there were connections between cultural groups within the rainforest but that these same groups had links that went beyond this environmental zone. We further propose that the proclamation of the Wet Tropics World Heritage Area has particularly influenced non-Aboriginal understandings of the past within this region.

An efficient threshold dynamics method for wetting on rough surfaces

The threshold dynamics method developed by Merriman, Bence and Osher (MBO) is an efficient method for simulating the motion by mean curvature flow when the interface is away from the solid boundary. Direct generalization of MBO-type methods to the wetting problem with interfaces intersecting the solid boundary is not easy because solving the heat equation in a general domain with a wetting boundary condition is not as efficient as it is with the original MBO method. The dynamics of the contact point also follows a different law compared with the dynamics of the interface away from the boundary. In this paper, we develop an efficient volume preserving threshold dynamics method for simulating wetting on rough surfaces. This method is based on minimization of the weighted surface area functional over an extended domain that includes the solid phase. The method is simple, stable with O(Nlog⁡N) complexity per time step and is not sensitive to the inhomogeneity or roughness of the solid boundary.

A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition

Advances in pore-scale imaging (e.g., μ-CT scanning), increasing availability of computational resources, and recent developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multi-phase flow on pore structures feasible. Quasi-static methods, where the viscous and the capillary limit are iterated sequentially, fall short in rigorously capturing crucial flow phenomena at the pore scale. Direct simulation techniques are needed that account for the full coupling between capillary and viscous flow phenomena. Consequently, there is a strong demand for robust and effective numerical methods that can deliver high-accuracy, high-resolution solutions of pore-scale flow in a computationally efficient manner. Direct simulations of pore-scale flow on imaged volumes can yield important insights about physical phenomena taking place during multi-phase, multi-component displacements. Such simulations can be utilized for optimizing various enhanced oil recovery (EOR) schemes and permit the computation of effective properties for Darcy-scale multi-phase flows.

An improvement of the Ts-NDVI space drought monitoring method and its applications in the Mongolian plateau with MODIS, 2000–2012

Surface soil moisture is a key variable to describe water and energy exchanges at the surface/atm interface and measure drought and aridification. The Ts-NDVI space is an effective method to monitor regional surface soil moisture status. Due to the disturbance of multiple factors, the established dry or wet boundary with monotemporal remote sensing data is unstable. This paper developed a Ts-NDVI triangle space with MODIS NDVI dataset to monitor soil moisture in the Mongolian Plateau in 2000–2012. Based on the temperature vegetation dryness index (TVDI), the spatiotemporal variations of drought were studied. The results indicated that (1) the general Ts-NDVI space method is an effective way to monitor regional soil moisture. However, if the single time space shows perfect structure, there would be no differences between the inverted results of the single time space and the general space. (2) The TVDI calculated in the paper is expected to show the water deficit for the region from low (bare soil) to high (full vegetation cover) NDVI values, and it is found to be in close negative agreement with precipitation and soil moisture; changes in the TVDI are dependent on the water status in the study area. (3) In the Mongolian Plateau, TVDI presented a zonal distribution with changes in Land Use/Land Cover types, vegetation cover, and latitude. Drought was serious in bare land, construction land, and grassland. Drought was widely spread throughout the Mongolian Plateau, and there was aridification in the study period. Vegetation degradation, overgrazing, and climate warming could be considered as the main reasons.

Development, testing and application of DrainFlow: A fully distributed integrated surface-subsurface flow model for drainage study

Hydrological and hydrogeological investigation of drained land is a complex and integrated procedure. The scale of drainage studies may vary from a high-resolution small scale project through to comprehensive catchment or regional scale investigations. This wide range of scales and integrated system behaviour poses a significant challenge for the development of suitable drainage models. Toward meeting these requirements, a fully distributed coupled surface-subsurface flow model titled DrainFlow has been developed and is described. DrainFlow includes both the diffusive wave equation for surface flow components (overland flow, open drain, tile drain) and Richard's equation for saturated/unsaturated zones. To overcome the non-linearity problem created from switching between wet and dry boundaries, a smooth transitioning technique is introduced to buffer the model at tile drains and at interfaces between surface and subsurface flow boundaries. This gives a continuous transition between Dirichlet and Neumann boundary conditions. DrainFlow is tested against five well-known integrated surface-subsurface flow benchmarks. DrainFlow as applied to some synthetic drainage study examples is quite flexible for changing all or part of the model dimensions as required by problem complexity, problem scale, and data availability. This flexibility enables DrainFlow to be modified to allow for changes in both scale and boundary conditions, as often encountered in real-world drainage studies. Compared to existing drainage models, DrainFlow has the advantage of estimating actual infiltration directly from the partial differential form of Richard's equation rather than through analytical or empirical infiltration approaches like the Green and Ampt equation.

Three-dimensional lattice Boltzmann simulations of microdroplets including contact angle hysteresis on topologically structured surfaces

In this study, the dynamical behavior of a droplet on topologically structured surface is investigated by using a three-dimensional color-gradient lattice Boltzmann model. A wetting boundary condition is proposed to model fluid-surface interactions, which is advantageous to improve the accuracy of the simulation and suppress spurious velocities at the contact line. The model is validated by the droplet partial wetting test and reproduction of the Cassie and Wenzel states. A series of simulations are conducted to investigate the behavior of a droplet when subjected to a shear flow. It is found that in Cassie state, the droplet undergoes a transition from stationary, to slipping and finally to detachment states as the capillary number increases, while in Wenzel state, the last state changes to the breakup state. The critical capillary number, above which the droplet slipping occurs, is small for the Cassie droplet, but is significantly enhanced for the Wenzel droplet due to the increased contact angle hysteresis. In Cassie state, the receding contact angle nearly equals the prediction by the Cassie relation, and the advancing contact angle is close to 180°, leading to a small contact angle hysteresis. In Wenzel state, however, the contact angle hysteresis is extremely large (around 100°). Finally, high droplet mobility can be easily achieved for Cassie droplets, whereas in Wenzel state, extremely low droplet mobility is identified.

Partial wetting boundary conditions on micro-structure surface for Lattice Boltzmann method

Abstract Three-dimensional liquid droplet resting on the square pillar-structure surface is simulated by a lattice Boltzmann model combined with partial wetting boundary condition. Simulations are applied to two geometric setups at the Cassie–Baxter state. Different discretization schemes to calculate the wall order parameter gradient on the faces, edges and corner of the pillar are investigated to examine their influences on the capability to predict the enhanced hydrophobicity on the droplet. Discretization of wall derivatives along the edge and corner of the pillar, which accounts for the wall normal direction, produces results closer to the measured values. In strong contrast, the enhanced hydrophobicity is underpredicted if the wall normal derivative is not discretized correctly. Both predictions and measured values indicate that pillar height shows slight dependence on apparent contact angles. Also, apparent contact angle of Cassie–Baxter theory is pillar height independent and it also overpredicts the hydrophobicity. This can be attributed partly to the present investigated structure, which is close to the threshold surface roughness.

Relaxation Rates for a Perturbation of a Stationary Solution to the Thin-Film Equation

In this work we study the stability of a stationary solution to the thin-film equation with linear mobility and partial wetting boundary conditions. The method used is strongly based on the gradient-flow structure of the problem. We obtain natural relaxation rates of perturbations to the stationary solution by showing that the energy is in fact convex in a neighborhood around the stationary solution.

Computational study of bouncing and non-bouncing droplets impacting on superhydrophobic surfaces

We numerically investigate bouncing and non-bouncing of droplets during isothermal impact on superhydrophobic surfaces. An in-house, experimentally-validated, finite-element method based computational model is employed to simulate the droplet impact dynamics and transient fluid flow within the droplet. The liquid-gas interface is tracked accurately in Lagrangian framework with dynamic wetting boundary condition at three-phase contact line. The interplay of kinetic, surface and gravitational energies is investigated via systematic variation of impact velocity and equilibrium contact angle. The numerical simulations demonstrate that the droplet bounces off the surface if the total droplet energy at the instance of maximum recoiling exceeds the initial surface and gravitational energy, otherwise not. The non-bouncing droplet is characterized by the oscillations on the free surface due to competition between the kinetic and surface energy. The droplet dimensions and shapes obtained at different times by the simulations are compared with the respective measurements available in the literature. Comparisons show good agreement of numerical data with measurements and the computational model is able to reconstruct the bouncing and non-bouncing of the droplet as seen in the measurements. The simulated internal flow helps to understand the impact dynamics as well as the interplay of the associated energies during the bouncing and non-bouncing.

Reductions in Anisotropic Errors from Implementation of Phase-Field Wetting Boundary Condition for Off-Grid Objects

In simulations of multiphase fluid flow using the phase-field method (PFM), the wetting boundary condition is required for off-grid objects. In this study, we propose an improved implementation of the wetting boundary condition for off-grid objects to reduce anisotropic errors arising from use of a rectangular grid. Our implementation of the phase-field wetting boundary condition conforms to the immersed-boundary formulation of solid–fluid interfaces; therefore, we call the immersed-boundary phase-field implementation (IB-PFI). We performed simulations with and without IB-PFI for (a) droplets adhering to circular objects and (b) capillary flow in a parallel-plate channel. In simulations without IB-PFI, anisotropic errors were induced by off-grid objects, and the results deviated from theoretical predictions. In contrast, simulations with IB-PFI suppressed the anisotropic errors and agreed with the theoretical predictions. Thus, IB-PFI extends the applicability of the PFM to simulations of multiphase fluid flows under numerous geometric conditions.