Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.     

A novel probe design to study wetting front kinematics during forced convective quenching

The kinematics of the wetting front, i.e., the loci of the boundary between stable vapor film and the presence of bubbles, during quenching operations largely determines the evolution of the microstructural and displacement fields which, in turn, control the properties of the quenched product. Thus, it is important to develop techniques that allow its precise characterization. To this end, a novel probe design (conical-end cylinder) was coupled with an experimental set-up that guarantees fully developed flow to study wetting front kinematics during forced convective quenching of AISI 304 stainless steel probes in water at 60 °C, flowing at 0.20 and 0.60 m/s. Conventional probes (flat-end cylinder) were also quenched for comparison.The wetting front was not symmetric when flat-end cylindrical probes were quenched, even for fully developed flow and relatively low values of quenchant velocity. Computer simulation of the vorticity field near the probe base (considering an isothermal system at ambient temperature) showed that there is a significant vorticity gradient in that region which may favour the chaotic collapse of the vapor film. In contrast, a similar calculation did not show any noticeable vorticity gradient for the conical-end cylindrical probe even at high quenchant velocities. The conical-end cylindrical probe and a fully developed flow ensured that the vapor film collapsed uniformly around the probe due to the fact that the formation of the wetting front was concentrated, initially, at the probe tip. This condition permits a constant advance of the wetting front and a stable transition between boiling regimes, facilitating the study of the kinematics of the wetting front.For the experimental conditions studied the following parameters were derived: (1) wetting front velocity, (2) nucleate boiling length, (3) duration of the nucleate boiling stage and (4) width of the vapor film. The duration of the nucleate boiling stage could be estimated using existing equations, obtaining results that are comparable to the experimentally determined values.For the experimental conditions studied the different boiling regimes and its transitions could be precisely defined along the surface heat flux history curve during quenching, resulting in six different zones.     

On dual-grid level-set method for contact line modeling during impact of a droplet on hydrophobic and superhydrophobic surfaces

In this paper, a numerical methodology for modeling contact line motion in a dual-grid level-set method (DGLSM) – solved on a uniform grid for interface which is twice that for the flow equations – is presented. A quasi-dynamic contact angle model – based on experimental inputs – is implemented to model the dynamic wetting of a droplet, impacting on a hydrophobic or a superhydrophobic surface. High-speed visualization experiments are also presented for the impact of a water droplet on hydrophobic surfaces, with non-bouncing at smaller and bouncing at larger impact velocity. The experimental results for temporal variation of the droplet shapes, wetted-diameter and maximum height of the droplet match very well with the DGLSM based numerical results. The validation of the numerical results is also presented with already published experimental results, for the non-bouncing on a hydrophobic and bouncing on a superhydrophobic surface, at a constant impact velocity. Finally, a qualitative as well as quantitative performance of the DGLSM as compared to the traditional level set method (LSM) is presented by considering our experimental results. The accuracy of the partially refined DGLSM is close to that of the fine-grid based LSM, at a computation cost which is close to that of the coarse-grid based LSM. The DGLSM is demonstrated as an improved LSM for the computational multi-fluid dynamics (CMFD) simulations involving contact line motion.     

梯度润湿表面上液滴定向迁移及合并行为的格子Boltzmann模拟

采用改进的格子Boltzmann方法，对梯度润湿性表面上液滴的定向迁移及合并行为进行了数值模拟，该模型在精度和稳定性上都有很大改善，同时，研究了梯度润湿性表面上液滴定向迁移和合并的动力学特性，并对液滴尺寸及润湿梯度对液滴动力学特性的影响规律进行了分析。数值结果表明，液滴在梯度润湿性表面运动时会发生形变，且动态接触角逐渐减小。润湿梯度对液滴定向迁移行为有显著影响，润湿梯度越大，液滴左右侧接触线位移越大，润湿长度增加越快。但是液滴尺寸对接触线位移影响较小。润湿梯度对液桥宽度基本无影响，但对液滴初始合并时间有显著影响。     

离散型织构表面液滴的铺展及其接触线的力学特性分析

针对离散型织构表面上液滴的铺展过程,采用数值模拟和润湿性实验相结合的方法,引入织构润湿因子θ*,得到了不同类型的离散型织构对固体表面润湿性的影响,在此基础之上分析了液滴铺展过程中接触线的力学特性,以期从微观界面力学的角度解释微织构对液滴铺展过程的促进作用.研究表明:离散型织构增大了液滴铺展过程中的固-液接触面积,位于铺展前沿的液体分子部分浸润织构内部,导致液面曲率和液滴内部的拉普拉斯压力增大,相邻离散型织构间的液体获得了额外的驱动力和能量,铺展速度加快,平衡接触角减小;槽状离散型织构对表面润湿性的影响程度最大,液滴在其上铺展过程具有各向异性特性.另外数值仿真分析表明,接触线的钉扎效应与固体表面粗糙度的大小和微织构类型密切相关,表面粗糙度越大,钉扎效应越明显,其中槽状织构对接触线的钉扎作用还具有方向性.      

Numerical simulation of bubble formation on orifice plates with a moving contact line

The formation of bubbles on an orifice plate involves a moving contact line, especially in case of poor wetting conditions. The dynamics of the moving contact line and contact angle have a significant impact on the bubble departure size. Therefore, for the numerical simulation, an appropriate contact line boundary condition is essential for a correct prediction of the bubble formation. Numerical tests have been performed on two kinds of contact line models, one is a contact line velocity dependent model (Model-A, a commonly used model) and the other is a stick-slip model (Model-B). The calculation results using Model-A depend greatly on the prescribed maximum contact line velocity. With Model-B a parameter-independent prediction can be obtained provided that the mesh is sufficiently fine. The dynamic advancing and receding contact angles, which are two required inputs to both models, have a significant influence on the predicted bubble departure diameter, if the contact line moves beyond the inner rim of the orifice. The effect of wettability on the bubble departure size is realized via the variation of the maximum contact diameter. When the contact line sticks to a small region near the inner rim of the orifice, such as the bubble formation on a thin-walled nozzle, the effects of the contact angle and contact line models are negligible.     

表面微织构对球盘点接触润滑摩擦性能的影响

基于统一Reynolds方程系统模型开展了富油点接触工况下微织构表面润滑摩擦性能的数值模拟研究.在通过实验标定数值模拟中润滑剂流变参数的基础上,系统分析了微织构表面摩擦系数周期变化的全过程,初步揭示了微织构的减摩机理.结果表明：数值模拟结果与实验结果有较好的吻合;瞬时摩擦系数达到最小值时,微坑单元一般处于名义Hertz接触区域的前边界;当微坑运动到Hertz接触区域内时,微坑前沿局部膜厚减小,而微坑后边沿膜厚局部增大,形成局部膜厚增大区;局部膜厚增大区的大小对微织构的润滑摩擦性能有较大影响,其面积越大,减摩效果越好.     

Elastoplastic contact of rough surfaces: a line contact model for boundary regime of lubrication

This paper introduces an improved friction model accounting for elastoplastic behavior of interacting asperities along contiguous rough surfaces for a line contact solution. It is based on Greenwood and Tripp’s original boundary friction model and specifically tailored for a boundary regime of lubrication. The numerical solution of Reynolds’ equation is achieved by implementing Elrod’s cavitation algorithm for a one dimensional line contact. The transience in the numerical solution is retained by accounting for the squeeze film term in Reynolds’ equation under fixed loading conditions and varying sliding motion. A sliding bearing rig is used to measure friction and compare the results with the prediction made using the approach highlighted above. The numerical/experimental results show good agreement.     

Interaction of a Wetting Front with an Impervious Wall – a New Superposition Method for the Boussinesq Equation

The interaction of the wetting front, described by the Boussinesq equation, with an impervious wall is considered using a superposition principle. A number of approximate solutions are compared with the numerical solution of the Boussinesq equation. The results show that the superposition approach provides an excellent method for obtaining an approximate solution.     

Delamination of an elastic film from an elastic–plastic substrate during adhesive contact loading and unloading

Adhesive contact between a rigid sphere and an elastic film on an elastic–perfectly plastic substrate was examined in the context of finite element simulation results. Surface adhesion was modeled by nonlinear springs obeying a force-displacement relationship governed by the Lennard–Jones potential. A bilinear cohesive zone law with prescribed cohesive strength and work of adhesion was used to simulate crack initiation and growth at the film/substrate interface. It is shown that the unloading response consists of five sequential stages: elastic recovery, interface damage (crack) initiation, damage evolution (delamination), film elastic bending, and abrupt surface separation (jump-out), with plastic deformation in the substrate occurring only during damage initiation. Substrate plasticity produces partial closure of the cohesive zone upon full unloading (jump-out), residual tensile stresses at the front of the crack tip, and irreversible downward bending of the elastic film. Finite element simulations illustrate the effects of minimum surface separation (i.e., maximum compressive surface force), work of adhesion and cohesive strength of the film/substrate interface, substrate yield strength, and initial crack size on the evolution of the surface force, residual deflection of the elastic film, film-substrate separation (debonding), crack-tip opening displacement, and contact instabilities (jump-in and jump-out) during a full load–unload cycle. The results of this study provide insight into the interdependence of contact instabilities and interfacial damage (cracking) encountered in layered media during adhesive contact loading and unloading.     

Theory of ice-skating

Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect).     

Recent progress in the moving contact line problem: a review

As pointed out long ago by Laplace, viscosity may become a large perturbation to capillary phenomena, especially close to solid surfaces where molecules may stick. A spectacular consequence of this is the impossibility for a triple line to move on a solid if the liquid/vapor interface is considered as a material surface and if the usual no slip boundary condition is enforced. As shown recently this specific phenomenon of contact line motion can be described by coupled van der Waals and fluid equations, yielding a rational theory that is divergence free and consistent with the equilibrium results. Far from the triple line, the equations of fluid mechanics are recovered in their usual form. In this approach, the contact line move close to the solid by evaporation or condensation, which requires (for evaporation) the molecules to jump above a high potential barrier on their way from the liquid to the vapor. An Arrhenius factor makes this process intrinsically slow, compared to molecular speeds. For (realistic) very small Arrhenius factors, the motion of the triple line induces a dynamical change of the functions in the van der Waals equations. This may lead to dynamical wetting and dewetting transitions, that is, to a change of the contact angle from a finite to a zero value or conversely. The dynamical wetting transition has been observed in liquids flowing down a plate (see Blake and Ruschak, Nature 282 (1979) 489–491) cusps on the contact line appear when it recedes faster than the speed of transition. Similar ideas account well also for the known sensitivity of contact line mobility to vapor pressure. To cite this article: Y. Pomeau, C. R. Mecanique 330 (2002) 207–222.     

Comparative study of two lattice Boltzmann multiphase models for simulating wetting phenomena: implementing static contact angles based on the geometric formulation

Wetting phenomena are widespread in nature and industrial applications. In general, systems concerning wetting phenomena are typical multicomponent/multiphase complex fluid systems. Simulating the behavior of such systems is important to both scientific research and practical applications. It is challenging due to the complexity of the phenomena and difficulties in choosing an appropriate numerical method. To provide some detailed guidelines for selecting a suitable multiphase lattice Boltzmann model, two kinds of lattice Boltzmann multiphase models, the modified S-C model and the H-C-Z model, are used in this paper to investigate the static contact angle on solid surfaces with different wettability combined with the geometric formulation (Ding, H. and Spelt, P. D. M. Wetting condition in diffuse interface simulations of contact line motion. Physical Review E, 75(4), 046708 (2007)). The specific characteristics and computational performance of these two lattice Boltzmann method (LBM) multiphase models are analyzed including relationship between surface tension and the control parameters, the achievable range of the static contact angle, the maximum magnitude of the spurious currents (MMSC), and most importantly, the convergence rate of the two models on simulating the static contact angle. The results show that a wide range of static contact angles from wetting to non-wetting can be realized for both models. MMSC mainly depends on the surface tension. With the numerical parameters used in this work, the maximum magnitudes of the spurious currents of the two models are on the same order of magnitude. MMSC of the S-C model is universally larger than that of the H-C-Z model. The convergence rate of the S-C model is much faster than that of the H-C-Z model. The major foci in this work are the frequently-omitted important details in simulating wetting phenomena. Thus, the major findings in this work can provide suggestions for simulating wetting phenomena with LBM multiphase models along with the geometric formulation.     

The wetting problem of fluids on solid surfaces. Part 2: the contact angle hysteresis

In part 1 (Gouin, [13]), we proposed a model of dynamics of wetting for slow movements near a contact line formed at the interface of two immiscible fluids and a solid when viscous dissipation remains bounded. The contact line is not a material line and a Young-Dupré equation for the apparent dynamic contact angle taking into account the line celerity was proposed. In this paper we consider a form of the interfacial energy of a solid surface in which many small oscillations are superposed on a slowly varying function. For a capillary tube, a scaling analysis of the microscopic law associated with the Young-Dupré dynamic equation yields a macroscopic equation for the motion of the contact line. The value of the deduced apparent dynamic contact angle yields for the average response of the line motion a phenomenon akin to the stick-slip motion of the contact line on the solid wall. The contact angle hysteresis phenomenon and the modelling of experimentally well-known results expressing the dependence of the apparent dynamic contact angle on the celerity of the line are obtained. Furthermore, a qualitative explanation of the maximum speed of wetting (and dewetting) can be given.Received: 5 June 2001, Accepted: 24 May 2003, Published online: 29 July 2003PACS: 02.90, 47.50, 66.20, 68.03, 68.08     

Capillary effects on a particle rolling on a plane surface in the presence of a thin liquid film

An experimental study has been performed of the effects of a liquid film on a particle rolling on a planar surface using a combination of laser-induced fluorescence and particle-image velocimetry. Contact angle hysteresis leads to asymmetry of the liquid meniscus, resulting in a difference in contact angle between the front and rear sections of the meniscus relative to the rolling particle. This asymmetry results in a capillary torque that resists the rolling motion of the particle. The particle rolling motion also induces a viscous transport of fluid from the front to the rear of the particle, which acts to shift the location of the contact point. The laser-induced fluorescence method is used to characterize the meniscus asymmetry and the resulting change in contact angle on the two sides of the particle. Particle-image velocimetry in various horizontal and vertical cross-sectional planes is used to examine the flow trajectories and velocity magnitude within the meniscus in the presence of rolling. All experiments are conducted at small capillary number, so that the meniscus is approximately circular in shape.     

Finite element framework for describing dynamic wetting phenomena

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid–fluid free surface and a liquid–solid interface, with the three‐phase contact line moving across the solid, is considered. For this class of flows, different finite element method (FEM) implementations have been used in the literature, and in some cases, these produced apparently contradictory results. In the present paper, a robust framework for the FEM simulation of dynamic wetting flows is developed, which, by consistently adhering to the FEM methodology, leaves no room for ad hoc ‘optional’ variations in the numerical handling of these flows. The developed approach makes it possible to conduct a convergence study, assess the spatial resolution required to achieve a preset accuracy and provide the corresponding benchmark calculations. This analysis allows one to identify numerical artefacts, which had previously been interpreted as physical effects, and demonstrates that suppressing numerical errors using a ‘strong’ implementation of a boundary condition creates bigger and less detectable errors elsewhere in the computational domain. We provide practical recommendations on the spatial resolution required by a numerical scheme for a given set of non‐dimensional similarity parameters and give a user‐friendly step‐by‐step guide specifying the entire implementation, which allows the reader to easily reproduce all presented results including the benchmark calculations. It is also shown how the developed framework accommodates generalizations of the mathematical model accounting for additional physical effects, such as gradients in surface tensions. Copyright © 2011 John Wiley & Sons, Ltd.     

Three-Phase Effective Contact Angle in a Model Pore

We consider a model pore (2D) in which a sharp interface between two fluids contact a third fluid which wets the solid boundary. If the configuration is capillary dominated, the geometry can be determined analytically in terms of the effective contact angle. This angle depends not only on the interfacial tensions, but also on the capillary pressures. However, if the height of the cusp formed by the wetting fluid is much smaller than the pore width, the effective contact angle is a simple function of the interfacial tensions. It turns out to be the same function as in the case of an undeformed wetting layer of molecular thickness. The analytical expression for the effective contact angle has been confirmed by a numerical technique, known as the lattice-Boltzmann method. This method, in turn, has been validated with Neumann's law for the three-phase contact angles.     

Practice of vehicle soiling investigations: A review

Recent progress concerning experimental and numerical methods for practical investigations of vehicle soiling are reviewed in this paper. Wind tunnel tests and available measurement techniques are analyzed and compared with respect to their possible applications and to the results they may deliver. Different computational models for liquid films generated by spray impingement on vehicle surfaces are then considered. Models relying either on a dispersed or on a continuous approach are compared, resulting advantages and shortcomings are discussed. It is finally shown that, in spite of considerable progress during the last years, substantial work remains to be done in order to capture the complexity of real film flow dynamics for an accurate representation of wetting processes, film separation and break-up interacting with turbulent flows.