The diffuse-interface model (DIM) is a tool for studying interfacial dynamics. In particular, it is used for modeling contact lines, i.e., curves where a liquid, gas, and solid are in simultaneous contact. As well as all other models of contact lines, the DIM implies an additional assumption: that the flow near the liquid/gas interface is isothermal. In this work, this assumption is checked for the four fluids for which all common models of contact lines fail. It is shown that, for two of these fluids (including water), the assumption of isothermality does not hold.
In this paper, starting from the Born-Green-Yvon (BGY) equation, we derive a general expression for the contact value of the singlet distribution function near a hard wall for anisotropic fluids. This relation includes two separate contributions. One is connected to the partial bulk pressure relative to a given orientation of the molecules. The second one is connected to the anchoring phenomena and is characterized by the direct interaction between the molecules and the wall. From this relation, we then formulate the contact theorem for the density and the order parameter profiles. The results…
When a Coulombic fluid is confined between two parallel charged plates, an exact relation links the difference of ionic densities at contact with the plates, to the surface charges of these boundaries. It no longer applies when the boundaries are curved, and we work out how it generalizes when the fluid is confined between two concentric spheres (or cylinders), in two and in three space dimensions. The analysis is thus performed within the cell model picture. The generalized contact relation opens the possibility to derive new exact expressions, of particular interest in the regime of strong c…
In immiscible two-phase flows, contact line denotes the intersection of the fluid-fluid interface with the solid wall. When one fluid displaces the other, the contact line moves along the wall. A classical problem in continuum hydrodynamics is the incompatibility between the moving contact line and the no-slip boundary condition, as the latter leads to a non-integrable singularity. The recently discovered generalized Navier boundary condition (GNBC) offers an alternative to the no-slip boundary condition which can resolve the moving contact line conundrum. We present a variational derivation o…
We present a simple analytical model and an exact numerical study which explain the role of roughness on different length scales for the fluid contact angle on rough solid surfaces. We show that there is no simple relation between the distribution of surface slopes and the fluid contact angle. In particular, surfaces with the same distribution of slopes may exhibit very different contact angles depending on the range of length-scales over which the surfaces have roughness.
The dynamic of contact formation between soft materials immersed in a fluid is accompanied by fluid drainage and elastic deformation. As a result, controlling the coupling between lubrication pressure and elasticity provides strategies to design materials with reversible and dynamic adhesion to wet or flooded surfaces. We characterize the elastic deformation of a soft coating with nanometer-scale roughness as it approaches and contacts a rigid surface in a fluid environment. The lubrication pressure during the approach causes elastic deformation and prevents contact formation. We observe defor…
We reconcile two scaling laws that have been proposed in the literature for the slip length associated with a moving contact line in diffuse interface models, by demonstrating each to apply in a different regime of the ratio of the microscopic interfacial width $l$ and the macroscopic diffusive length $l_D= (Mη)^{1/2}$, where $η$ is the fluid viscosity and $M$ the mobility governing intermolecular diffusion. For small $l_D/l$ we find a diffuse interface regime in which the slip length scales as $ξ\sim(l_Dl)^{1/2}$. For larger $l_D/l>1$ we find a sharp interface regime in which the slip length …
We present an extension of the multiparticle collision dynamics method for flows with complex interfaces, including supramolecular near-contact interactions mimicking the effect of surfactants. The new method is demonstrated for the case of (i) short range repulsion of droplets in close contact, (ii) arrested phase separation and (iii) different pattern formation during spinodal decomposition of binary mixtures.
Using molecular-dynamics simulation, we have calculated the interfacial free energy, γ, between a hard-sphere fluid and hard spherical and cylindrical colloidal particles, as functions of the particle radius R and the fluid packing fraction η= ρσ^3/6, where ρand σare the number density and hard-sphere diameter, respectively. These results verify that Hadwiger's theorem from integral geometry, which predicts that γfor a fluid at a surface, with certain restrictions, should be a linear combination of the average mean and Gaussian surface curvatures, is valid within the precision of the calculati…
Transient fluid removal at soft interfaces: Contact-time-controlled squeeze-out in a cylinder-on-flat contact
Peter Grünberg Institute (PGI-1), Forschungszentrum Jülich（于利希研究中心）；State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences（中国科学院兰州化学物理研究所固体润滑国家重点实验室）；MultiscaleConsulting（多尺度咨询公司）
Vapor-liquid menisci of the truncated and shifted Lennard-Jones fluid between parallel planar walls are investigated by molecular dynamics simulation. Thereby, the characteristic energy of the unlike dispersive interaction between fluid molecules and wall atoms is systematically varied to determine its influence on the contact angle. The temperature is varied as well, covering most of the range between the triple point temperature and the critical temperature of the bulk fluid. The transition between obtuse and acute angles is found to occur at a temperature-independent magnitude of the fluid-…
We examine the nanoscale behavior of an equilibrium three-phase contact line in the presence of long-ranged intermolecular forces by employing a statistical mechanics of fluids approach, namely density functional theory (DFT) together with fundamental measure theory (FMT). This enables us to evaluate the predictive quality of effective Hamiltonian models in the vicinity of the contact line. In particular, we compare the results for mean field effective Hamiltonians with disjoining pressures defined through (I) the adsorption isotherm for a planar liquid film, and (II) the normal force balance …
We report molecular dynamics results for the contact values of the radial distribution functions of binary additive mixtures of hard disks. The simulation data are compared with theoretical predictions from expressions proposed by Jenkins and Mancini [J. Appl. Mech. \textbf{54}, 27 (1987)] and Santos et al. [J. Chem. Phys. \textbf{117}, 5785 (2002)]. Both theories agree quantitatively within a very small margin, which renders the former still a very useful and simple tool to work with. The latter (higher-order and self-consistent) theory provides a small qualitative correction for low densitie…
We report on the onset of fluid entrainment when a contact line is forced to advance over a dry solid of arbitrary wettability. We show that entrainment occurs at a critical advancing speed beyond which the balance between capillary, viscous and contact line forces sustaining the shape of the interface is no longer satisfied. Wetting couples to the hydrodynamics by setting both the morphology of the interface at small scales and the viscous friction of the front. We find that the critical deformation that the interface can sustain is controlled by the friction at the contact line and the visco…
Low voltage electrowetting on dielectrics on substrates with thin layer of lubricating fluid to reduce contact angle hysteresis is reported here. On smooth and homogeneous solid surfaces, it is extremely difficult to reduce contact angle hysteresis (contact angle difference between advancing and receding drop volume cycle) and the electrowetting hysteresis (contact angle difference between advancing and receding voltage cycle) below 10°. On the other hand, electrowetting hysteresis on rough surfaces can be relatively large (>30°) therefore they are of no use for most of the fluidic devices. In…
Liquid-liquid wetting failure is investigated in a two-dimensional Couette system with two immiscible fluids of arbitrary viscosity. The problem is solved exactly using a sharp interface treatment of hydrodynamics (lubrication theory) as a function of the capillary number, viscous ratio and separation of scale, i.e. slip length versus macroscopic scale of the system. The existence of critical velocities, above which no stationary solutions are found, is analyzed in detail in terms of the relevant parameters of the system. Comparisons with existing analysis for other geometries are also carried…
We present a new ternary free energy lattice Boltzmann model. The distinguishing feature of our model is that we are able to analytically derive and independently vary all fluid-fluid surface tensions and the solid surface contact angles. We carry out a number of benchmark tests: (i) double emulsions and liquid lenses to validate the surface tensions, (ii) ternary fluids in contact with a square well to compare the contact angles against analytical predictions, and (iii) ternary phase separation to verify that the multicomponent fluid dynamics is accurately captured. Additionally we also descr…
The contact values $g(σ,σ')$ of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution $f(σ)$ are considered. A ``universality'' assumption is introduced, according to which, at a given packing fraction $η$, $g(σ,σ')=G(z(σ,σ'))$, where $G$ is a common function independent of the number of components (either finite or infinite) and $z(σ,σ')=[2 σσ'/(σ+σ')]μ_2/μ_3$ is a dimensionless parameter, $μ_n$ being the $n$-th moment of the diameter distribution. A cubic form proposal for the $z$-dependence of $G$ is made and known exact consistency condition…
The stability of sand castles is determined by the structure of wet granulates. Experimental data about the size distribution of fluid pockets are ambiguous about their origin. We discovered that contact angle hysteresis plays a fundamental role in the equilibrium distribution of bridge volumes, and not geometrical disorder as commonly conjectured, which has substantial consequences on the mechanical properties of wet granular beds, including a history dependent rheology and lowered strength. Our findings are obtained using a novel model where the Laplace pressures, bridge volumes and contact …
We study the nanoscale behaviour of the density of a simple fluid in the vicinity of an equilibrium contact line for a wide range of Young contact angles between 40 and 135 degrees. Cuts of the density profile at various positions along the contact line are presented, unravelling the apparent step-wise increase of the film height profile observed in contour plots of the density. The density profile is employed to compute the normal pressure acting on the substrate along the contact line. We observe that for the full range of contact angles, the maximal normal pressure cannot solely be predicte…
In this paper the effect of pressure on the contact angle of a water drop on superhydrophobic Carbon Nanotube (CNT) forests is studied. Superhydrophobic CNT forests are obtained from a new and simple functionalization strategy, based on the gold-thiol affinity. Using a specifically devised experimental setup, we then show that these surfaces are able to withstand high excess pressures (larger than 10 kPa) without transiting toward a roughness-invaded state, therefore preserving their low adhesion properties. Together with the relatively low technical cost of the process, this robustness versus…
A new first-principles statistical mechanics formulation is proposed to describe slow and dilated granular fluids, where prolonged intergranular contacts vitiate collision theory. The contacts, where all the important physics takes place, are regarded as quasi-particles that can appear and disappear. A contact potential, $ν$, is defined as a measure of the fluctuations and the mean coordination number per particle and its fluctuations are calculated as a function of it. This formulation extends the Edwards statistical mechanics to slow dynamic systems and converges to it when the motion stops.…
We present a new diffuse interface model for the dynamics of inextensible vesicles in a viscous fluid. A new feature of this work is the implementation of the local inextensibility condition in the diffuse interface context. Local inextensibility is enforced by using a local Lagrange multiplier, which provides the necessary tension force at the interface. To solve for the local Lagrange multiplier, we introduce a new equation whose solution essentially provides a harmonic extension of the local Lagrange multiplier off the interface while maintaining the local inextensibility constraint near th…
The dynamic interaction of complex fluid interfaces is highly sensitive to near-contact interactions occurring at the scale of ten of nanometers. Such interactions are difficult to analyse because they couple self-consistently to the dynamic morphology of the evolving interface, as well as to the hydrodynamics of the interstitial fluid film. In this work, we show that, above a given magnitude threshold, near-contact interactions trigger non-trivial micro-vorticity patterns, which in turn affect the effective near-contact interactions, giving rise to persistent fluctuating ripples at the fluid …
Interfacial flows close to a moving contact line are inherently multi-scale. The shape of the interface and the flow at meso- and macroscopic scales inherit an apparent interface slope and a regularization length, both called after Voinov, from the dynamical processes at work at the microscopic level. Here, we solve this inner problem in the case of a volatile fluid at equilibrium with its vapor. The evaporative/condensation flux is then controlled by the dependence of the saturation temperature on interface curvature -- the so-called Kelvin effect. We derive the dependencies of the Voinov ang…
When a fluid surface adheres to a substrate, the location of the contact line adjusts in order to minimize the overall energy. This adhesion balance implies boundary conditions which depend on the characteristic surface deformation energies. We develop a general geometrical framework within which these conditions can be systematically derived. We treat both adhesion to a rigid substrate as well as adhesion between two fluid surfaces, and illustrate our general results for several important Hamiltonians involving both curvature and curvature gradients. Some of these have previously been studied…
Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this a…
Transient fluid removal at soft interfaces: Stationary squeeze-out and dynamic scraping in a block-on-flat contact
Peter Grünberg Institute (PGI-1), Forschungszentrum Jülich（彼得·格林伯格研究所）；State Key Laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences（中国科学院兰州化学物理研究所固体润滑国家重点实验室）；MultiscaleConsulting（多尺度咨询公司）；Sumitomo Rubber Industries, Ltd.（住友橡胶工业株式会社）；Decathlon Footwear industrial community（迪卡侬鞋类产业社区）
The electric double layer structure in an electrolyte close to a solid substrate near the three-phase contact line is approximated by considering the linearized Poisson-Boltzmann equation in a wedge geometry. The mathematical approach complements the semi-analytical solutions reported in the literature by providing easily available characteristic information on the double layer structure. In particular, the model contains a length scale that quantifies the distance from the fluid-fluid interface over which this boundary influences the electric double layer. The analysis is based on an approxim…
In this paper, we aim to investigate the implementation of contact angles in the pseudopotential lattice Boltzmann modeling of wetting at a large density ratio. The pseudopotential lattice Boltzmann model [X. Shan and H. Chen, Phys. Rev. E 49, 2941 (1994)] is a popular mesoscopic model for simulating multiphase flows and interfacial dynamics. In this model, the contact angle is usually realized by a fluid-solid interaction. Two widely used fluid-solid interactions: the density-based interaction and the pseudopotential-based interaction, as well as a modified pseudopotential-based interaction f…
We present a model based on the lattice Boltzmann equation that is suitable for the simulation of dynamic wetting. The model is capable of exhibiting fundamental interfacial phenomena such as weak adsorption of fluid on the solid substrate and the presence of a thin surface film within which a disjoining pressure acts. Dynamics in this surface film, tightly coupled with hydrodynamics in the fluid bulk, determine macroscopic properties of primary interest: the hydrodynamic slip; the equilibrium contact angle; and the static and dynamic hysteresis of the contact angles. The pseudo- potentials em…
We present a thermodynamically consistent model of a ternary fluid interacting with elastic membranes. Following a free-energy modelling approach and taking into account the thermodynamics laws, we derive the equations governing the ternary fluid flow and dynamics of the membranes. We also provide the numerical framework for simulating such fluid-structure interaction problems. It is based on the lattice Boltzmann method, employed for resolving the evolution equations of the ternary fluid in an Eulerian description, coupled to the immersed boundary method, allowing for the membrane equations o…
We model an infinitely long liquid bridge confined between two plates chemically patterned by stripes of same width and different contact angle, where the three-phase contact line runs, on average, perpendicular to the stripes. This allows us to study the corrugation of a contact line in the absence of pinning. We find that, if the spacing between the plates is large compared to the length scale of the surface patterning, the cosine of the macroscopic contact angle corresponds to an average of cosines of the intrinsic angles of the stripes, as predicted by the Cassie equation. If, however, the…
I discuss fluid flow at the interface between solids with anisotropic roughness. I show that for randomly rough surfaces with anisotropic roughness, the contact area percolate at the same relative contact area as for isotropic roughness, and that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out.
From extensive molecular dynamics simulations on immiscible two-phase flows, we find the relative slipping between the fluids and the solid wall everywhere to follow the generalized Navier boundary condition, in which the amount of slipping is proportional to the sum of tangential viscous stress and the uncompensated Young stress. The latter arises from the deviation of the fluid-fluid interface from its static configuration. We give a continuum formulation of the immiscible flow hydrodynamics, comprising the generalized Navier boundary condition, the Navier-Stokes equation, and the Cahn-Hilli…
Elastomers swollen with non-polar fluids show potential as anti-adhesive materials. We study the effect of oil fraction and contact time on the adhesion between swollen spherical probes of PDMS (polydimethylsiloxane) and flat glass surfaces. The PDMS probes are swollen with pre-determined amount of 10 cSt silicone oil to span the range where the PDMS is fluid free (via solvent extraction) up to the limit where it is oil saturated. Probe tack measurements show that adhesion decreases rapidly with an increase in oil fraction. The decrease in adhesion is attributed to excess oil present at the PD…
We characterize the spatiotemporal deformation of an elastic film during the radial drainage of fluid from a narrowing gap. Elastic deformation of the film takes the form of a dimple and prevents full contact to be reached. With thinner elastic film the stress becomes increasingly supported by the underlying rigid substrate and the dimple formation is suppressed, which allows the surfaces to reach full contact. We highlight the lag due to viscoelasticity on the surface profiles, and that for a given fluid film thickness deformation leads to stronger hydrodynamic forces than for rigid surfaces.
