On the Wetting of a Surface by a Very Viscous Fluid

The movement of a small viscous droplet on a flat surface is considered in self-spreading, in roundup, and as a result of an adhesion gradient. Edge conditions based on the dynamic contact angle are discussed within the context of lubrication theory. Tangential slip at the contact line is shown to be small compared to the normal velocity. The shapes of the droplet and its contact line are calculated, and nonlinear and inertial effects assessed.     

A remark on isolated singularities of surfaces with bounded mean curvature: the non-minimizing and non-perpendicular case

The length of the free boundary of twodimensional weak surfaces with bounded mean curvature is studied in the case of non-perpendicular contact angles and for non-minimizing stationary surfaces. Isolated singularities are excluded if the contact angle is bounded away from zero and if the solution is assumed to lie on one side of the supporting surface.     

Minimal surfaces,corners, and wires

Weierstrass representations are given for minimal surfaces that have free boundaries on two planes that meet at an arbitrary dihedral angle. The contact angles of a surface on the planes may be different. These surfaces illustrate the behavior of soapfilms in convex and nonconvex comers. They can also be used to show how a boundary wire can penetrate a soapfilm with a free end, as in the overhand knot surface. They should also cast light on the behavior of capillary surfaces.     

Axisymmetric torsional fretting contact between a spherical punch and an FGPM coating

The axisymmetric torsional fretting contact between a rigid conducting spherical punch and a functionally graded piezoelectric material (FGPM) coating is studied in this paper. The exponential model is used to simulate the inhomogeneous electro-mechanical properties of the FGPMs coating. The conducting spherical punch with a constant surface electric potential is considered in the contact. A normal force and a cyclic torque are applied to the two contact bodies. The applied torque produces an outer annular slip area and an inner stick area. The torsion angle is produced within the inner stick area as a rigid body. With the aid of the Hankel integral transform technique, we can reduce the contact problem to the singular integral equations of the Cauchy type. Then the unknown electro-mechanical fields and stick/slip area can be obtained numerically. The effect of the gradient index on the surface electro-mechanical fields is discussed at loading and unloading phases. The Mises stress and principal stress at the contact surface are also discussed to predict the possible location of fretting damage and failure.     

Surface Deformation due to Shear and Ploughing in a Halfspace

Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

裂缝三级摩擦因数及影响因素研究(以砂岩（颗粒胶结体）为例)

讨论摩擦面的摩擦因数模型．认为砂岩的摩擦因数分为砂粒球面摩擦因数、微裂纹平面摩擦因数、凸凹构成的裂缝摩擦因数3个层次,分别代表3类不同的成因,3个层次的耦合是真实岩石摩擦因数的决定因素．岩石摩擦因数是在砂粒球面材料摩擦因数基础上,经过后两种形式的放大而形成岩石的宏观摩擦因数．裂纹表面凸起的平均角度或者分形维数是影响岩石摩擦因数分异的最大影响因素,而颗粒排布模式导致的分异相对小得多．颗粒接触的静摩擦因数大于动摩擦因数的成因与颗粒的平均接触角度有关．     

Accurate modeling of contact using cubic splines

In this paper, we develop and implement a new method for the accurate representation of contact surfaces. This approach overcomes the difficulties arising from the use of traditional node-to-linear surface contact algorithms. In our proposed method, contact surfaces were modeled accurately using C¹-continuous cubic splines, which interpolate the finite element nodes. In this case, the unit normal vectors are defined uniquely at any point on the contact surfaces. These splines preserve the local deformation of the nodes on each flexible contact surface. Consequently, a consistent linearization of the kinematic contact constraints, based on the spline interpolation, was derived. Moreover, the gap between two contact surfaces was modeled accurately using an efficient surface-to-surface contact search algorithm. Since the continuity of the splines is not affected by the number of nodes, accurate stress distribution can be obtained with less finite elements at the contact surface than that using the traditional linear discretization of the contact surface. Two numerical examples are used to illustrate the advantages of the proposed representation. They show a significant improvement in accuracy compared to traditional piecewise element-based surface interpolation. This approach overcomes the problem of mismatch in a finite element mesh. This is very useful, since most realistic engineering problems involve contact areas that are not known a priori.     

The reduction in the vapour pressure in a closed volume due to condensation at the contact interface with a cold liquid

The reduction in the vapour pressure in a closed volume as a consequence of condensation at the interface with a cold liquid is investigation. Approximate formulae are obtained that describe the pressure drop when a vapour is in contact with cold water in the form of a liquid layer on a horizontal surface and also in the form of drops.     

Capillary Drops: Contact angle hysteresis and sticking drops

This paper is concerned with the homogenization of a capillary equation for liquid drops lying on an inhomogeneous solid plane. We show in particular that the homogenization of the Young–Laplace law leads to a contact angle condition of the form , which justifies the so-called contact angle hysteresis phenomenon.     

Hydrodynamic assist and the dynamic contact angle in the coalescence of liquid drops

^** Email: decentsp{at}for.mat.bham.ac.uk The coalescence of two viscous liquid drops in an inviscid gasor in a vacuum is studied using the interface formation model.In the very early stages of coalescence during the formationof the ‘liquid-bridge’ connecting the two drops,this model predicts a moving contact line and a dynamic contactangle. This paper examines the dynamic evolution of this contactangle, and for small Reynolds number and small Capillary number,relevant particularly in micro-fluidics, a non-linear differentialequation is derived for the contact angle and solved computationally.It is found that the contact angle evolution can only be evaluatedby determining information about the flow away from the contactline. This is a manifestation of so-called hydrodynamic assist,studied experimentally in the context of curtain coating byBlake et al. (1999 Experimental evidence of non-local hydrodynamicinfluence on the dynamic contact angle. Phys. Fluids, 11, 1995–2007).For small Capillary number and small Reynolds number, the free-surfaceevolution is determined for the coalescence of two cylindersof equal radius. Finally, some comments are made on experimentsin coalescence, as well as on issues arising in a computationalsolution of the full model described here.     

Elastic-plastic halfspace simulation

Due to the roughness of technical surfaces only the surface peaks are in contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface asperities in order to analyse the tribological properties of surfaces. The real contact area is usually small in initial contact. This leads to large contact pressures which in turn lead to the plastic deformation of surface roughness peaks. Therefore an elastic-plastic model is necessary. The halfspace model seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite-Element-Method. This leads to a much smaller system of equations which should allow reasonable calculation times even for large contact surfaces. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Applicable Boundary Condition at the Moving Contact Line in Case of a Free Surface Reorientation after Step Reduction in Gravity

In this study the sudden change in the acceleration level on a free surface in a right circular cylinder is investigated numerically. The intention to describe the .uid motion encounters the difficulty modelling the moving contact‐line problem. In the numerical simulations the Navier slip boundary condition and a model for the dynamic contact angle are used. The model for the dynamic contact angle γ_d includes the dependence on the Capillary number as well as the contact angle hysteresis. We achieved very good agreement with experimental data.     

A Two-Dimensional Computational Droplet Contact Model

The interaction between capillary fluid films and micro-structural rough surfaces is one of the main challenges in studying self-cleaning mechanisms. The surface behavior of the deformable fluid film is governed by the Young-Laplace equation, which is highly non-linear. Therefore, a numerical solution is introduced using the finite element method, based on a continuum mechanical formulation. Surface and line contact at the fluid-structure interface are modeled by enforcing a contact constraint, and a contact angle, respectively. The numerical solution is validated against the analytical solution of a test case. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mechanical Modeling of Particle-Droplet Interaction Motivated by the Study of Self-Cleaning Mechanisms

Motivated by the study of self-cleaning surfaces, the interaction between a spherical solid particle and a water droplet is studied on the microsale level, in terms of the balance forces and the surface properties. To define the forces acting on the solid-liquid interface, the meniscus depression is computed from the Young-Laplace equation, using a non-linear finite element formulation. The equilibrium force is derived in terms of the contact angle, particle size, and the penetration. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Equilibria for anisotropic surface energies with wetting and line tension

We study the stability of surfaces trapped between two parallel planes with free boundary on these planes. The energy functional consists of anisotropic surface energy, wetting energy, and line tension. Equilibrium surfaces are surfaces with constant anisotropic mean curvature. We study the case where the Wulff shape is of “product form”, that is, its horizontal sections are all homothetic and have a certain symmetry. Such an anisotropic surface energy is a natural generalization of the area of the surface. In particular, we study the stability of parts of anisotropic Delaunay surfaces which arise as equilibrium surfaces. They are surfaces of the same product form of the Wulff shape. We show that, for these surfaces, the stability analysis can be reduced to the case where the surface is axially symmetric and the functional is replaced by an appropriate axially symmetric one. Moreover, we obtain necessary and sufficient conditions for the stability of anisotropic sessile drops.     

Thermal stress state of a bimaterial with a closed interfacial crack having rough surfaces

We have formulated the problem of thermoelasticity for a bimaterial whose components differ only in their shear moduli, with a closed interfacial crack having rough surfaces. The bimaterial is subjected to the action of compressive loads and heat flow normal to the interfacial surface. We have taken into account the dependence of thermal conductance of the defect on the contact pressure of its faces and heat conductivity of the medium that fills it. The problem is reduced to a Prandtl-type nonlinear singular integro-differential equation for temperature jump between the crack surfaces. An analytical solution of this problem has been constructed for the case of action of the heat flow only. We have analyzed the dependence of contact pressure of the defect faces, temperature jump between them, and the intensity factor of tangential interfacial stresses on the value of given heat flow, roughness of the surfaces, and ratio between the shear moduli of joined materials.     

Steady-State Frictional Heat Generation on a Periodic Sliding Contact

We investigate the motion of a periodic system of rigid, isolated, parabolic dies along the surface of a half-space. The action of friction forces results in heat generation in the contact region. We assume that the surfaces of the dies are thermally insulated and the half-space is a heat conductor. We reduce the problem under consideration to a set of two integral equations for the contact temperature and pressure. We solve these equations numerically and investigate the influence of thermal deformation on the distributions of temperature and pressure and on the dimensions of the contact region.     

Determination of a stochastic friction coefficient depending on a randomly rough surface

The goal of this contribution is to calculate the the friction coefficient for a scanned surface of a worn brake pad. The data shows that the asperities can be approximated by paraboloids which allows to calculate the contact force and area with the Hertz contact model if the deformation is elastic. The friction force is calculated with the Bowden-Tabor approach which suggests that the friction force is the force to shear apart contacting asperities. This is considered to be the dominant friction cause in dry contact. To generate many surfaces with similar peak statistics the spectral decomposition is used. The friction coefficient and it's stochastic properties is calculated for these surfaces. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Capillary oscillations at a circular orifice

We compute the normal frequencies and normal modes for the oscillation of the free surface of a perfect incompressible fluid inside a semi-infinite container with a circular orifice. In doing that, a dual integral equation system involving the Bessel functions must be solved. We discuss the cases where the contact line between the free surface and the container is pinned as well as the case where it moves with a constant contact angle.     

Axially symmetric problem of local separation of an elastic half-space from a rigid base due to a point source of cooling

An axially symmetric problem on the unilateral frictionless contact of an elastic half-space and a rigid thermally insulated base under the action of a subsurface source of cooling, which leads to local loss of contact over a circular region, is considered. The intensity of the source at which the local loss of contacts begins is determined. The dependence of the geometrical parameters of the gap between the surfaces of the bodies on the intensity of the source of cooling and its location relative to the surface is analyzed in detail.