In rough elastohydrodynamic lubricated contacts the geometry often exhibits two clearly separated scales: a macroscopic scale –the one of the bearing– and a microscopic scale, that of the surface roughness. In numerical simulation of lubricated contacts, this difference in scales leads to large systems of equations to solve. Assuming periodicity or pseudo-periodicity of the small scale, several methods to decouple the macro scale from the micro scale have been proposed, the formal approach being the homogenization theory. However, the approximation errors due to the classical asymptotic assumptions can be considerable. In this work we introduce a homogenized model which takes into account the non-negligible pressures and deformations of the micro scale, thus extending the applicability of the classical asymptotic homogenized approaches.

This article examines the influence of low thermal inertia coatings, such as diamond-like carbon coatings, on the lubrication of point contacts operating under zero entrainment velocity conditions. Stationary thermal elasto-hydrodynamic simulations are performed to analyze modifications to the thermal viscosity wedge mechanism induced by the presence of such coatings. Three configurations, namely a steel-steel contact, a DLC coated steel-DLC coated steel contact and a steel-DLC coated steel contact, are investigated. For each configuration, temperature, pressure and film thickness profiles are presented in order to discuss the tribological performances (film thickness and traction) of low inertia coatings under these very specific lubrication conditions. In particular, the detrimental effect of having only one coated surface is highlighted and explained.

This article deals with the lubrication of cam-follower contacts in automobile racing applications. Time-dependent thermal elastohydrodynamic line contact simulations are performed to analyze the contact performance achieved with a shear-thinning lubricant under highly dynamic conditions. Comparisons between different simulations are used to quantify the respective influence of shear thinning, thermal softening, and transient effects on friction and film thickness. Furthermore, this article highlights the formation and transport of a transient dimple responsible for an increase in lift close to the conditions where reversals of entrainment occur. Temperature distributions across the film thickness and pressure variations are reported to discuss the underlying phenomena.

For practical applications, there are several points of interest in the numerical simulation of transient Thermal Elastohydrodynamic (TEHD) lubrication. Among others, is the possibility to investigate the impact of transient effects depending on the dynamic characteristics of the contact. In this regard, the paper presents an original study on the characteristic times involved in a generic line contact lubricated with a non-Newtonian fluid. The paper highlights the dependency of the dominant heat transfer mode on the Slide-to-Roll Ratio (SRR), leading to the formulation of new thermal characteristic times. Based on results from time-dependent computations, it also provides a criterion linking the onset of transient effects to the dominant thermal characteristic time which has been validated on various operating conditions.

In recent years, Diamond-like carbon (DLC) coatings have been increasingly used in tribological applications thanks to their ability to mitigate friction. Among other factors, the low thermal conductivity of these coatings was shown to play a significant part, especially in the EHL regime. By disrupting the heat removal, the presence of DLCs or other low thermal inertia coatings induces higher temperatures in the central region of the contact than for steel-steel configurations. These higher temperatures in turn lead to a reduction in viscous friction without notable consequences on the film thickness. While valid for low to moderate sliding conditions, this statement however does not apply to infinite sliding conditions where the temperature balance strongly affects the film thickness through the so-called “thermal viscosity wedge mechanism”. The present work therefore investigated the influence of low thermal inertia coatings on the lubrication of contacts operating under infinite sliding conditions. Thermal Elastohydrodynamic (TEHD) simulations of circular steel-steel contacts with and without low thermal inertia coatings were performed. Pressure and film thickness profiles as well as temperature distributions obtained in both configurations with a Newtonian lubricant were compared and analyzed. Results show that the use of low thermal inertia coatings tends to counteract the thermal viscosity wedge mechanism and result in lower central and minimal film thicknesses in infinite sliding conditions.

During their life cycle, complex tribological systems such as gears and cam-followers are subjected to extremely severe operating constraints. Those invariably involve substantial shear rates, pressures and temperatures within the lubricant, in addition to dynamic applied conditions of load, speeds and conjunction geometry [1]. In recent years, the use of transient TEHD models is progressively becoming a standard for the simulation of gears and cam-follower systems. New advances focus on topics such as roughness, starvation, boundary lubrication, etc. Surprisingly, a clear understanding of the onset and magnitude of the transient effects in TEHD configurations is still lacking. The present study aims at addressing this point by providing a comprehensive numerical analysis of the transient phenomena occurring within the conjunction, their respective influence (depending on the operating conditions and material parameters), and their associated time scales. As a prerequisite, the system of equations, boundary conditions and numerical scheme used in the model are described. In addition, developments to solve transient fully-flooded TEHD problems are detailed, on the basis of a previous work [2] dedicated to the study of steady state cases. Then, the phenomena at the origin of transient effects in a TEHD contact are reviewed along with their characteristic time. In this context, a particular focus is placed on the thermal problem. The complexity in finding a relevant thermal characteristic time is illustrated by the influence of the slide-to-roll ratio (SRR) on the contact performance (film thickness and friction) [3]. The dependency of the dominant heat transfer mode on the SRR is showed. A distinction between low sliding, pure sliding and high sliding conditions is made. Each configuration is thoroughly analyzed, leading to the formulation of new thermal characteristic times. Finally, in order to determine the onset of transient effects, time-dependent TEHD computations are performed. A reference configuration consisting of two contacting cylinders subjected to a sinusoidal load variation (of amplitude Aw and period tw) is used. Transient evolutions of the central film thickness and friction coefficient are compared to quasi-steady solutions for the three different SRR cases and varying tw. For this purpose, characteristic variables of a periodic TEHD problem, namely the mean value (hcm) and amplitude (Ahc) of the central film thickness and the mean value of the friction coefficient (Cfm), are extracted from each computation. Those are, in turn, used to create a set of normalized variables (Δhcm, ΔAhc and ΔCfm) allowing to calculate deviations induced by the transient effects. Results, as the example plotted on Fig.1, show that the onset of transient effects of the different configurations can be matched if related to their dominant physical characteristic time tφ. A parametric study on the operating conditions (load, entrainment velocity, amplitude of fluctuation) and material properties further validates this conclusion.

The paper presents recent improvements and results on the on-demand injection of small electrically neutral water drops in oil by high electric field pulses. The technique consists in applying a voltage pulse promoting the deformation of a water meniscus at the end of a capillary tube through the action of electric forces. For pulses of calibrated energy, the transient deformation can lead to the inertia-based ejection of a small uncharged droplet. Application of in-house developed multi-stage electric pulses offers, in contrast to usual single pulses, wider ranges of droplet size, improved reproducibility and stable ejection trajectories. Influence of the main parameters on the extracted droplet diameter is presented: it is shown that, by using capillary tubes of outer tip diameter close to 0.5 mm, it is possible to obtain, in a reproducible way, drops of diameter ranging from less than 15 μm up to more than 250 μm.

Cette these porte sur l'utilisation de champs electriques pour faciliter l'elimination de l'eau coproduite avec le petrole brut, sous la forme d'emulsions stables, lors des etapes d'extraction et de dessalement. Ce procede, connu sous le nom d'electrocoalescence, s'appuie sur la capacite qu'ont les forces electrostatiques a promouvoir l'attraction et la coalescence de gouttelettes d'eau proches afin d'en augmenter la taille et ainsi d'en accelerer la sedimentation par gravite. Bien que les premieres observations experimentales datent deja d'un siecle, de nombreuses zones d'ombres subsistent, notamment en ce qui concerne l'optimisation de l'efficacite des electrocoalesceurs de derniere generation. Dans ce contexte, une demarche, combinant simulation numerique multiphysique et experimentation, a ete mise en place pour etudier les phenomenes de mouvement, de deformation et d'instabilite d'interfaces eau-huile induit par la presence d'un champ electrique. La contribution la plus marquante concerne la modelisation et l'analyse de l'effet des forces electrostatiques sur le mecanisme d'amincissement du film d'huile separant les gouttes. Les resultats numeriques mettent en evidence la singularite du probleme et l'inadaptabilite des modeles theoriques de lubrification classiquement adoptees pour representer la coalescence dans les ecoulements diphasiques. Une nouvelle expression asymptotique pour le calcul du temps de drainage entre les gouttelettes de l'emulsion est proposee et utilisee pour deduire un critere predisant la probabilite d'electrocoalescence lors d'une collision dans un ecoulement cisaille. En parallele, un dispositif sophistique, permettant de reproduire experimentalement le phenomene et d'ameliorer la representativite du critere, a ete construit. Enfin, en reponse a un point bloquant decele lors de la phase de conception de ce dernier, une technique innovante d'injection a la demande de gouttes conductrices non chargees dans un liquide visqueux isolant, utilisant des impulsions electrostatiques, a ete developpe.

The basic process of coalescence of droplets in a flowing water-in-oil emulsion under the action of an electric field is considered. The coalescence probability depends on the ratio of time of close proximity of droplets and time of decrease of spacing down to drops contact. For two free drops aligned with the field, the dynamical problem consists in the deformation of the drops, their motion and the thinning of the oil film between the drops. For very small droplets, assuming a negligible interface deformation, a very small initial spacing and a high value of viscosity ratio leads to an order of magnitude estimate of the time required for the drops to achieve contact. Numerical simulations confirm that this time is roughly inversely proportional to the maximum initial electrostatic pressure p e0 at the facing interfaces and point up an influence of the electric Bond number defined as the ratio of electric and capillary forces.

In connection with the phenomenon of electrocoalescence of water droplets in oil, the electrically induced deformations of some water–oil interfaces are studied. Such problems involve the strong coupling of hydrodynamics and electrostatics as well as the accurate tracking/capturing of the evolving interfaces. The paper presents a Finite–Element Arbitrary Lagrangian–Eulerian (FE–ALE) approach in deforming meshes to investigate the time-dependent deformation of the interface between highly conductive water and an insulating immiscible fluid. The developed numerical scheme is first tested and then used to solve two 2D axisymmetric EHD problems. Computed results are compared with predictions from asymptotic developments and with experimental measurements.

Present research aims at determining the conditions leading to electrocoalescence of water drops in oil flows and at characterizing the interplay between fluid dynamics and electric field in the mechanism. We describe here the build-up of an experimental set-up designed to investigate the critical coalescence conditions in the case of two free water droplets in an oil shear flow under the action of an applied electric field. Drop pairs will be injected in a Poiseuille flow to study, by optical means, their relative motion, deformation and possible coalescence. Important part of this preliminary work concerns the injection of controlled charge free drop pairs using a newly developed EHD actuation technique. Second paper [1] deals with theoretical and numerical analyses in the same configuration.

— As a part of a study of electrocoalescence of water droplets in oil, the electrically induced deformations of water-oil interfaces are studied. Cases of large deformations of the interfaces involve the strong coupling of hydrodynamics and electrostatics, in which cases numerical simulation is needed. The paper presents different numerical simulations performed using the commercial software COMSOL MULTIPHYSICS™ in cases of water-air or water-oil configurations with axial symmetry. Electrohydrodynamics problems are solved using ALE approach in deforming meshes. Comparisons are presented with the results of analytical developments, asymptotic approaches or experiments.

The problem of instability of a horizontal interface between water and an insulating fluid, electrically influenced by a metallic sphere located just above it, is considered here with its relevance to the basic electrocoalescence phenomenon of close water droplets suspended in an insulating medium. Results are presented of preliminary experiments performed using visualisation and shadowscopy techniques. The evolution of the interface shape is characterised for various applied step voltages and for different values of the initial spacing s 0 between sphere and interface. An order of magnitude analysis leads to good estimates of the characteristic parameters and time scales.

As a part of a study of electrocoalescence of water droplets in oil, the controlled generation of small drops (diameter ~ 100 mum) is considered. The technique used consists in applying a voltage pulse promoting the deformation of a meniscus at the end of a capillary tube through the action of electric forces. For pulses of short enough duration, the transient deformation can lead to the ejection of a small drop electrically neutral. The experimental results of water drops extraction in oil are presented. Using capillary tubes of outer tip diameter varying from 0.5 mm to 1 mm, it is possible to obtain in a reproducible way drops of diameter ranging from 50 mum to 200 mum. For a given meniscus shape, the diameter of the extracted droplet depends on the voltage amplitude V and on the pulse duration Deltat. Order of magnitude considerations on the meniscus deformation process suggest that the main parameter which determines the size of the generated droplet is the product V2 Deltat. The experimental results support this guess for pulse durations low enough so that there is no electrical field (and, therefore, no surface charge) during the last stage of meniscus elongation and break-up. The possible use of this technique of drop-on-demand generation is discussed, taking into account the transient oil flow around the meniscus which most often brings the droplet off the system axis.

We investigate the deformation and coalescence of two closely spaced drops of conducting liquid suspended in an insulating fluid under the action of an electric field. The equations governing droplets deformation are derived in the case of drops subjected to a potential difference. The critical conditions for existence of a stationary solution are determined for drops anchored on capillary tubes in the asymptotic case of very close drops. In particular, electrocoalescence is predicted to occur when the interfaces distortions are such that the initial drops spacing has decreased by nearly 50%. A numerical simulation gives the critical conditions for any spacing between the drops. Results compare favourably with the asymptotic approach in the common range of application.