Viscoelastic Lubricant Research Articles

Effect of heat conduction on viscoelastic lubricant behavior during heat-assisted magnetic recording (HAMR): A numerical study

Heat-assisted magnetic recording (HAMR) is one of the critical technologies to overcome the areal density limitations of hard disk drives. In order to reveal the behavior of viscoelastic lubricants under HAMR conditions, the coupled physical field model of disk Fourier heat conduction model and viscoelastic lubricant model is established. The effects of Fourier heat conduction model and Gaussian distribution model on the disk temperature distribution and viscoelastic lubricant behavior are investigated. The lubricant deformation calculated by the Fourier heat conduction model is more accurate. The laser power overshoot method is proposed to improve the efficiency of HAMR writing process. The lubricant recovery ratio calculated by the Fourier heat conduction model is greater than that calculated by the Gaussian distribution model. The smaller the laser radius is, the greater the deformation of the lubricant is, and the lower the recovery ratio is.

Exploring slip flow of viscoelastic fluid with frictional heating effects: Uncertainty analysis using response surface methodology (RSM)

Viscoelastic fluid flow along a slippery plate finds applications in different fields such as examining friction and wear characteristics of bearing surfaces using viscoelastic lubricants, extrusion, coating and moulding processes, thin film deposition among others. The present article explores boundary layer flow generated by a slippery stretching plate in a viscoelastic fluid and conducts uncertainty analysis of the governing model via response surface methodology. In addition, the analysis includes viscous dissipation mechanism that represents the conversion of mechanical energy into heat induced by viscosity. The inclusion of the wall slip condition results in a non-linear Robin-type condition for the velocity field. A dependable and user-friendly built-in package “bvp4c” of MATLAB is used to provide the computational results. The solution is used to illustrate the implication wall slip phenomenon on the resisting wall shear. One noteworthy finding is that the inclusion of either the frictional heating effect or the elasticity results in a significant decrease in the surface cooling rate. As the contribution of the heat source term grows, the rate of surface cooling decreases. Strengthening the heat sink effect reverses this result. Contour plots for stream function and isotherms are generated and compared in Newtonian and second grade fluid cases.

An analytical study on nonlinear viscoelastic lubrication in journal bearings

This paper presents a novel analytical solution for journal-bearing viscoelastic lubrication using the perturbation method. The nonlinear Giesekus model was used for the constitutive equations to study the effects of fluid elasticity, shear-thinning viscometric functions, and strain-hardening elongational viscosity of viscoelastic lubrication. The investigation focuses on the impact of characteristic parameters such as mobility factor, eccentricity ratio, and Weissenberg number on the fluid film pressure distribution, load capacity, and shear stress. Although distinguishing between the normal stress differences and extensional viscosity in mixed viscoelastic flows is complicated, we investigated the role and contribution of these two factors. By increasing the elasticity of the fluid, the portion of both mentioned parameters increases consequently. Furthermore, analyses and comparisons show the contributions of the first normal stress and elongational viscosity to the load capacity of the bearing through the stress ratio and flow type parameter for the first time. The research findings indicate that fluid elasticity enhances the load capacity of the bearing compared to a Newtonian lubricant with the same effective viscosity. Moreover, the bearing load capacity is divided into two regions. In the linear region, the mobility factor and Weissenberg numbers have minimal effects leading to a linear increase in the load distribution, and in the exponential region, the load capacity changes are considerable. This research provides valuable insights into the behavior of viscoelastic lubrication in journal-bearing systems.

Contactless Rheology of Soft Gels Over a Broad Frequency Range

We report contactless measurements of the viscoelastic rheological properties of soft gels. The experiments are performed using a colloidal-probe atomic force microscope in a liquid environment and in dynamic mode. The mechanical response is measured as a function of the liquid gap thickness for different oscillation frequencies. Our measurements reveal an elastohydrodynamic coupling between the flow induced by the probe oscillation and the viscoelastic deformation of the gels. The data are quantitatively described by a viscoelastic lubrication model. The frequency-dependent storage and loss moduli of the polydimethylsiloxane gels are extracted from fits of the data to the model and are in good agreement with the Chasset-Thirion law. Our results demonstrate that contactless colloidal-probe methods are powerful tools that can be used for probing soft interfaces finely over a wide range of frequencies.

An investigation on nonlinear viscoelastic lubrication using FENE-P constitutive equation

An investigation on nonlinear viscoelastic lubrication using FENE-P constitutive equation

An Extended Reynolds Equation for Non-Newtonian Lubrication With the Upper Convected Maxwell Model

Abstract The upper convected Maxwell (UCM) model is one of the ways to describe lubricant’s viscoelasticity. In this paper, a new modified Reynolds equation for the UCM model is derived. This equation may be called extended as compared to its analogs because it incorporates the complete structure of the upper convected derivative without the explicit omitting of any term or using the perturbation technique. Then, a numerical scheme for solving the viscoelastic lubrication problems with the employment of the derived equation is described. A mixed Euler–Lagrange approach is used here: the constitutive rheological equations are resolved by a semi-Lagrangian technique and the extended Reynolds equation is discretized by the finite volume method. A constant surface slope problem is considered as a test case. Excellent agreement is achieved between the numerical solution at low Deborah number and one of the approximate solutions. The results of simulations with different types of time derivative used in Maxwell model both for two- and three-dimensional cases are also discussed.

The effect of fluid viscoelasticity in lubricated contacts in the presence of cavitation

In this work we study the influence of fluid viscoelasticity on the performance of lubricated contacts in the presence of cavitation. Several studies of viscoelastic lubricants have been carried out, but none of them have considered the possibility of the presence of cavitation. To describe the effect of viscoelasticity, we use the Oldroyd-B model. By assuming that the product between ϵ, i.e. the ratio between vertical and horizontal length scales, and the Weissenberg number (Wi), i.e. the ratio between polymer relaxation time and flow time scale, is small, we can linearise the viscoelastic thin film equations, following the approach pioneered by "Tichy, J., 1996, Non-Newtonian lubrication with the convected Maxwell model." Consequently, the zeroth-order in ϵWi corresponds to a Reynolds equation modified to describe also the film cavitation through the mass-conserving Elrod-Adams model. We consider the flow of viscoelastic lubricants using: (i) a cosine profile representing a journal bearing unwrapped geometry, and (ii) a pocketed profile to model a textured surface in lubricated contacts. The introduction of viscoelasticity decreases the length of cavitated region in the cosine profile due to the increasing pressure distribution within the film. Consequently, the load carrying capacity increases with Wi by up to 50% in the most favorable condition, confirming the beneficial influence of the polymers in bearings. On the other hand for the pocketed profile, results show that the load can increase or decrease at higher Wi depending on the texture position in the contact. The squeeze flow problem between two plates is also modeled for viscoelastic lubricants considering an oscillating top surface. For this configuration a load reduction is observed with increasing Wi due to the additional time needed to reform the film at high Wi. Furthermore, if viscoelastic effects increase, the cavitation region widens until reaching a value of Wi for which a full-film reformation does not occur after the initial film rupture.

A new approach for modeling viscoelastic thin film lubrication

Lubricants can exhibit significant viscoelastic effects due to the addition of high molecular weight polymers. The overall behavior of the mixture is vastly different from a simpler Newtonian fluid. Therefore, understating the influence of viscoelasticity on the load carrying capacity of the film is essential for lubricated contacts. A new modeling technique based on lubrication theory is proposed to take into account viscoelastic effects. As a result, we obtain a modified equation for the pressure, i.e. the viscoelastic Reynolds (VR) equation. We have first examined a parabolic slider to mimic a roller bearing configuration. An increase of the load carrying capacity is observed when polymers are added to the lubricant. Furthermore, our results are compared with existing models based on the lubrication approximation and direct numerical simulations (DNS). For small Weissenberg number (Wi), i.e. the ratio between the polymer relaxation time and the residence time scale, VR predicts the same pressure of the linearized model, in which ϵWi is the perturbation parameter (ϵ is the ratio between the vertical length scale and the horizontal length scale). However, the difference grows rapidly as viscoelastic effects become stronger. Excellent quantitative and qualitative agreement is observed between DNS and our model over small to moderate Weissenberg number. While DNS is numerically unstable at high values of the Weissenberg number, VR does not have the same issue allowing to capture the evolution of the stress and pressure also when the viscoelastic effects are strong. It is shown that even in high shear flows, normal stresses have the largest impact on load carrying capacity and thus cannot be neglected. Furthermore, the additional pressure due to viscoelasticity comprises two components, the first one due to the normal stress and the second one due to the shear stress. Afterwards, the methodology used for the parabolic slider is extended to a plane slider where, instead, the load decreases by adding polymers to the fluid. In particular, under the effect of the polymers surface slopes enhance the rate at which pressure gradients increase, whereas curvature opposes this along the contact. Therefore, the increase of the load carrying capacity observed for viscoelastic lubricants is due to its shape close to the inlet, which is steeper than the plane slider.

Friction of lubricated hydrogels: Influence of load, speed and lubricant viscosity

Agarose hydrogels are used to study the tribological response of hydrogel materials. We demonstrate that the dynamic frictional behaviour of agarose hydrogels is influenced by their mechanical properties, lubricant viscosity and applied load. Within the linear viscoelastic regime of the hydrogels, we find the Stribeck-type framework proposed previously for elastomers and other viscoelastic materials describes their tribological behaviour and dependency on lubricant viscosity. However, this breaks down when sufficient stress in the contact is applied so that the hydrogel undergoes yielding (i.e. elastic-plastic deformation). As a result, we find that the friction- normal load relationship differs from the classic trend (F ~ W2/3) observed in elastomers above finite loads. Conventional interpretations of the friction associated with hydrogels should be revised with consideration for the non-linear deformation of the hydrogels. We suggest that theories on viscoelastic lubrication are generally applicable to hydrogels within their linear viscoelastic regime, and propose a conceptual model that considers the effects of bulk mechanical properties and measurement conditions including lubricant viscosity, measuring geometry, speed and load.

Mathematical model of a radial bearing with a low-melting metal coating of design models of hydrodynamic viscoelastic lubricant formed by melting the surface of a bearing bush coated with a metallic low-melting coating

The work is based on equations of motion of viscoelastic lubricant (Maxwell fluid) for the case of “thin layer”, continuity and the formula of the rate of dissipation of mechanical energy. We found asymptotic solution to the degrees of small parameter K, characterizing the rate of dissipation of mechanical energy. This allows determining the molten surface of the bearing sleeve covered with a fusible metal melt, taking into account the dependence of the viscosity of the lubricant and the shear modulus of pressure in the adiabatic process. For zero approximation under adiabatic process conditions, i.e. without taking into account the melt surface, and a solution for the first approximation, i.e., taking into account the melt surface of the bearing sleeve covered with a fusible metal melt, the exact self-similar solution of the problem with incomplete (pre-emergency) filling of the working gap with a lubricant having viscoelastic properties is found.. On the basis of the results obtained for the zero and first approximation, the bearing capacity and friction force are found at incomplete filling of the working gap with a lubricant. In addition, for verification calculations of the obtained theoretical models, a numerical calculation was carried out and as a result, graphs showing a decrease in the friction coefficient by about 20% were constructed.

Soft lubrication: A generalized numerical methodology

A generalized numerical methodology is introduced to deal with the lubrication between soft solids exhibiting linear viscoelastic rheological properties. By means of this approach, it is shown that significant deviations from classic elasto-hydrodynamic theory occur in terms of film thickness, pressure distribution and friction. By focusing on a simple tribo-system, consisting in a sphere in contact with a layer, the influence of the contact configuration is investigated. Ultimately, viscoelastic lubrication is shown to be exhaustively governed by three parameters: the Hersey number and the dimensionless velocities of the two contacting bodies. Finally, numerically obtained friction values are compared with experiments to validate the methodology.

Viscoelastic Lubricant Deformation and Disk-to-Head Transfer During Heat-Assisted Magnetic Recording

One of the challenges in heat-assisted magnetic recording (HAMR) is the formation of write-induced head contamination at the near-field transducer. A possible mechanism that has been proposed for this contamination is the transfer of lubricant from the disk to the head due to temperature driven evaporation/condensation. Most previous studies on lubricant depletion due to laser heating have assumed the lubricant to be a viscous fluid and have modeled its behavior using the traditional lubrication theory. However, perfluoropolyether lubricants are viscoelastic fluids and are expected to exhibit a combination of viscous and elastic behavior at the time and length scales of HAMR conditions. In this paper, we use a modified Reynolds lubrication equation for the viscoelastic fluid that employs the linear Maxwell constitutive model. We use this modified lubrication equation to develop a model that predicts the disk-to-head lubricant transfer during HAMR writing. This model simultaneously determines the thermocapillary stress driven deformation and evaporation of the viscoelastic lubricant film on the disk, the diffusion of the vapor phase lubricant in the air bearing, and the evolution of the condensed lubricant film on the head. We investigate the effects of lubricant type (Zdol versus Ztetraol), head/disk temperature, initial lubricant thickness, and laser spot size on the lubricant transfer process. Simulation results show a significant difference between the rates of transfer for Zdol (timescale of nanoseconds) versus Ztetraol (timescale of microseconds). The amount of transfer increases with the disk temperature and the initial lubricant thickness.

Simultaneous design of non-Newtonian lubricant and surface texture using surrogate-based multiobjective optimization

Surface textures decrease friction in lubricated sliding with Newtonian fluids. Viscoelastic non-Newtonian lubricants can enhance frictional performance, but the optimal rheological material properties and their coupling to the texture design are non-obvious. In this study, we present a simultaneous design of both surface texture shape and non-Newtonian properties, which can be achieved by fluid additives that introduce viscoelasticity, shear thinning, and normal stress differences. Two models with different fidelity and computational cost are used to model laminar non-Newtonian fluid flow between a rotating flat plate and a textured disk. At lower fidelity, we use the Criminale-Ericksen-Filbey (CEF) constitutive model and a thin-film approximation for conservation of momentum (Reynolds equation). At higher fidelity, we use a fully nonlinear constitutive model typically applicable to polymer solutions (multimode Giesekus model) and the full 3-D momentum equations. Fluid additive design is parameterized by two relaxation modes each having a timescale, added viscosity, and a nonlinear anisotropic drag parameter. To manage the computational complexity and constraints between design variables, we use our previously developed multiobjective adaptive surrogate modeling-based optimization (MO-ASMO) method. A new data-driven extension of MO-ASMO is introduced that constructs general boundaries to prevent attempts to evaluate designs that would lead to simulation failure. We demonstrate the efficiency of our MO-ASMO method and provide insights into co-designing the lubricant and textured surface. The Pareto-optimal solutions include fluid designs with both high and low viscoelastic additive loading. We rationalize this trade-off and discuss how the optimal design targets can be physically realized.

Thrust Slip Bearings in a Turbulent Friction Mode with the Rheological Properties of a Viscoelastic Lubricant

Based on the concept of the turbulent flow of a viscoelastic lubricant, a two-component lubrication system consisting of mineral oil and a viscoelastic lubricant that represents a melt of fusible metals is considered. The results of studies on the tribological characteristics such as friction forces and the bearing capacity of friction assemblies are presented taking into account the viscosity and shear modulus of the molten layer depending on the temperature. Ways to improve the properties of lubricants through the introduction of additives and fillers therein are considered.

Effect of Rheology and Slip on Lubricant Deformation and Disk-to-Head Transfer During Heat-Assisted Magnetic Recording (HAMR)

The high-temperature laser heating during heat-assisted magnetic recording (HAMR) causes the media lubricant to deform and transfer to the head via evaporation/condensation. The ability of the lubricant to withstand this writing process and sufficiently recover post-writing is critical for robust read/write performance. Moreover, the media-to-head lubricant transfer causes a continuous deposition of contaminants originating from the media at the head near field transducer, challenging the reliability of HAMR drives. Most previous studies on the effects of laser exposure on lubricant depletion have assumed the lubricant to be a viscous fluid and have modeled its behavior using traditional lubrication theory. However, Perfluoropolyether lubricants are viscoelastic fluids and are expected to exhibit a combination of viscous and elastic behavior at the timescale of HAMR. In this paper, we introduce a modification to the traditional Reynolds lubrication equation using the linear Maxwell constitutive equation and a slip boundary condition. We study the deformation and recovery of the lubricant due to laser heating under the influence of thermocapillary stress and disjoining pressure. Subsequently, we use this modified lubrication equation to develop a model that predicts the media-to-head lubricant transfer during HAMR. This model simultaneously determines the deformation and evaporation of the viscoelastic lubricant film on the disk, the diffusion of the vapor phase lubricant in the air bearing, and the evolution of the condensed lubricant film on the head. We investigate the effect of viscoelasticity, lubricant type (Zdol vs Ztetraol), molecular weight, slip, and disjoining pressure on the lubricant transfer process.

Transient viscoelastic lubrication analyses of UHMWPE hip replacements

Abstract The viscoelasticity of the UHMWPE liner may play an important role in the lubrication performance of soft artificial hip joints. All the previous lubrication analyses for UHMWPE hip implants assumed that the UHMWPE liner was linear elastic. In order to investigate the influence of viscoelasticity of the UHMWPE liner, a transient viscoelastic lubrication model was developed. The results showed that the viscoelasticity played a significant role in the lubrication performance of UHMWPE hip implants. Moreover, the retardation time and the ratio of loss and storage modulus of the UHMWPE liner had important effects on the lubrication performance of hip implants. These findings provide new insights into the lubrication mechanisms of UHMWPE artificial hip joints.

Modulating carbohydrate-based hydrogels as viscoelastic lubricant substitute for articular cartilages

Viscosupplementation is a therapeutic approach for osteoarthritis treatment, where the synovial fluid, the natural lubricant of the joints, is replaced by viscoelastic solutions with rheological properties comparable or better than the starting material. This study presents the development of an innovative platform for viscosupplementation, based on the optimization of polysaccharide-based colloidal hydrogel, aiming to reduce on-site enzyme degradation and enhance the possibility of hyaluronic acid substitution with alternative biomaterials. Catanionic vesicles are proposed as physical crosslinker that can guarantee the formation of a ‘soft’, tunable network, offering a dual-therapeutic approach: on the mechanical relief perspective, as well as on the drug/gene delivery strategy. This research focuses on the fabrication and optimization of colloidal networks, driven by the synergistic interaction among catanionic vesicles and cationic modified cellulose polymers. This study tests the hypothesis that cellulose-like polymers can be arranged into functional matrix, mimicking the mechanical properties of healthy synovial fluids.

Influence of fluid viscosity and wetting on multiscale viscoelastic lubrication in soft tribological contacts.

Friction (and lubrication) between soft contacts is prevalent in many natural and engineered systems and plays a crucial role in determining their functionality. The contribution of viscoelastic hysteresis losses to friction in these systems has been well-established and defined for dry contacts; however, the influence of fluid viscosity and wetting on these components of friction has largely been overlooked. We provide systematic experimental evidence of the influence of lubricant viscosity and wetting on lubrication across multiple regimes within a viscoelastic contact. These effects are investigated for comparatively smooth and rough elastomeric contacts (PTFE-PDMS and PDMS-PDMS) lubricated by a series of Newtonian fluids with systematically controlled viscosity and static wetting properties, using a ball-on-disc tribometer. The distinct tribological behaviour, characterised generally by a decrease in the friction coefficient with increasing fluid viscosity and wettability, is explained in terms of lubricant dewetting and squeeze-out dynamics and their impact on multi-scale viscoelastic dissipation mechanisms at the bulk-, asperity-, sub-asperity- and molecular-scale. It is proposed that lubrication within the (non-molecularly) smooth contact is governed by localised fluid entrapment and molecular-scale (interfacial) viscoelastic effects, while additional rubber hysteresis stimulated by fluid-asperity interactions, combined with rapid fluid drainage at low speeds within the rough contact, alter the general shape of the Stribeck curve. This fluid viscosity effect is in some agreement with theoretical predictions. Conventional methods for analysing and interpreting tribological data, which typically involve scaling sliding velocity with lubricant viscosity, need to be revised for viscoelastic contacts with consideration of these indirect viscosity effects.

Lubrication of soft viscoelastic solids

Lubrication flows appear in many applications in engineering, biophysics and nature. Separation of surfaces and minimisation of friction and wear is achieved when the lubricating fluid builds up a lift force. In this paper we analyse soft lubricated contacts by treating the solid walls as viscoelastic: soft materials are typically not purely elastic, but dissipate energy under dynamical loading conditions. We present a method for viscoelastic lubrication and focus on three canonical examples, namely Kelvin–Voigt, standard linear and power law rheology. It is shown how the solid viscoelasticity affects the lubrication process when the time scale of loading becomes comparable to the rheological time scale. We derive asymptotic relations between the lift force and the sliding velocity, which give scaling laws that inherit a signature of the rheology. In all cases the lift is found to decrease with respect to purely elastic systems.

Mechanisms for three kinds of limiting shear stresses appearing in the traction modes of viscous, viscoelastic, and glassy states of lubricants

We present that the tractional flow of a lubricant shows three kinds of limiting shear stresses at which the shear stresses take place independently of the shear rates in its viscous, viscoelastic, and glassy states. We propose three models on the mechanisms for the limiting shear stresses, based on the data of Brillouin spectra and viscosity of viscoelastic liquids previously reported by us and based on the data of the deformation of glassy polymers referred from others. The Brillouin spectra of a viscoelastic lubricant measured at up to 5 GPa at 25 and 80 °C show that we could not observe a frequency dispersion in sound waves below 0.8 GPa at 80 °C, while we can observe the frequency dispersion above 0.1 MPa at 25 °C owing to the viscosity of the lubricant. This result predicts the viscous limiting shear stress in the viscous state owing to the disappearance of meso-structures by heating and shearing under pressure. The viscosity of a polymer measured around the glass transition temperature (Tg) shows that Tg determined by the viscosity measurement is 27 K lower than that determined by calorimetry. This result predicts the elastic limiting shear stress in the viscoelastic state near the glass transition pressure (Pg) owing to the shear thinning effect by shearing a lubricant film. In addition, there is the plastic limiting shear stress in the glassy state owing to the yield stress at which the tractional flow of a glassy lubricant behaves as a plastic solid.