Showing papers on "Lubrication theory published in 2021"

Revisiting steady viscous flow of a generalized Newtonian fluid through a slender elastic tube using shell theory

Abstract: A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross-sectional area. The latter gives rise to a non-constant pressure gradient in the flow-wise direction and, hence, to a nonlinear flow rate--pressure drop relation (unlike the Hagen--Poiseuille law for a rigid tube). Many biofluids are non-Newtonian, and are well approximated by generalized Newtonian (say, power-law) rheological models. Consequently, we analyze the problem of steady low Reynolds number flow of a generalized Newtonian fluid through a slender elastic tube by coupling fluid lubrication theory to a structural problem posed in terms of Donnell shell theory. A perturbative approach (in the slenderness parameter) yields analytical solutions for both the flow and the deformation. Using matched asymptotics, we obtain a uniformly valid solution for the tube's radial displacement, which features both a boundary layer and a corner layer caused by localized bending near the clamped ends. In doing so, we obtain a ``generalized Hagen--Poiseuille law'' for soft microtubes. We benchmark the mathematical predictions against three-dimensional two-way coupled direct numerical simulations (DNS) of flow and deformation performed using the commercial computational engineering platform by ANSYS. The simulations show good agreement and establish the range of validity of the theory. Finally, we discuss the implications of the theory on the problem of the flow-induced deformation of a blood vessel, which is featured in some textbooks.

Convective Mass/Heat Analysis of an Electroosmotic Peristaltic Flow of Ionic Liquid in a Symmetric Porous Microchannel with Soret and Dufour

Abstract: This research deals with the mathematical model for the development of the peristaltic principle of the combination of the pressure and electroosmotic flow (EOF) of ionic liquid across microchannels with electrokinetic effects. For thermomechanical dynamics, the convective conditions on the boundary for mass and heat transfer at the walls of the channel are quantified. For the microchannel, a porous structure is presumed. Soret, Dufour, and Joule heating are also listed in the scope of the problem addressed. The corresponding equations for the ionic fluid flow, mass, and heat transfer along with the Poisson–Boltzmann equation within the electrical double layer (EDL) are studied. The exact solution has been obtained based on lubrication theory (i.e., low Reynolds number and long wavelength approximations). The channel height is therefore believed to be much higher than the electrical double layer (EDL) thickness. Various dimensionless pertinent parameters illustrate the important aspects of electroosmotically controlled flow and subsequent convective mass/heat transfer attributes in a microchannel. A linear dependency on the fluid flow rate is exhibited by the pressure drop. The analysis shows that the electroosmotic parameter gives a reducing effect on the channel permeability. The distribution of temperature and concentration is greatly affected by convective heat and mass parameters, respectively. In biomedical engineering, the application areas of the study proposed are for the design of the devices such as a microfluidic pump to pump a small amount of ionic liquids by regulating the variation in temperature and concentration.

Boundary layer flow of magneto-nanomicropolar liquid over an exponentially elongated porous plate with Joule heating and viscous heating: a numerical study

Abstract: Micropolar fluids are used in lubrication theory, thrust bearing technologies, cervical flows, lubricants, paint rheology, and the polymer industry. This study develops the numerical simulation of the magneto-Darcy flow of a polarized nanoliquid with Joule heating and viscous heating mechanisms on an exponentially elongated surface. The effects of linearized Rosseland radiation and temperature-dependent heat generation are considered. The flow is generated by an exponential form of elongation of a flexible sheet. The porous matrix and nanoparticle effects are characterized by the Darcy expression and the two-component Buongiorno model correspondingly. The resulting partial differential systems are solved numerically using the Runge–Kutta-based shooting technique to interpret the importance of key parameters in physical quantities. A direct comparison is made to validate the results. Our results demonstrated that arbitrary movement of the nanoparticles significantly advances the temperature profile by reducing the concentration of nanoparticles. Both Joule heating and viscous heating mechanisms improve the structure of the thermal boundary layer. The porous matrix reduces the velocity of the nanoliquid and thus the width of the velocity boundary layer is reduced.

Water lubrication of graphene oxide-based materials

Abstract: Water is as an economic, eco-friendly, and efficient lubricant that has gained widespread attention for manufacturing. Using graphene oxide (GO)-based materials can improve the lubricant efficacy of water lubrication due to their outstanding mechanical properties, water dispersibility, and broad application scenarios. In this review, we offer a brief introduction about the background of water lubrication and GO. Subsequently, the synthesis, structure, and lubrication theory of GO are analyzed. Particular attention is focused on the relationship between pH, concentration, and lubrication efficacy when discussing the tribology behaviors of pristine GO. By compounding or reacting GO with various modifiers, amounts of GO-composites are synthesized and applied as lubricant additives or into frictional pairs for different usage scenarios. These various strategies of GO-composite generate interesting effects on the tribology behaviors. Several application cases of GO-based materials are described in water lubrication, including metal processing and bio-lubrication. The advantages and drawbacks of GO-composites are then discussed. The development of GO-based materials for water lubrication is described including some challenges.

Rheology of a concentrated suspension of spherical squirmers: monolayer in simple shear flow

Abstract: A concentrated, vertical monolayer of identical spherical squirmers, which may be bottom heavy, and which are subjected to a linear shear flow, is modelled computationally by two different methods: Stokesian dynamics, and a lubrication-theory-based method. Inertia is negligible. The aim is to compute the effective shear viscosity and, where possible, the normal stress differences as functions of the areal fraction of spheres . This suggests that lubrication theory, based on near-field interactions alone, contains most of the relevant physics, and that taking account of interactions with more distant particles than the nearest is not essential to describe the dominant physics.

Regimes of wettability-dependent and wettability-independent bouncing of a drop on a solid surface

Abstract: Tiny drops of millimetre size are known to bounce on a solid surface if the surface is superhydrophobic. Recent experiments show that bouncing can occur even on hydrophilic surfaces under conditions where the drop is supported on a thin cushion of gas preventing it from making contact with the surface. We present a detailed insight into this observation by simulating bouncing dynamics of a drop on a flat solid surface using axisymmetric direct numerical simulations. The dynamics of drop motion is governed by three important dimensionless parameters, namely, Reynolds number, Weber number, and capillary number,. We generate a phase diagram in the plane separating the wettability-independent (non-contact bouncing) and wettability-dependent (contact bouncing) regions. We show that is the optimum value of Weber number which can support a gas cushion for the widest range of Reynolds numbers. The phase diagram is further divided into five sub-regions based on the shape of the drop and the gas film beneath it. The simulations can reproduce experimentally reported gas films of with excellent agreement spatially and temporally. Simulations also reproduce well-known scaling laws for a variety of parameters characterising the gas film. New scaling laws for the radial extent of the gas film as well as time taken for impact are derived. For higher Weber and Reynolds numbers, a bouncing drop captures a gas bubble inside it consistent with simple experiments carried out for water drops bouncing on superhydrophobic surfaces.

A new approach for modeling viscoelastic thin film lubrication

Abstract: 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 ( W i ), 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 ϵ W i 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.

Calendering analysis of non-isothermal viscous nanofluid containing Cu-water nanoparticles using two co-rotating rolls:

Abstract: This study is a non-isothermal analysis of the calendering process using a water based nanofluid with Cu-nanoparticles. The basic flow equations are simplified under the lubrication approximation t...

Regimes of Soft Lubrication.

Abstract: Elastohydrodynamic lubrication, or simply soft lubrication, refers to the motion of deformable objects near a boundary lubricated by a fluid, and is one of the key physical mechanisms to minimise friction and wear in natural and engineered systems. Hence it is of particular interest to relate the thickness of the lubricant layer to the entrainment (sliding/rolling) velocity, the mechanical loading exerted onto the contacting elements, and properties of the elastic boundary. In this work we provide an overview of the various regimes of soft lubrication for two-dimensional cylinders in lubricated contact with compliant walls. We discuss the limits of small and large entrainment velocity, which is equivalent to large and small elastic deformations, as the cylinder moves near thick or thin elastic layers. The analysis focusses on thin elastic coatings, both compressible and incompressible, for which analytical scaling laws are not yet available in the regime of large deformations. By analysing the elastohydrodynamic boundary layers that appear at the edge of the contact, we establish the missing scaling laws - including prefactors. As such, we offer a rather complete overview of physically relevant limits of soft lubrication.

Mass transport by an oscillatory electroosmotic flow of power-law fluids in hydrophobic slit microchannels

Abstract: In this work, we study the hydrodynamics, concentration field, and mass transport of species due to an oscillatory electroosmotic flow that obeys a power law. An additional aspect that is considered in the analysis corresponds to the effect of the slippage condition at the walls of the microchannel. The governing equations that describe the involved phenomena are the following: equation of Poisson–Boltzmann for the electrical potential in the electric double layer, the momentum equation, and the species transport equation. These equations were simplified with the aid of the lubrication theory and were numerically solved by using a conventional finite difference scheme. Our results suggest that, under the slippage effects, the best conditions can be promoted for the mass transport of species for different values of the Schmidt number and Womersley numbers less than unity, and even it is maximized up to two orders of magnitude when $${\text {Wo}}>1$$ . In the analysis, the cross-over phenomenon appears for the mass transport for different species and it is identified for both Newtonian and non-Newtonian fluids. For shear-thinning fluids with slippage at the microchannel walls, the cross-over phenomenon occurs, and the species with less diffusivity can be transported up to ten times faster in comparison with Newtonian fluids when the no-slip effect is considered.

Axisymmetric evolution of gravity-driven thin films on a small sphere

Abstract: We study the axisymmetric evolution of a liquid film on a solid sphere governed by gravity, capillarity and viscous forces. The lubrication equations established in spherical coordinates are numerically solved using finite elements and local similarity solutions are obtained. Results show that the evolution behaves differently at early and late stages. At the early stage, the interface evolves in such a way that the capillary effect can be ignored. At the late stage, there emerge four zones from top to bottom: a thin film, a ridge ring, a dimple ring and a pendant drop. Each zone is governed by the balance of different forces, and hence is characterized by an individual physical mechanism. Consequently, the pendant drop is quasi-static, and the film thicknesses of other regions follow different scaling laws. The position of the dimple remains unchanged at the late stage.

Linear stability and nonlinear dynamics in a long-wave model of film flows inside a tube in the presence of surfactant

Abstract: A long-wave model based on lubrication theory is developed for the flow of a viscous liquid film lining the interior of a tube in the presence of an insoluble surfactant on the interface; no thin-film assumption is made. Linear stability analysis identifies two modes; in the absence of base flow, the ‘interface’ mode is the only unstable mode. The growth rates of this mode serve as an accurate predictor of how surfactant concentration increases plug formation time, and the effects of film thickness on this increase are quantified. In the presence of base flow, both the interface mode and ‘surfactant’ mode may be unstable, resulting in a richer variety of free-surface dynamics. In previous work, turning points in families of travelling wave solutions for a falling viscous film lining the interior of a vertical tube with a clean interface have been shown to be a good indicator of , provided the interface mode is linearly stable. When both modes are unstable, interpretation of these turning points as they relate to plug formation is more complicated. The study concludes by examining the impact of film thickness on growth rates and travelling wave solutions for core–annular flow with surfactant.

Fluid structure-interaction in a deformable microchannel conveying a viscoelastic fluid

Abstract: We theoretically analyze the interaction between a viscoelastic fluid flow, whose constitutive equation is the simplified Phan–Thien–Tanner model, and a deformable slender shallow microchannel. The microchannel top wall displacement is analyzed considering two cases: a) as a thin plate, using the Kirchhoff–Love theory, and b) as a thick plate, based on the Reissner–Mindlin theory. The mathematical model is nondimensionalized, and dimensionless parameters related to problem physics arise that control the fluid–structure interaction. The governing equations that describe the hydrodynamic field are simplified using the lubrication theory, and the displacement of the top wall is analyzed for each plate theory, relating the hydrodynamic pressure and the volumetric flow rate. These equations are implicit in the pressure and are solved numerically. The effect of dimensionless parameters on the pressure drop-volumetric flow rate relationship is analyzed, showing that for a viscoelastic fluid flowing through deformable channels, the volumetric flow rate is higher than the case of a Newtonian fluid under the same pressure. Our results are compared against those published in the specialized literature, showing an excellent agreement.

A novel two-indenter based micro-pump for lab-on-a-chip application: modeling and characterizing flows for a non-Newtonian fluid

Abstract: Inspired by the feeding mechanisms of a nematode, a novel two-indenter (2I) micro-pump is analyzed theoretically for transport and mixing of a non-Newtonian fluid for the purpose of lab-on-a-chip applications. Considering that the viscous forces dominate the flows in microscopic regime, the concept lubrication theory was adopted to device the two-dimensional flow model of the problem. By approximating the movements of the indenter as a sinusoidal function, the details of the flow were investigated for variations in—frequency of contraction of the first value keeping the second valve at higher occlusion, and occlusion. The study indicates that occlusive nature of the second valve leads to the large pressure barrier which prevents the fluid to enter into the neighboring compartment. Transport occurs as the lumen opens to develop a suction pressure. Pressure barrier is found to be highest for dilatants followed by Newtonian and pseudo-plastics. Shear stress dependency on frequency the contraction of the first value is highest for lower values of flow behavior index. In conclusion, the study provides details connecting the flows resulting from the indentation of the front-end indenter to the frequency of indentation, geometry and rheology of the fluid, thus facilitating optimal design of the micro-pumps.

Near-contact approach of two permeable spheres

Abstract: An analysis is presented for the axisymmetric lubrication resistance between permeable spherical particles. Darcy's law is used to describe the flow in the permeable medium and a slip boundary condition is applied at the interface. The pressure in the near-contact region is governed by a non-local integral equation. The asymptotic limit .

Effect of shear flow on the hydrodynamic drag force of a spherical particle near a wall evaluated using optical tweezers and microfluidics.

Abstract: The hydrodynamic drag force on a spherical particle in shear flow near-wall is investigated using optical tweezers and microfluidics. Simple shear flow is applied using a microfluidic channel at different volumetric flow rates. The hydrodynamic drag force exerted on the particle is detected from the displacement of the trapped particle. The effect of the wall is obtained from the force balance of the trapping and hydrodynamic drag force employing the exact solution of the theoretical model using the lubrication theory for a sphere near the wall. Here, we report the experimentally obtained hydrodynamic drag force coefficient under the influence of shear flow. The drag correction factor increases with decreasing distance from the wall due to the effect of the wall surface. We found that the calculated hydrodynamic drag force coefficient is in quantitative comparison with the theoretical prediction for a shear flow past a sphere near-wall. This study provides a straightforward investigation of the effect of the shear flow on the hydrodynamic drag force coefficient on a particle near the wall. Furthermore, these pieces of information can be used in various applications, particularly in optimizing microfluidic designs for mixing and separations of particles or exploiting the formation of the concentration gradient of particles perpendicular to flow directions caused by the non-linear hydrodynamic interactions.

On the effect of lubrication forces on the collision statistics of cloud droplets in homogeneous isotropic turbulence

Abstract: We investigate the dynamics of inertial particles in homogeneous isotropic turbulence, under one-way momentum coupling, using a new computational approach that incorporates the effect of long-range many-body aerodynamic interactions along with the short-range lubrication forces. The implementation couples hybrid direct numerical simulations (HDNS) with the analytical solutions of two rigid spheres moving in an unbounded fluid. Concerning the velocity field seen by the particles, the algorithm switches from the flow solution in terms of HDNS to analytical formulae when the separation distance between particles becomes comparable to their average radius. Standard HDNS is unable to correctly represent the short-range interactions since this method is based on the superposition of the Stokes solutions for single spheres. Our results show that for the turbulent kinetic energy dissipation rates typical of atmospheric clouds, the radial relative velocities (RRVs) of the droplets increase, and the radial distribution function (RDF) decreases in the near-contact region if the lubrication forces are taken into account. These changes are more pronounced when the effect of gravity is considered. Away from the contact region, there is not much change in RRVs and RDFs. For turbulent clouds with lower dissipation rates lubrication forces significantly enhance the average RRV in the limit of low Stokes number. This enhancement, however, is statistically insignificant because the number of particle pairs at close proximity is very small. The effect of mass loading on the collision statistics is also investigated, demonstrating an increase in RRV and a reduction in RDF with the droplet concentration.

Achieving Stable Patterns in Multicomponent Polymer Thin Films Using Marangoni and van der Waals Forces.

Abstract: Liquid-air interfaces can be deformed by surface-tension gradients to create topography, a phenomenon useful for polymer film patterning A recently developed method creates these gradients by photochemically patterning a solid polymer film Heating the film to the liquid state leads to flow driven by the patterned surface-tension gradients, but capillary leveling and diffusion of surface-active species facilitate eventual dissipation of the topography However, experiments demonstrate that using blends of high- and low-molar-mass polymers can considerably delay the decay in topography To gain insight into this observation, we develop a model based on lubrication theory that yields coupled nonlinear partial differential equations describing how the film height and species concentrations evolve with time and space Incorporation of a nonmonotonic disjoining pressure is found to significantly increase the lifetime of topographical features, making the model predictions qualitatively consistent with experiments A parametric study reveals the key variables controlling the kinetics of film deformation and provides guidelines for photochemically induced Marangoni patterning of polymer films

A Coupled Model of Angular-Contact Ball Bearing–Elastic Rotor System and Its Dynamic Characteristics Under Asymmetric Support

Abstract: This paper provides the dynamic model of an angular-contact ball bearing–elastic rotor system to study its dynamic characteristics when an asymmetric support mode is used. After defining global and local coordinate systems, necessary vectors (such as position, velocity, force and moment vector) are calculated according to the geometric relationship between each part (ball, cage and ring) of the bearing. The interactive forces between each part are obtained based on lubrication theory and Hertz contact theory. A typical rotor is discretized by finite element method (FEM) and each node of the rotor has 5 degrees of freedom (DOFs). Some constraint equations are built to form a coupled dynamic model of angular-contact ball bearing–elastic rotor system. The validity of this coupled model is verified by comparing the numerical results and experimental data. After analyzing the coupled model, it is found that the vibration spectrum of rotor includes the VC (varying compliance) frequencies of two bearings, the bending resonance frequency of rotor and the rotating frequency when the system has asymmetric ball bearings. Moreover, when the preloading forces of bearings increase, the support stiffness becomes larger and the rotor displacement decreases; moreover, the motions of balls and cage become more stable. Generally, the presented coupled model can be applied to analyze the vibration features of all parts in any ball bearing–rotor system comprehensively.

Non-unique bubble dynamics in a vertical capillary with an external flow

Abstract: We study bubble motion in a vertical capillary tube under an external flow. Bretherton (J. Fluid Mech., vol. 10, issue 2, 1961, pp. 166–188) has shown that, without external flow, a bubble can spontaneously rise when the Bond number (, thus suggesting non-unique, history-dependent solutions for the steady-state film thickness under the same external flow conditions. Furthermore, inertialess symmetry-breaking shape profiles at steady state are found as the bubble transits near the tipping points of the solution branches, which are shown in both experiments and three-dimensional numerical simulations.

Deformation and relaxation of viscous thin films under bouncing drops

Abstract: Thin, viscous liquid films subjected to impact events can deform. Here we investigate free-surface oil-film deformations that arise owing to the build up of air under the impacting and rebouncing of water drops. Using digital holographic microscopy, we measure the three-dimensional surface topography of the deformed film immediately after the drop rebound, with a resolution down to 20 nm. We first discuss how the film is initially deformed during impact, as a function of film thickness, film viscosity and drop impact speed. Subsequently, we describe the slow relaxation process of the deformed film after the rebound. Scaling laws for the broadening of the width and the decay of the amplitude of the perturbations are obtained experimentally and found to be in excellent agreement with the results from a lubrication analysis. We finally arrive at a detailed spatio–temporal description of the oil-film deformations that arise during the impact and rebouncing of water drops.

Thin-film smoothed particle hydrodynamics fluid

Abstract: We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with the dimensionality reduced using the asymptotic lubrication theory and customize a set of differential operators based on the weakly compressible Smoothed Particle Hydrodynamics (SPH) for evolving pointset surfaces. The key insight is that the compressible nature of SPH, which is unfavorable in its typical usage, is helpful in our application to co-evolve the thickness, calculate the surface tension, and enforce the fluid incompressibility on a thin film. In this way, we are able to two-way couple the surface deformation with the in-plane flows in a physically based manner. We can simulate complex vortical swirls, fingering effects due to Rayleigh-Taylor instability, capillary waves, Newton's interference fringes, and the Marangoni effect on liberally deforming surfaces by presenting both realistic visual results and numerical validations. The particle-based nature of our system also enables it to conveniently handle topology changes and codimension transitions, allowing us to marry the thin-film simulation with a wide gamut of 3D phenomena, such as pinch-off of unstable catenoids, dripping under gravity, merging of droplets, as well as bubble rupture.

Design of logarithmic crowned roller for tapered roller bearings based on the elastohydrodynamic lubrication model

Abstract: The purpose of this paper is to study the film-forming capacity of logarithmic crowned roller for tapered roller bearing (TRB) and to design a tapered roller profile based on an elastohydrodynamic lubrication model.,A coupled model, incorporating a quasi-static model of TRBs and an elastohydrodynamic lubrication model was developed to investigate the load distribution of TRB and to evaluate the lubrication state of tapered roller/raceway contact.,The model is verified with published literature results. Parametric analysis is conducted to investigate the effect of crown drop on azimuthal load distribution of the roller, film thickness and pressure distribution in the contact area. The result shows that crown drop has little influence on the azimuthal load distribution; also, the film thickness and the pressure distribution are asymmetric. When the tapered roller is designed and manufactured, the crown drop of the small end should be larger than that in the large end.,Precise roller profile design is conducive to improve the fatigue life of TRBs. Currently, most crown design methods neglect the influence of lubrication, which can lead to a non-suitable roller profile. Therefore, the present work is undertaken to optimize roller profiles based on lubrication theory.

Electroosmotically driven flow of micropolar bingham viscoplastic fluid in a wavy microchannel: application of computational biology stomach anatomy

Abstract: A comprehensive mathematical model is presented to study the peristaltic flow of Bingham viscoplastic micropolar fluid flow inside a microlength channel with electro-osmotic effects. The electro-osmotic effects are produced due to an axially applied electric field. The circulation of this electric potential is calculated by utilizing Poisson Boltzmann equation. The dimensionless form of mathematical equations is obtained by using lubrication theory and Debye-Huckel approximation. We have obtained analytical solutions for the final dimensionless governing equations. Finally, the graphical results are added to further discuss the physical aspects of the problem. Electro-osmotic is mainly helping to control the flow and axial velocity decreases with an increase in the electric field but micro-angular velocity increases with an increase in electric field.