Showing papers on "Lubrication theory published in 2017"

Electro-osmotic flow of couple stress fluids in a micro-channel propagated by peristalsis

Abstract: A mathematical model is developed for electro-osmotic peristaltic pumping of a non-Newtonian liquid in a deformable micro-channel. Stokes' couple stress fluid model is employed to represent realistic working liquids. The Poisson-Boltzmann equation for electric potential distribution is implemented owing to the presence of an electrical double layer (EDL) in the micro-channel. Using long wavelength, lubrication theory and Debye-Huckel approximations, the linearized transformed dimensionless boundary value problem is solved analytically. The influence of electro-osmotic parameter (inversely proportional to Debye length), maximum electro-osmotic velocity (a function of external applied electrical field) and couple stress parameter on axial velocity, volumetric flow rate, pressure gradient, local wall shear stress and stream function distributions is evaluated in detail with the aid of graphs. The Newtonian fluid case is retrieved as a special case with vanishing couple stress effects. With increasing the couple stress parameter there is a significant increase in the axial pressure gradient whereas the core axial velocity is reduced. An increase in the electro-osmotic parameter both induces flow acceleration in the core region (around the channel centreline) and it also enhances the axial pressure gradient substantially. The study is relevant in the simulation of novel smart bio-inspired space pumps, chromatography and medical micro-scale devices.

Soft Matter Lubrication: Does Solid Viscoelasticity Matter?

Abstract: Classical lubrication theory is unable to explain a variety of phenomena and experimental observations involving soft viscoelastic materials, which are ubiquitous and increasingly used in e.g. engineering and biomedical applications. These include unexpected ruptures of the lubricating film and a friction–speed dependence, which cannot be elucidated by means of conventional models, based on time-independent stress–strain constitutive laws for the lubricated solids. A new modeling framework, corroborated through experimental measurements enabled via an interferometric technique, is proposed to address these issues: Solid/fluid interactions are captured thanks to a coupling strategy that makes it possible to study the effect that solid viscoelasticity has on fluid film lubrication. It is shown that a newly defined visco-elasto-hydrodynamic lubrication (VEHL) regime can be experienced depending on the degree of coupling between the fluid flow and the solid hysteretic response. Pressure distributions show a m...

Analytical study of electro-osmosis modulated capillary peristaltic hemodynamics

Abstract: A mathematical model is developed to analyse electro-kinetic effects on unsteady peristaltic transport of blood in cylindrical vessels of finite length. The Newtonian viscous model is adopted. The analysis is restricted under Debye-Huckel linearization (i.e. wall zeta potential less than or equal to 25mV is sufficiently small). The transformed, non-dimensional conservation equations are derived via lubrication theory and long wavelength and the resulting linearized boundary value problem is solved exactly. The case of a thin electric double layer (i.e. where only slip electro-osmotic velocity considered) is retrieved as a particular case of the present model. The response in pumping characteristics (axial velocity, pressure gradient or difference, volumetric flow rate, local wall shear stress) to the influence of electro-osmotic effect (inverse Debye length) and Helmholtz-Smoluchowski velocity is elaborated in detail. Visualization of trapping phenomenon is also included and the bolus dynamics evolution with electro-kinetic effects examined. A comparative study of train wave propagation and single wave propagation is presented under the effects of thickness of EDL and external electric field. The study is relevant to electrophoresis in haemotology, electrohydrodynamic therapy and biomimetic electro-osmotic pumps.

Viscoplastic boundary layers

Abstract: In the limit of a large yield stress, or equivalently at the initiation of motion, viscoplastic flows can develop narrow boundary layers that provide either surfaces of failure between rigid plugs, the lubrication between a plugged flow and a wall or buffers for regions of predominantly plastic deformation. Oldroyd ( Proc. Camb. Phil. Soc. , vol. 43, 1947, pp. 383–395) presented the first theoretical discussion of these viscoplastic boundary layers, offering an asymptotic reduction of the governing equations and a discussion of some model flow problems. However, the complicated nonlinear form of Oldroyd’s boundary-layer equations has evidently precluded further discussion of them. In the current paper, we revisit Oldroyd’s viscoplastic boundary-layer analysis and his canonical examples of a jet-like intrusion and flow past a thin plate. We also consider flow down channels with either sudden expansions or wavy walls. In all these examples, we verify that viscoplastic boundary layers form as envisioned by Oldroyd. For each example, we extract the dependence of the boundary-layer thickness and flow profiles on the dimensionless yield-stress parameter (Bingham number). We find that, while Oldroyd’s boundary-layer theory applies to free viscoplastic shear layers, it does not apply when the boundary layer is adjacent to a wall, as has been observed previously for two-dimensional flow around circular obstructions. Instead, the boundary-layer thickness scales in a different fashion with the Bingham number, as suggested by classical solutions for plane-parallel flows, lubrication theory and, for flow around a plate, by Piau ( J. Non-Newtonian Fluid Mech. , vol. 102, 2002, pp. 193–218); we rationalize this second scaling and provide an alternative boundary-layer theory.

Probing the Effect of Salinity and pH on Surface Interactions between Air Bubbles and Hydrophobic Solids: Implications for Colloidal Assembly at Air/Water Interfaces.

Abstract: In this work, a bubble probe atomic force microscope (AFM) was employed to quantify the interactions between two air bubbles and between an air bubble and an octadecyltrichlorosilane (OTS)-hydrophobized mica under various aqueous conditions. The key parameters (e.g., surface potentials, decay length of hydrophobic attraction) were obtained by analyzing the measured forces through a theoretical model based on Reynolds lubrication theory and an augmented Young-Laplace equation by including effect of disjoining pressure. The bubble-OTS hydrophobic attraction with a decay length of 1.0 nm was found to be independent of solution pH and salinity. These parameters were further used to predict the attachment of OTS-hydrophobized particles onto the air/water interface, demonstrating that particle attachment driven by hydrophobic attraction could be facilitated by suppressing electrical double-layer repulsion at low pH or high salinity condition. This facile methodology can be readily extended to quantify interactions of many other colloidal particles with gas/water and oil/water interfaces, with implications for colloidal assembly at different interfaces in many engineering applications.

Extended lubrication theory: improved estimates of flow in channels with variable geometry

Abstract: Lubrication theory is broadly applicable to the flow characterization of thin fluid films and the motion of particles near surfaces. We offer an extension to lubrication theory by starting with Stokes equations and considering higher-order terms in a systematic perturbation expansion to describe the fluid flow in a channel with features of a modest aspect ratio. Experimental results qualitatively confirm the higher-order analytical solutions, while numerical results are in very good agreement with the higher-order analytical results. We show that the extended lubrication theory is a robust tool for an accurate estimate of pressure drop in channels with shape changes on the order of the channel height, accounting for both smooth and sharp changes in geometry.

Elastic deformation of soft coatings due to lubrication forces.

Abstract: Elastic deformation of rigid materials with soft coatings (stratified materials) due to lubrication forces can alter the interpretation of dynamic surface forces measurements and prevent contact formation between approaching surfaces. Understanding the role of elastic deformation on the process of fluid drainage is necessary, in particular for the case where one (or both) of the interacting materials consists of a rigid substrate with a soft coating. We combine lubrication theory and solid linear elasticity to describe the dynamic of fluid drainage past a compliant stratified boundary. The analysis presented covers the full range of coating thicknesses, from an elastic foundation to a half-space for an incompressible coating. We decouple the individual contributions of the coating thickness and material properties on the elastic deformation, hydrodynamic forces, and fluid film thickness. We obtain a simple expression for the shift in contact position during force measurements that is valid for many experimental conditions. We compare directly the effect of stratification on the out-of-contact deformation to the well-known effect of stratification on indentation. We show that corrections developed for stratification in contact mechanics are not applicable to elastohydrodynamic deformation. Finally, we provide generalized contour maps that can be employed directly to estimate the elastic deformation present in most dynamic surface force measurements.

Analysis of Turbulence and Convective Inertia in a Water-Lubricated Tilting-Pad Journal Bearing Using Conventional and CFD Approaches

Abstract: The influence of turbulence and convective fluid inertia in a water-lubricated journal bearing was investigated using two types of models: a “conventional” solution based on traditional lubrication theory (Reynolds equation) and a more rigorous computational fluid dynamics (CFD) program containing a full Navier-Stokes solution The calculations reveal that turbulence accounts for around 50% of the load capacity in the water-lubricated bearing studied, highlighting the importance of accurate characterization of turbulence in such applications Convective inertia, also referred to as transport inertia because it depends only on the spatial parameters within the film rather than time-dependent journal motions, was found to lower the static film pressures (load capacity) by about 6% compared to an inertialess solutionHydrodynamic pressures calculated by the conventional Reynolds solution were initially about 30% lower than those of the more rigorous CFD model for the water-lubricated bearing operatin

The influence of surface texturing on the transition of the lubrication regimes between a piston ring and a cylinder liner

Abstract: This article employs a mixed lubrication model to investigate the performance of the textured surface. The Jakobsson–Floberg–Olsson model is used to obtain the hydrodynamic support of the textured ...

Roll coating analysis of a third grade fluid

Abstract: This paper studies the roll-coating process of an incompressible viscoelastic fluid, where the roll and the web have equal velocities. The lubrication approximation theory is used to simplify the e...

Slip-enhanced drop formation in a liquid falling down a vertical fibre

Abstract: For a liquid film falling down along a vertical fibre, classical theory (Kalliadasis & Chang J. Fluid Mech., vol. 261, 1994, pp. 135–168; Yu & Hinch J. Fluid Mech., vol. 737, 2013, pp. 232–248) showed that drop formation can occur due to capillary instability when the Bond number is below the critical value , where is the fluid density, is the gravitational acceleration, is the fibre radius, is the surface tension and is the unperturbed film thickness. However, the experiment by Quere (Europhys. Lett., vol. 13 (8), 1990, pp. 721–726) found , which is slightly greater than the above theoretical value. Here we offer a plausible way to resolve this discrepancy by including additional wall slip whose amount can be measured by the slip parameter , where is the slip length. Using lubrication theory, we find that wall slip promotes capillary instability and, hence, enhances drop formation. In particular, when slip effects are strong ( ), the transition films and the drop height scale as and , respectively, distinct from those found by Yu & Hinch for the no-slip case where is the travelling speed. In addition, for , is found to increase with according to , offering a possible explanation why the found by Quere is slightly greater than that predicted by the no-slip model. Using the above expression, the estimated slip length in Quere’s experiment is found to be of the order of several micrometres, consistent with the typical slip length range 1– for polymeric liquids such as silicone oil used in his experiment. The existence of wall slip in Quere’s experiment is further supported by the observation that the film thinning kinetics exhibits the no-slip result for early times and changes to the strong slip result , where is the film thickness. We also show that when the film is ultrathin, although capillary instability can become further amplified by strong slip effects, the instability can be arrested by the equally intensified gravity draining in the weakly nonlinear regime whose dynamics is governed by the Kuramoto–Sivashinsky equation.

On the viscoplastic squeeze flow between two identical infinite circular cylinders.

Abstract: Direct numerical simulations of closely interacting infinite circular cylinders in a Bingham fluid are presented, and results compared to asymptotic solutions based on lubrication theory in the gap Unlike for a Newtonian fluid, the macroscopic flow outside of the gap between the cylinders is shown to have a large effect on the pressure profile within the gap and the resulting lubrication force on the cylinders The presented results indicate that the asymptotic lubrication solution can be used to predict the lubrication pressure only if the surrounding viscoplastic matrix is yielded by a macroscopic flow This has implications for the use of sub-grid-scale lubrication models in simulations of non-colloidal particulate suspensions in viscoplastic fluids

An extended Landau-Levich model for the dragging of a thin liquid film with a propagating surface acoustic wave

Abstract: In this paper we revisit the Landau and Levich analysis of a coating flow in the case where the flow in the thin liquid film is supported by a Rayleigh surface acoustic wave (SAW), propagating in the solid substrate. Our theoretical analysis reveals that the geometry of the film evolves under the action of the propagating SAW in a manner that is similar to the evolution of films that are being deposited using the dip coating technique. We show that in a steady state the thin-film evolution equation reduces to a generalized Landau–Levich equation with the dragging velocity, imposed by the SAW, depending on the local film thickness. We demonstrate that the generalized Landau–Levich equation has a branch of stable steady state solutions and a branch of unstable solutions. The branches meet at a saddle-node bifurcation point corresponding to the threshold value of the SAW intensity. Below the threshold value no steady states were found and our numerical computations suggest a gradual thinning of the liquid film from its initial geometry.

A Comparison of the Roughness Regimes in Hydrodynamic Lubrication

Abstract: This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, wit ...

Buoyant miscible displacement flows in rectangular channels

Abstract: Buoyant displacement flows of two miscible fluids in rectangular channels are studied, theoretically and experimentally. The scenario considered involves the displacement of a fluid by a slightly heavier one at nearly horizontal channel inclinations, where inertial effects are weak and laminar stratified flows may be expected. In the theoretical part, a lubrication approximation model is developed to simplify the displacement flow governing equations and furnish a semi-analytical solution for the heavy and light fluid flux functions. Three key dimensionless parameters govern the fluid flow motion, i.e. a buoyancy number, the viscosity ratio and the channel cross-section aspect ratio. When these parameters are specified, the reduced model can deliver the interface propagation in time, leading and trailing front heights, shapes and speeds, cross-sectional velocity fields, etc. In addition, the model can be exploited to provide various classifications such as single or multiple fronts as well as main displacement flow regimes at long times such as no sustained backflows, stationary interface flows and sustained backflows. Focusing on the variation of the buoyancy number, a large number of iso-viscous displacement experiments are performed in a square duct and the results are compared with those of the lubrication model. Qualitative displacement flow features observed in the theory and experiments are in good agreement, in particular, in terms of the main displacement flow regimes. The quantitative comparisons are also reasonable for small and moderate imposed displacement flow velocities. However, at large flow rates, a deviation of the experimental results from the model results is observed, which may be due to the presence of non-negligible inertial effects.

Boundary-induced autophoresis of isotropic colloids: anomalous repulsion in the lubrication limit

Abstract: When suspended in a liquid solution, chemically active colloids may self-propel due to an asymmetry in either particle shape or the interfacial distribution of solute absorption. We here consider a chemically homogeneous spherical particle which undergoes self-diffusiophoresis due to the presence of nearby inert wall. In particular, we focus upon the near-contact limit where it was recently observed (Yariv, Phys. Rev. Fluids, vol. 1 (3), 2016, 032101) that the solute-concentration profile within the narrow gap separating the particle and the wall cannot be uniquely determined by a gap-scale analysis. We here revisit this near-contact limit using matched asymptotic expansions, the inner region being the gap domain and the outer region being on the particle scale. Asymptotic matching with the Hankel-transform representation of the outer distribution of solute concentration serves to determine both the scaling and magnitude of the corresponding inner profile. The ensuing gap-scale pressure field, set by a lubrication mechanism, gives rise to an anomalous particle–wall interaction, scaling as an irrational power of the gap clearance.

The dam-break problem for eroding viscoplastic fluids.

Abstract: Natural gravity-driven flows can increase in volume by eroding the bed on which they descend. This process is called basal entrainment and is thought to play a key role in the bulk dynamics of geophysical flows. Although its study is difficult using field measurements, basal entrainment is more easily amenable to analysis using laboratory experiments. We studied basal entrainment by conducting dam-break experiments releasing a fixed amount of viscoplastic fluid (a Herschel–Bulkley fluid) on a sloping, erodible bed of fixed depth. Entrainment was observed continuously, far from the sidewalls, using cameras. Bed material was quickly entrained, which led to flow advancement. Although the slope inclination had clear effects on the entrainment mechanisms, as shown by the internal measurements, this did not translate into faster front progression. Instead, the depth and length of the entrainable material were the most important controlling parameters of front velocity, as the surge scoured out the entrainable layer, pushing the entrainable material downstream and following the rigid bed’s geometry. Bulk measurements (front position and flow depth profile) were also compared with predictions from lubrication theory.

From red cells to soft lubrication, an experimental study of lift generation inside a compressible porous layer

Abstract: It is a new concept for porous media flow that a hydrodynamic lifting force is generated inside a highly compressible porous layer as a planing surface glides over it. The concept originated from the observation of the pop-out phenomena of red blood cells over the endothelial glycocalyx layer (EGL) lining the inner surface of our blood vessels (Feng & Weinbaum, J. Fluid Mech., vol. 422, 2000, pp. 282–317). In the current paper, we report an experimental study to examine this concept. A novel testing set-up was developed that consists of a running conveyer belt covered with a soft porous sheet, and a fully instrumented upper planar board, i.e. planing surface. The generation of pore pressure was observed and captured by pressure transducers when the planing surface glides over the porous sheet. Its distribution strongly depends on the relative velocity between the planing surface and the running belt, the mechanical and transport properties of the porous sheet as well as the compression ratios at the leading and trailing edges. The relative contribution of the transiently trapped air to the total lift was evaluated by comparing the pore pressure to the total lifting pressure measured by a load cell mounted between two adjacent pressure transducers. For a typical running condition with a polyester porous material ( , , , where , , are the porous layer thickness at the leading and trailing edges, respectively; is the un-deformed porous layer thickness; and is the velocity of the running belt), over 68 % of the local lift is generated by the pore pressure. The results conclusively verified the validity of lift generation in a highly compressible porous layer as a planing surface glides over it. This study provides the foundation for the application of highly compressible porous media for soft lubrication with minimal frictional losses. It also sheds some light on the biophysics study of the EGL.

Stokes' third problem for Herschel-Bulkley fluids.

Abstract: Herschel–Bulkley materials can be set in motion when a sufficiently high shear stress or body force is applied to them. We investigate the behaviour of a layer of Herschel–Bulkley fluid when it is suddenly tilted and subject to gravitational forces. The material’s dynamic response depends on the details of its constitutive equation. When its rheological behaviour is viscoelastoplastic with no thixotropic behaviour, the material is set in motion instantaneously along its entire base. When its rheological behaviour involves two yield stresses (static and dynamic yield stresses), the material must be destabilised before it starts to flow. This problem is thus similar to a Stefan problem, with an interface that separates the sheared and unsheared regions and moves from top to bottom. We estimate the time needed to set the layer in motion in both cases. We also compare the solution to the local balance equations with the solution to the depth-averaged mass and momentum equations and show that the latter does not provide consistent solutions for this flow geometry.

Lubrication force model for a pendular liquid bridge of power-law fluid between two particles

Abstract: The validity of the lubrication force model on particles in the normal direction due to a pendular liquid bridge of power-law fluid based on the Reynolds lubrication theory is investigated by comparing it with Direct Numerical Simulation (DNS) results. It is found that the model can predict the force with less than 10% error when the dimensionless separation distance is smaller than 0.05. In the DNS results, a spike of the pressure at the edge of the bridge as well as a drop in pressure around the axis connecting the centres of the particles are observed on the particle surface. It is revealed that these phenomena are caused by the component of the viscous stress tensor which is neglected in the lubrication theory. A new closed-form solution of the lubrication force model is also proposed in this study which can be easily incorporated into the Discrete Element Method (DEM) framework.

MHD mixed convection stagnation point flow of a viscous fluid over a lubricated vertical surface

Abstract: Purpose An attempt is made to study magnetohydrodynamic viscous fluid impinging orthogonally toward a stagnation point on a vertical surface lubricated with power law fluid. It has been assumed that the surface temperature varies linearly with the distance from the stagnation point. The problem is governed by system of partial differential equations for both the base fluid and the lubricant. The continuity of velocity and shear stress is assumed at the interface layer between the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions. The influence of various important parameters is presented in the form of graphs and tables. The limiting cases for full and no-slip conditions are deduced from the present solutions. A comparison of the present results with the existing results in the special case validates the obtained numerical solutions. The purpose of this study is to see the behaviour of flow characteristics in the presence of lubrication. Design/methodology/approach The authors’ problem is governed by system of partial differential equations for both the base fluid and the lubricant. Dimensionless variables are introduced to transform original problem into ordinary differential equations. The obtained ordinary differential equation along with boundary conditions are highly nonlinear and coupled. An implicit finite-difference scheme known as the Keller-Box method is implemented to obtain the numerical solutions. Findings Some findings of this study are that the lubricant increases the velocity of the base fluid inside the boundary layer. In the case of full slip, the effects of viscosity are suppressed by the lubricant. The temperature of the base fluid decreases by increase in lubrication on the surface. By increasing the slip on the surface, the skin friction decreases and local Nusselt number increases, but the rate of increase or decrease is less in magnitude for the case of opposing flow. The similarity solutions only exist for n = 1/2. A non-similar solution is obtained for the other values of the power-law index n. Originality/value The study of flow phenomenon over a lubricated surface has important applications in machinery components such as fluid bearings and mechanical seals. Coating is another major application of lubrication including the preparation of thin films, printing, painting, etc. The authors hope that the current study will provide the roadmap for the future studies in this direction.

Trapping and displacement of liquid collars and plugs in rough-walled tubes

Abstract: A liquid film wetting the interior of a long circular cylinder redistributes under the action of surface tension to form annular collars or occlusive plugs. These equilibrium structures are invariant under axial translation within a perfectly smooth uniform tube and therefore can be displaced axially by very weak external forcing. We consider how this degeneracy is disrupted when the tube wall is rough, and determine threshold conditions under which collars or plugs resist displacement under forcing. Wall roughness is modelled as a non-axisymmetric Gaussian random field of prescribed correlation length and small variance, mimicking some of the geometric irregularities inherent in applications such as lung airways. The thin film coating this surface is modelled using lubrication theory. When the roughness is weak, we show how the locations of equilibrium collars and plugs can be identified in terms of the azimuthally averaged tube radius; we derive conditions specifying equilibrium collar locations under an externally imposed shear flow, and plug locations under an imposed pressure gradient. We use these results to determine the probability of external forcing being sufficient to displace a collar or plug from a rough-walled tube, when the tube roughness is defined only in statistical terms.

Analysis of vibration characteristic for helical gear under hydrodynamic conditions

Abstract: Based on the elasto-hydrodynamic lubrication theory, a 2-degree-of-freedom nonlinear dynamic model of helical gears with double-sided film is proposed, in which the minimum film thickness behaves a...

Dynamics of spreading thixotropic droplets

Abstract: The effect of thixotropy on the two-dimensional spreading of a sessile drop is modelled using lubrication theory. Thixotropy is incorporated by the inclusion of a structure parameter, λ, measuring structure build-up governed by an evolution equation linked to the droplet micromechanics. A number of models are derived for λ coupled to the interface dynamics; these range from models that account for the cross-stream dependence of λ to simpler ones in which this dependence is prescribed through appropriate closures. Numerical solution of the governing equations show that thixotropy has a profound effect on the spreading characteristics; the long-time spreading dynamics, however, are shown to be independent of the initial structural state of the droplet. We also compare the predictions of the various models and determine the range of system parameters over which the simple models provide sufficiently good approximations of the full, two-dimensional spreading dynamics.

Dynamics and stability of three-dimensional ferrofluid films in a magnetic field

Abstract: We consider the interfacial dynamics of a thin, ferrofluid film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. The fluid is assumed to be weakly conducting, and its dynamics are governed by a coupled system of the steady Maxwell, Navier–Stokes, and continuity equations. The magnetization of the film is a function of the magnetic field, and is prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure, velocity, and magnetic fields inside the film. The potential in the gas phase is solved by means of Fourier Transforms. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape, via use of the kinematic condition, and the magnetic field. We study the three-dimensional evolution of the film to spanwise perturbations by solving the nonlinear equations numerically. The constant-volume configuration is considered, which corresponds to a slender drop flowing down an incline. A parametric study is then performed to understand the effect of the magnetic field on the stability and structure of the interface.