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This article presents a vibration model of neighboring rolling parts that takes into account non-smooth symmetric collisions. This model was used to examine the motion state of the rolling element and the collision force between nearby rolling elements. It also determined the motion posture and overall collision form of the rolling element after setting the functional slot. Afterwards, the level of disorderly movement and the structure of the moving object were examined and confirmed through the use of a phase diagram of the motion system in relation to zero symmetry, the Lyapunov exponent, and a platform for measuring irregular vibrations in the bearing. This work aims to clarify the factors that contribute to the persistent chaotic state of rolling elements in bearing vibration. [ABSTRACT FROM AUTHOR]

With the increasing demand for active friction control, we newly proposed to use dielectrophoresis to change the flow of PG-droplet-containing PAO4 to reduce the friction coefficient. The friction result with a 1-mm roller shows 20% reduction in friction coefficient (from 0.065 to 0.052) at AC 100 V, and in situ observation exhibits that PG tracks are formed over the contact area. On the other hand, at a high bias of 1000 V, the friction coefficient increases to 0.065. In this situation, in situ observation exhibits that PG forms a horseshoe-shaped track covering only the roller edges. Controlled friction tests and FEM analysis using 5-mm rollers revealed a unique behavior; a balanced bias effectively attracts the PG to the roller surface, and surface forces can resist mild dielectrophoretic forces to spread the PG across the roller surface. The present study strongly suggests the importance that the bias strength should be controlled to achieve a balance between surface force and dielectrophoretic force in order to obtain excellent lubrication conditions.

This article presents a vibration model of neighboring rolling parts that takes into account non-smooth symmetric collisions. This model was used to examine the motion state of the rolling element and the collision force between nearby rolling elements. It also determined the motion posture and overall collision form of the rolling element after setting the functional slot. Afterwards, the level of disorderly movement and the structure of the moving object were examined and confirmed through the use of a phase diagram of the motion system in relation to zero symmetry, the Lyapunov exponent, and a platform for measuring irregular vibrations in the bearing. This work aims to clarify the factors that contribute to the persistent chaotic state of rolling elements in bearing vibration.

[Display omitted] The Landau-Levich-Derjaguin (LLD) theory is widely applied to predict the film thickness in the dip-coating process. However, the theory was designed only for flat plates and thin fibers. Fifty years ago, White and Tallmadge attempted to generalize the LLD theory to thick rods using a numerical solution for a static meniscus and the LLD theory to forcedly match their numeric solution with the LLD asymptotics. The White-Talmadge solution has been criticized for not being rigorous yet widely used in engineering applications mostly owing to the lack of alternative solutions. A new set of experiments significantly expanding the range of White-Tallmadge conditions showed that their theory cannot explain the experimental results. We then hypothesized that the results of LLD theory can be improved by restoring the non-linear meniscus curvature in the equation. With this modification, the obtained equation should be able to describe static menisci on any cylindrical rods and the film profiles observed at non-zero rod velocity. To test the hypothesis, we distinguished capillary forces from viscous forces by running experiments with different rods and at different withdrawal velocities and video tracking the menisci profiles and measuring the weight of deposited films. The values of film thickness were then fitted with a mathematical model based on the modified LLD equation. We also fitted the meniscus profiles. The results show that the derived equation allows one to reproduce the results of the LLD theory and go far beyond those to include rods of different radii. A new set of experimental data together with the White-Tallmadge experimental data are explained with the modified LLD theory. A set of simple formulas approximating numeric results have been derived. These formulas can be used in engineering applications for the prediction of the coating thickness. [ABSTRACT FROM AUTHOR]

In this paper, we studied the squeeze flow between circular disks of a new class of fluids defined by an implicit relation referred to as stress power law fluids. The constitutive response of these fluids was written expressing the symmetric part of the velocity gradient as a tensorial function of the Cauchy stress. We assumed that the aspect ratio between the gap separating the disks and the radius was small so that a lubrication expansion could be adopted. We wrote the general problem and looked for a solution that could be written in terms of the small aspect ratio parameter. We obtained a sequence of problems that could be solved iteratively at each order, and we focused on the leading and first order, deriving explicit expressions for the velocity field, stress, and pressure.

Gels are a drug delivery platform that is being evaluated for application of active pharmaceutical ingredients, termed microbicides, that act topically against vaginal and rectal mucosal infection by sexually transmitted HIV. Despite success in one Phase IIb trial of a vaginal gel delivering tenofovir, problems of user adherence to designed gel application scheduling have compromised results in two other trials. The microbicides field is responding to this dilemma by expanding behavioral analysis of the determinants of adherence while simultaneously improving the pharmacological, biochemical, and biophysical analyses of the determinants of microbicide drug delivery. The intent is to combine results of these two complementary perspectives on microbicide performance and epidemiological success to create an improved product design paradigm. Central to both user sensory perceptions and preferences, key factors that underlie adherence, and to vaginal gel mucosal drug delivery, that underlies anti-HIV efficacy, are gel properties (e.g. rheology) and volume. The specific engineering problem to be solved here is to develop a model for how gel rheology and volume, interacting with loaded drug concentration, govern the transport of the microbicide drug tenofovir into the vaginal mucosa to its stromal layer. These are factors that can be controlled in microbicide gel design. The analysis here builds upon our current understanding of vaginal gel deployment and drug delivery, incorporating key features of the gel's environment, the vaginal canal, fluid production and subsequent gel dilution, and vaginal wall elasticity. These have not previously been included in the modeling of drug delivery. We consider the microbicide drug tenofovir, which is the drug most completely studied for gels: in vitro , in animal studies in vivo , and in human clinical trials with both vaginal or rectal gel application. Our goal is to contribute to improved biophysical and pharmacological understanding of gel functionality, providing a computational tool that can be used in future vaginal microbicide gel design. [ABSTRACT FROM AUTHOR]

We derive a general evolution equation for a shallow layer of a generalised Newtonian fluid undergoing two-dimensional gravity-driven flow on an inclined plane. The flux term appearing in this equation is expressed in terms of an integral involving the prescribed constitutive relation and, crucially, does not require explicit knowledge of the velocity profile of the flow; this allows the equation to be formulated for any generalised Newtonian fluid. In particular, we develop general solutions for travelling waves on a mild slope and for kinematic waves on a moderately steep slope; these results provide simple and accessible models of, for example, the propagation of non-Newtonian mud and debris flows. [ABSTRACT FROM AUTHOR]

The gear lubrication oil-supply model was established, and with considering the equivalent thickness hoil, the slide-roll oil ratioξ and friction coefficient μ and other factors, an starved EHL full numerical solution of the gear transmission was obtained in line contacts under thermal condition based on the multigrid method. The results show that with the increase of the degree of inlet starvation, the oil film thickness is reduced and the average temperature is raised, and oil film pressure distribution tends to dry friction state of Hertz contact, which may lead to lubrication failure. By analyzing the relationship of the parameters such as hoil, ξ,μ and other factors oil and the temperature rise, we can draw that the temperature rise of the gear contact area is a direct cause of lubrication failure under a starvation condition. Also through the mist lubrication experiments, the micro EHL numerical results with macroscopic oil-supply is linked, which provides a basis for reference for gear lubrication flow design. Elastic hydrodynamic lubrication (EHL) is the main lubrication in gear meshing transmission process of low speed and heavy loading form. Traditional EHL research are based on sufficient oil supply conditions, namely the upstream boundary lubrication area far enough away from the contact area, oil supply quantity is big enough. If the upstream boundary near the contact zone too, can reduce oil, lubricant film thickness decreases, the lubrication state which called oil starvation lubrication. The research of gear transmission thermal EHL temperature rise under the condition of oil starvation started in recent years, Venner [1] discussed the elastic deformation between the point contact under this oil starvation condition, Lu Leilei[2] researched the influence of rough surface under the condition of oil starvation to non- newtonian thermal film lubrication point contact, Tan Hongen[3] studied the analysis problem of point contact EHL under the condition of oil starvation, Lv Xianqi[4] and Yang Peiran[5] also made analysis to the gear lubrication flow problem. [ABSTRACT FROM AUTHOR]

Abstract: Drug delivery of topical microbicidal molecules against HIV offers promise as a modality to prevent sexual transmission of the virus. Success of any microbicide product depends, in an interactive way, upon its drug (the microbicide active pharmaceutical ingredient, API) and its delivery system (e.g. a gel, film or intravaginal ring). There is a widespread agreement that more effective drug delivery vehicles, as well as better APIs, must be developed to improve the efficacy of microbicide products. Non-Newtonian gels are primary microbicide vehicles, but those to date have been created with limited understanding of how their properties govern their spreading and retention in the vagina, which, in turn, govern successful drug delivery. Here, we apply fundamental fluid mechanical and physicochemical transport theory to help better understand how successful microbicide API delivery depends upon properties of a gel and the vaginal environment. We address several critical components of this complex process, including: elastohydrodynamic flow of the bolus of a non-Newtonian fluid; and mass transfer due to inhomogeneous dilution of the gel by vaginal fluid contacting it along a moving boundary (the locally deforming vaginal epithelial surface). Local dilution of gel alters local rheological properties. We evaluated this experimentally, delineating the way that constitutive parameters of a shear-thinning gel are modified by dilution. We supplement the Reynolds lubrication equation with a mass conservation equation to model diluting fluid movement across the moving vaginal epithelial surface and into the gel bolus. This is a physicochemically complex phenomenon that is not well understood. We implement a boundary flux model based upon the elevated hydrodynamic pressures in the cells. Results show that this model produces fluxes that lie within the range of mean values that have been reported. Further experimental characterization of the vaginal wall is required for a more precise set of parameters and a more sophisticated theoretical treatment of epithelium. [Copyright &y& Elsevier]

Abstract: A recent study in South Africa has confirmed, for the first time, that a vaginal gel formulation of the antiretroviral drug Tenofovir, when applied topically, significantly inhibits sexual HIV transmission to women . However the gel for this drug, and anti-HIV microbicide gels in general, have not been designed using full understanding of how gel spreading and retention in the vagina govern successful drug delivery. Elastohydrodynamic lubrication theory can be applied to model such spreading of microbicide gels, which are inherently non-Newtonian . A yield stress is emerging as one of the important properties of microbicide gel vehicle deployment, as this may improve retention within the vaginal canal. On the other hand, a yield stress may decrease the initial extent of the coating flow. Here, we first explain a certain yield stress paradox observed generally in many lubrication flows. Four conditions are determined, via scaling analysis, which mitigate the inconsistency in the use of lubrication theory to analyze the specific problem of elastic wall squeezing flow of yield stress fluid. Parameters characterizing these conditions are obtained experimentally for a test gel. Using them, it is shown that the lubrication approximation may be applied to the elastic wall-squeezing problem for this gel. [Copyright &y& Elsevier]

The present paper deals with non-Newtonian viscoelastic flows of Oldroyd-B type in thin domains. Such geometries arise for example in the context of lubrication. More precisely, we justify rigorously the asymptotic model obtained heuristically by proving the mathematical convergence of the Navier–Stokes/Oldroyd-B system towards the asymptotic model. [ABSTRACT FROM AUTHOR]

This letter incorporates squeezing flow with the Hertz contact theory in analyzing the dynamic behavior of an AFM tip in contact with an elastic substrate and a liquid film. To the first order of approximation, a new dynamic equation describing the motion of the AFM tip is presented, from which closed-form solutions of the stored contact modulus and loss contact modulus are obtained. The results show that the stored contact modulus depends on the frequency of the oscillation, the elastic properties of the elastic material and the mass of the tip, while it is independent of the viscosity of the liquid film. These provide a theoretical basis for the characterization of the elastic properties of biological materials and nanostructures by using the technique of continuous stiffness measurement. [ABSTRACT FROM AUTHOR]

We have investigated the hydrodynamic drag force between charged particles in electrolyte solutions, specifically the electroviscous force that arises from the distortion of the electrical double layers by the flow field. We report an improvement on the thin-double-layer theory (S.G. Bike, D.C. Prieve, J. Colloid Interface Sci. 136 (1990) 95–112), using a more accurate boundary condition for the radial charge current. The differences become important when the double layers start to overlap. We have found that nonlinear hydrodynamic effects are small, whereas nonlinear electric effects can be significant, in some instances leading to qualitatively different behavior. If the ion diffusivities are highly asymmetric, the electroviscous force can be reduced by an order of magnitude when there is an excess of the mobile ions in the double layer. The common supposition that there are substantial differences in the electroviscous force predicted by constant-charge and constant-potential boundary conditions is incorrect; our calculations show that it is an artifact introduced by the Debye–Hückel approximation. [Copyright &y& Elsevier]

Classical shallow-ice theory assumes that bed topography under ice sheets has slopes comparable to the surface slope of the ice sheet. A modification of the classical steady-state theory which allows for significant bed topography on shorter length scales has recently been developed by Morland (Proc. R. Soc L. Ser. A., 456, 1711-1739), but his theory requires explicit integration of the ice-flow equations over the topography length scale, which may be below the grid size of typical numerical ice sheet models. Here we present a method for parameterising the effect of basal topography of wavelengths much greater than ice thickness but much smaller than the horizontal extent of the ice sheet on the bulk flow of the ice sheet. In particular, we are able to show through the use of a multiple-scales expansion technique that the effect of such topography is described by a simple correction factor applied to the classical expression for ice flux. This correction factor dispenses with the need to integrate explicitly over the topography length scale and could allow the effect of such topography to be included in numerical models with limited grid size. Examples are given for the practical implementation of this 'correction factor method' in calculations of the steady-state shape of ice sheets. [ABSTRACT FROM AUTHOR]

• Flow-wise variation of fracture aperture is inherently coupled to permeation into surrounding rock. • Hydraulic conductivity and permeation velocity self-consistently calculated via perturbation theory. • Novel analytical expressions for velocity profile and conductivity validated against flow simulations. We investigate the flow-wise variation of the hydraulic conductivity inside a non-uniformly shaped fracture with permeable walls. Using lubrication theory for viscous flows, in conjunction with the Beavers–Joseph–Saffman boundary condition at the permeable walls, we obtain an analytical expression for the velocity profile, conductivity, and wall permeation velocity. These predictions highlight the effects of geometric variation (through the local slope of the aperture's flow-wise variation), the permeability of the walls (through a dimensionless slip coefficient), and the effect of flow inertia (through a Reynolds number). The theory is validated against an OpenFOAMⓇ solver for the Navier–Stokes equations subject to a tensorial slip boundary condition, showing good agreement. The mathematical results have implications on system-level (multiscale) modeling of hydraulically fractured reservoirs, in which the Darcy conductivity of each non-uniform passage must be accurately accounted for, throughout the fractured porous rock. [ABSTRACT FROM AUTHOR]