Lubricated rolling over a pool

Experiments are conducted to explore the rolling of a cylinder over a pool of viscous fluid. The speed, width and loading of the cylinder are varied along with the initial depth and length of the viscous pool. Depending on the conditions, the cylinder will either ride on a lubrication film or remain in solid contact with the underlying substrate. For the former situation, a lubrication theory is presented that describes the pressure underneath the cylinder and the thickness of the film. The theory approximates the flow by the one-dimensional Reynolds equation with the addition of one term, with an adjustable parameter, to account for the flux of fluid to the cylinder sides. Once this parameter is calibrated against experiment, the theory predicts peak lubrication pressures, gap sizes and film thicknesses to within approximately ten per cent. For lubricated rolling, the film splits evenly between the cylinder and substrate downstream of the nip. The printer's instability arises during the splitting process, patterning the residual fluid films on the substrate and cylinder. If the pool length is less than the cylinder circumference, the fluid adhering to the cylinder is rotated back into contact with the substrate, and when there is sufficient adhered fluid a lubrication film forms that can again be modelled by the theory. Conversely, if there is insufficient adhered fluid, no contiguous lubrication film is formed; instead, the pattern from the printer's instability ‘prints’ from the cylinder to the substrate.

Viscous transfer of momentum across a shallow laminar flow

In a shallow channel, the flow transfers most of its momentum vertically. Based on this observation, one often neglects the momentum that is transferred across the stream – the core assumption of the shallow-water theory. In the context of viscous flows, this approximation is referred to as the ‘lubrication theory’, in which one assumes that the shear stress exerted by the fluid on the substrate over which it flows is proportional to its velocity. Here, we revise this theory to account for the momentum that viscosity transfers across a shallow laminar flow, while keeping the problem low-dimensional. We then test the revised lubrication theory against analytical and numerical solutions of the exact problem. We find that, at a low computational cost, the present theory represents the actual flow more accurately than the classical lubrication approximation. This theoretical improvement, devised with laboratory rivers in mind, should also apply to other geophysical contexts, such as ice flows or forming lava domes.

Galerkin finite element analysis for peristaltic flow of micropolar fluid through porous soaked inclined tube independent of wavelength

In this novel numerical investigation, the application of well-renowned numerical technique known as Galerkin finite element method on full form of Navier-Stokes equations presented peristaltic flow of non-Newtonian fluid confined by a uniformly saturated porous medium. The rheological aspects of non-Newtonian material are discussed by considering micropolar fluid. The flow model consists of system of nonlinear partial differential equations with mixed boundary condition. The flow also experienced an externally applied magnetic field. The effects of inertial forces and the results independent of wavelength are obtained by dropping the presumptions of lubrication theory in modelling the governing equations. The numerical solution for formulated problem in terms of partial differential expressions is worked out via Galerkin finite technique in view of six nodal triangular elements. The enhancement in the inertial forces gives impressive pressure enhancement against wavelength while opposed the fluid flow in the vicinity of peristaltic walls of the tube but supported the fluid flow in the central region of the tube. The present results are also compared with the available results after applying lubrication theory and found in reliable agreement.

Digital Slot: A Tool for Optimization and Development of New Hydraulic Fracturing Technologies

We present the digital slot — a tool for the development of new hydraulic fracturing technologies via digitization of slurry flow in narrow channels. We consider slurry containing fluid, proppant, and fiber components. The flow is described by a continuum mathematical model based on the lubrication theory. The numerical algorithm utilizes Lagrangian approach with finite volume pressure solver. We present the results of laboratory validation and simulation examples showing the key effects affecting solids transport in hydraulic fracturing: settling, bridging, gravity slumping, materials degradation, viscosity contrast, and bank formation.

Wind turbine main-bearing lubrication – Part 1: An introductory review of elastohydrodynamic lubrication theory

This paper is the first in a two-part study on lubrication in wind turbine main-bearings. Elastohydrodynamic lubrication is a complex field, the formulas and results from which should not be applied blindly, but with proper awareness and consideration of their context, validity and limitations in any given case. The current paper, “Part 1”, therefore presents an introductory review of elastohydrodynamic lubrication theory in order to provide this necessary background and context in an accessible form, promoting cross-disciplinary understanding. Fundamental concepts, derivations and formulas are presented, followed by the more advanced topics of: starvation, dynamic effects, surface roughness interactions and grease lubrication. “Part 2” applies the presented material in order to analyse wind turbine main-bearing lubrication in the context of available film thickness formulas and related results from lubrication theory. Aside from the main-bearing, the material presented here is also applicable to other lubricated non-conformal contacts in wind turbines, including pitch and yaw bearings and gear-teeth.

Water lubrication of graphene oxide-based materials

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.