Showing papers on "Lubrication theory published in 1989"

Measurements of and Relation Between the Adhesion and Friction of Two Surfaces Separated by Molecularly Thin Liquid Films

Abstract: A new technique is described for sliding (shearing) two molecularly smooth surfaces laterally past each other in liquids while monitoring their exact contact area, the normal and transverse forces, and the surface separation. First, we show that the elastic deformations of two initially curved surfaces in adhesive contact are the same under static and dynamic (i.e., sliding) conditions. Detailed results are then presented of how the shear properties of thin films of water and a simple nonpolar liquid are “quantized” with the number of layers. Results with water as the intervening liquid, as well as the effects of humidity on sliding in air, reveal that more complex mechanisms are operating than with simple liquids which appear to be related to the complex “hydration” forces between two surfaces in water or in aqueous salt solutions. The results suggest a close correlation between the static forces and shear properties of very thin liquid films, and the molecular structure of the liquids confined within such films.

The lubrication force between two viscous drops

Abstract: The hydrodynamic force resisting the relative motion of two unequal drops moving along their line of centers is determined for Stokes flow conditions. The drops are assumed to be in near‐contact and to have sufficiently high interfacial tension that they remain spherical. The squeeze flow in the narrow gap between the drops is analyzed using lubrication theory, and the flow within the drops near the axis of symmetry is analyzed using a boundary integral technique. The two flows are coupled through the nonzero tangential stress and velocity at the interface. Depending on the ratio of drop viscosity to that of the continuous phase, and also on the ratio of the distance between the drops to their reduced radius, three possible flow situations arise, corresponding to nearly rigid drops, drops with partially mobile interfaces, and drops with fully mobile interfaces. The results for the resistance functions are in good agreement with an earlier series solution using bispherical coordinates. These results have important implications for droplet collisions and coalescence.

Slow spreading of a sheet of Bingham fluid on an inclined plane

Abstract: To study the dynamics of fluid mud with a high concentration of cohesive clay particles, we present a theory for a thin sheet of Bingham-plastic fluid flowing slowly on an inclined plane. The physics is discussed on the approximate basis of the lubrication theory. Because of the yield stress, the free surface need not be horizontal when the Bingham fluid is in static equilibrium, nor parallel to the plane bed when in steady flow. We then show that there is a variety of gravity currents that can advance at a constant speed and with the same profile. Experimental confirmation of one type is presented. By solving a nonlinear partial differential equation, transient flows due either to a steady upstream discharge or to the sudden release of a finite fluid mass on another fluid layer are studied. In the first case there is a mud front which ultimately propagates as a constant speed as a steady gravity current. In the second case, when the ambient layer is sufficiently shallow that there is no initial motion, the flow induced by the new fluid can terminate after the disturbance has travelled a finite distance. The extent of the final spread is examined. Disturbances due to an external pressure travelling parallel to the free surface are also examined. It is found in particular that a travelling localized pulse of pressure gradient not only generates a localized mud disturbance which travels along with the forcing pressure, but further leaves behind a permanent footprint.

Motion of nonaxisymmetric red blood cells in cylindrical capillaries.

Abstract: We analyze theoretically the single-file flow of asymmetric red blood cells along cylindrical capillaries. Red cells in narrow capillaries are typically nonaxisymmetric, with the cell membrane moving continuously around the cell. In our analysis, cell shape and streamlines of membrane motion are prescribed. Lubrication theory is used to compute velocities and pressures in the fluid surrounding the cell. Conditions of zero lift, zero torque, zero drag, and energy conservation in the cell are imposed. Predicted tank-treading frequency, cell inclination and transverse displacement are small. Cell asymmetry and tank-treading are found to have little effect on the apparent viscosity of blood in capillaries with diameters up to 7 microns.

Non-Newtonian flow modelling in the screw regions of an intermeshing corotating twin screw extruder

Abstract: We model the low of a non-Newtonian fluid obeying a power-law model through the screw elements of a self-wiping intermeshing corotating twin screw extruder. The flow is modelled for a power-law viscosity function using both a finite element method and a lubrication theory modified FAN procedure. The finite element method yields machine direction and transverse velocity fields. The screw pumping correlations developed from the two methods agree within ten percent.

Simulation of Flow and Mixing in an Internal Mixer

Abstract: A mathematical model is developed for simulation of flow in an internal mixer with two counter rotating non-intermeshing rotors is presented. The model presumes rotors with a screw flight which is separated into two sections. The mixing chamber is taken to be fully filled and rotor curvature neglected in analogy to screw extruder analyses. Lubrication theory is used and the fluid presumed Newtonian. The flow patterns within the mixing chamber are computed. The conditions under which rotor designs lead to global circulation patterns within the mixing chamber and good distributive mixing are considered. We also investigated the extent of fluid motion over rotor tips which should lead to dispersive mixing.

The line contact problem of elastohydrodynamic lubrication - II. Numerical solutions of the integrodifferential equations in the transition and exit layers

Abstract: The solution of the line contact problem of elastohydrodynamic lubrication in the asymptotic regime developed by Bissett (Proc. R. Soc. Lond. A 424, 393-407 (1989)) exhibits two regions of rapid change: a transition layer between the inlet and contact zones, and a downstream exit layer. In these regions the governing Reynolds equation of lubrication theory is essentially nonlinear, although pressure and surface displacement continue to be linearly related by the singular integral equation of plane elasticity. In combination, the system in each region reduces to a nonlinear singular integrodifferential equation with Cauchy kernel for the surface displacement, to be satisfied on either an infinite interval (transition layer) or a semi-infinite interval (exit layer). A method is developed along lines used by Spence & Sharp (Proc. R. Soc. Lond. A 400, 289 (1985), Proc. R. Soc. Lond. A 422, 173 (1989)) and Spence et al. (J. Fluid Mech. 174, 135 (1987)) for approximating the solution in either case by a finite number of trigonometric terms (up to 900). Rapid convergence is achieved by judicious allowance for end point behaviours as deduced by asymptotic analysis of the governing equations. The equations contain an eigenvalue, representing the scaled exit film thickness, which also characterizes the film thickness in the contact zone. This eigenvalue is found with high accuracy in the course of solving the transition layer problem. Close agreement with certain results of Hooke & O'Donoghue (J. mech. Engng Sci. 14 (1), 34 (1972)) is exhibited.

Stresslet resistance functions for low Reynolds number flow using deforming spheres

Abstract: The stresslets of two rigid spheres in an ambient pure straining flow are obtained at low Reynolds number by defining and solving an equivalent problem of flow around deforming spheres. If the spheres are separated by a small gap, the stresslet of each sphere (the symmetric first moment of the surface stress) is a singular function of the gap width. For spheres in an ambient pure straining flow, the singularities manifest themselves as the slow convergence of numerical calculations. The methods of lubrication theory are used to calculate the singularities in the stresslets and it is shown that these new singularities can be related to singularities already found in other resistance functions. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.

Static and dynamic characteristics of porous journal bearings with nonuniform permeability.

Abstract: The present study is a theoretical analysis to evaluate the static and dynamic characteristics of oil-filled porous journal bearings with nonuniform permeability. Three types of nonuniform distributions of permeability are analyzed. For the first type, the permeability of the inside is lower than that of the outside. For the second type, the permeability of the loaded part is lower than that of the unloaded part. For the third type, the permeability of the bearing ends is lower than that of the middle. It is found that all nonuniform type bearings have a higher load carrying capacity, lower total side leakage flow, larger oil film coefficients, and higher stability threshold speed compared with the corresponding values of uniform type bearings, in which permeability is equal to the higher of nonuniform type bearings. Furthermore, the second nonuniform type has a higher load carrying capacity and a lower total side leakage flow than the other nonuniform types.

A Study on The Numerical Analysis of Fluid Film Lubrication by the Boundary-Fitted Coordinates System : The Case of Steady Gas-Lubrication

Abstract: A new method on the discretization of the steady gas-lubricated Reynolds equation is presented. The present method is derived by applying the boundary-ditted coordinates system to the divergence formulation method. Generalized algebraic equations for node pressures derived from the present method can be widely used to represent arbitrary film configuration and arbitrary bearing shape. This algebraic equation is shown by the separation of three components: the Poiseuille flow; the Couette flow; the correcting component of slip flow by rarefaction of the gas. The Couette flow component is discretized by a new upstream scheme derived from an extension of the simple upstream scheme, and the other components are discretized by an approximation of linearized distribution. Discretization of four representative boundary conditions are shown. Examples on a herringbone grooved journal bearing used in a misaligned large eccentricity and a small number of grooves are shown.

Pressure Boundary Conditions of High-Speed Thrust Bearings

Abstract: This paper describes a study on the boundary conditions at the inlet edge of high-speed thrust bearings in a turbulent flow regime, taking into account the inertia effects The basic lubrication equations in terms of pressure and stream function are solved for finite-width bearings by applying a numerical calculation technique combining control volume integration and Newton-Raphson linearization method Moreover, an analytical solution is given for infinitely long bearings Static bearing performance characteristics such as pressure distribution, load-carrying capacity, pressure center and inlet flow rate are calculated for three kinds of inlet boundary conditions in relation to three types of lubrication conditions, namely: the flooded condition, the overflooded condition and the starved condition Some samples of the numerical results are presented in graphic form, and the relationship between the inlet boundary conditions and static bearing performance is discussed

Foil bearing lubrication theory including compressibility effects

Abstract: An analysis is presented to determine the film thickness in a foil bearing. Using the Reynolds equation and including the compressibility effects of the gas, an equation was developed applicable to the film thickness in a foil bearing. The bearing was divided into three regions, namely, the entrance region, middle region and exit region. solutions are obtained for the film thickness in each region.

On the slider-bearing flow of a viscoelastic fluid

Abstract: This paper considers the slider-bearing flow of a model viscoelastic fluid. It is shown that the standard lubrication theory leads to some results which are in good agreement with a full numerical solution by a Boundary Element Method. The normal load per unit width is enhanced by a term of O( N 1 L ), where N 1 is the first normal stress difference and L is the bearing length, while the drag force remains essentially unchanged. This leads to a reduction in the frictional coefficient, which increases with Weissenberg number. The full slider bearing flow problem consists of three regions: the inlet flow, the bearing flow, and the outlet flow. The two free surfaces associated with the inlet and outlet flows must be found as parts of the solution. The full problem is unsteady, and the main effect of the free surfaces is to decrease the load-carrying capacity of the bearing. A simple global balance of momentum can account for the observed numerical behaviour.

潤滑油の粘弾性に関する研究 : 第1報,粘弾性モデルの構築と基礎方程式の導出

Abstract: Under severe lubricating conditions such as in a gear lubrication, the lubricating oil will be expected to behave as viscoelastic fluid. The Navier-Stokes equations cannot be applied to the fluid analysis when the fluid characteristics are obtained theoretically for the severe lubricating conditions mentioned above. The author constructed the models for viscoelasticity which can be applied to both the boundary lubrication and the elastohydrodynamic one, taking the viscoelasticity of lubricating oil into consideration. The basic equations were derived from the new model constructed in the paper.