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Lubrication theory

About: Lubrication theory is a research topic. Over the lifetime, 1713 publications have been published within this topic receiving 50261 citations. The topic is also known as: Fluid bearing.


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Journal ArticleDOI
TL;DR: In this paper, a two-dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered and a new contact line condition based on mass balance is formulated and used, which represents a leading-order superposition of spreading and evaporative effects.
Abstract: A two‐dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered. Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil, viscous spreading, contact‐angle hysteresis, and mass loss on the behavior of the droplet. A new contact‐line condition based on mass balance is formulated and used, which represents a leading‐order superposition of spreading and evaporative effects. Evolution equations for steady and unsteady droplet profiles are found and solved for small and large capillary numbers. In the steady evaporation case, the steady contact angle, which represents a balance between viscous spreading effects and evaporative effects, is larger than the advancing contact angle. This new angle is also observed over much of the droplet lifetime during unsteady evaporation. Further, in the unsteady case, effects which tend to decrease (increase) the contact angle promote (delay) evaporation. In the ‘‘large’’ capillary number limit, matched asymptotics are used to describe the droplet profile; away from the contact line the shape is determined by initial conditions and bulk mass loss, while near the contact‐line surface curvature and slip are important.

267 citations

Journal ArticleDOI
TL;DR: In this article, the hydrodynamic force resisting the relative motion of two unequal drops moving along their line of centers is determined for Stokes flow conditions, where the drops are assumed to be in near contact and to have sufficiently high interfacial tension that they remain spherical.
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.

262 citations

Book
28 Apr 2009
TL;DR: In this article, the Navier-Stokes equations for high-Re flows were applied to a two-layer model of the Boussinesq system in dimensionless form.
Abstract: Introduction Classification The Navier-Stokes equations Non-stratified ambient currents Shallow-water (SW) formulation for high-Re flows Motion of the interface and the continuity equation One-layer model A useful transformation The full behavior by numerical solution Dam-break stage Similarity solution The validity of the inviscid approximation The steady-state current and nose jump conditions Benjamin's analysis Jump condition Box models for 2D geometry Fixed volume current with inertial-buoyancy balance Inflow volume change Two-layer SW model Introduction The governing equations Boussinesq system in dimensionless form Jumps of interface for H < 2 Energy and work in a two-layer model Axisymmetric currents, SW formulation Governing equations A useful transformation The full behavior by numerical solution Dam-break stage Similarity solution The validity of the inviscid approximation Some comparisons Box models for axisymmetric geometry Fixed volume current with inertial-buoyancy balance Inflow volume change Effects of rotation Axisymmetric case Rotating channel Buoyancy decays: particle-driven, porous boundary, and entrainment Particle-driven currents Axisymmetric particle-driven current Extensions of particle-driven solutions Current over a porous bottom Axisymmetric current over a porous bottom Entrainment Non-Boussinesq systems Introduction Formulation Dam-break and initial slumping motion The transition and self-similar stages Summary Lubrication theory formulation for viscous currents 2D geometry Axisymmetric current Current in a porous medium II Stratified ambient currents and intrusions Continuous density transition Introduction The SW formulation SW results and comparisons with experiments and simulations Dam break Critical speed and nose-wave interaction Similarity solution The validity of the inviscid approximation Axisymmetric and rotating cases SW formulation SW and NS finite-difference results The validity of the inviscid approximation The steady-state current Steady-state flow pattern Results Comparisons and conclusions Intrusions in 2D geometry Introduction Two-layer stratification Linear transition layer Rectangular lock configurations Cylindrical lock in a fully linearly-stratified tank Similarity solution Non-symmetric intrusions Intrusions in axisymmetric geometry Introduction Two-layer stratification Fully linearly-stratified tank, part-depth locks Box models for 2D geometry Fixed volume and inertial-buoyancy balance S = 1, inflow volume change Box models for axisymmetric geometry Fixed volume and inertial-buoyancy balance S = 1, inflow volume change Lubrication theory for viscous currents with S = 1 2D geometry Axisymmetric geometry Energy Introduction 2D geometry Axisymmetric geometry SW equations: characteristics and finite-difference schemes Characteristics Numerical solution of the SW equations Navier-Stokes numerical simulations Formulation A finite-difference code Other codes Some useful formulas Leibniz's Theorem Vectors and coordinate systems

239 citations

Journal ArticleDOI
TL;DR: Apparent viscosity is shown to increase with decreasing flow rate, in agreement with previous experimental and theoretical studies.
Abstract: Flow of red blood cells along narrow cylindrical vessels, with inside diameters up to 8 μm, is modelled theoretically. Axisymmetric cell shapes are assumed, and lubrication theory is used to describe the flow of the suspending fluid in the gaps between the cells and the vessel wall. The models take into account the elastic properties of the red blood cell membrane, including its responses to shear and bending. At moderate or high cell velocities, about 1 mm/s or more, the membrane stress may be approximated by an isotropic tension which is maximal at the nose of the cell and falls to zero at the rear. Cell shape and apparent viscosity are then independent of flow rate. At lower flow velocities, membrane shear and bending stresses become increasingly important, and models are developed to take these into account. Apparent viscosity is shown to increase with decreasing flow rate, in agreement with previous experimental and theoretical studies.

232 citations

Journal ArticleDOI
TL;DR: In this paper, a matched asymptotic expansion technique was used to obtain the Stokes flow solution for a rigid sphere of radius a moving uniformly in a direction parallel to a fixed infinite plane wall when the minimum clearance between the sphere and the plane is very much less than a.
Abstract: A new method using a matched asymptotic expansions technique is presented for obtaining the Stokes flow solution for a rigid sphere of radius a moving uniformly in a direction parallel to a fixed infinite plane wall when the minimum clearance ea between the sphere and the plane is very much less than a. An ‘inner’ solution is constructed valid for the region in the neighbourhood of the nearest points of the sphere and the plane where the velocity gradients and pressure are large; in this region the leading term of the asymptotic expansion of the solution satisfies the equations of lubrication theory. A matching ‘outer’ solution is constructed which is valid in the remainder of the fluid where velocity gradients are moderate but it is possible to assume that e = 0. The forces and couples acting on the sphere and the plane are shown to be of the form (α0+α1e) log e + β0 + O(e) where α0, α1 and β0 are constants which have been determined explicitly.

231 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202325
202265
202155
202062
201970
201864