Some advances in lubrication-type theories (original) (raw)
Related papers
Contact Line Instabilities of Thin Liquid Films
Physical Review Letters, 2001
We present results of fully nonlinear time-dependent simulations of a thin liquid film flowing down an inclined plane. Within the lubrication approximation, and assuming complete wetting, we find that varying the inclination angle considerably modifies the shape of the emerging patterns (fingers versus sawtooth). Our results strongly suggest that the shape of the patterns is not necessarily related to either partial or complete coverage of the substrate, a technologically important feature of the flow. We find quantitative agreement with reported experiments and suggest new ones.
Proper initial conditions for the lubrication model of the flow of a thin film of fluid
arXiv (Cornell University), 1998
A lubrication model describes the dynamics of a thin layer of fluid spreading over a solid substrate. But to make forecasts we need to supply correct initial conditions to the model. Remarkably, the initial fluid thickness is not the correct initial thickness for the lubrication model. Theory recently developed in [12, 14] provides the correct projection of initial conditions onto a model of a dynamical system. The correct projection is determined by requiring that the model's solution exponentially quickly approaches that of the actual fluid dynamics. For lubrication we show that although the initial free surface shape contributes the most to the model's initial conditions, the initial velocity field is also an influence. The projection also gives a rationale for incorporating miscellaneous small forcing effects into the lubrication model; gravitational forcing is given as one example.
Physical Review Letters, 2010
Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.
2011
In this paper we consider the flows of a thin films for which the Reynolds number is small. This is true in many practical situations. We deduced the lubrication model for slider bearings (a slider bearing consists of a thin layer of viscous fluid confined between nearly parallel walls that are in relative tangential motion). Another application of the lubrication model is the flow of a thin film with a free boundary, with zero surface tension and respectively flow driven by surface tension gradient (Marangoni flow). 2000 Mathematics Subject Classification: 76D27, 76D05, 76D08, 76D45.
Friction Control in Thin-Film Lubrication
The Journal of Physical Chemistry B, 1998
A novel method is proposed for controlling and reducing friction in thin-film boundary lubricated junctions, through coupling of small amplitude (of the order of 1 Å) directional mechanical oscillations of the confining boundaries to the molecular degrees of freedom of the sheared interfacial lubricating fluid. Extensive grandcanonical molecular dynamics simulations revealed the nature of dynamical states of confined sheared molecular films, their structural characteristics, and the molecular scale mechanisms underlying transitions between them. Control of friction in the lubricated junction is demonstrated, with a transition from a high-friction stick-slip shear dynamics of the lubricant to an ultralow kinetic friction state (termed as a superkinetic friction regime), occurring for Deborah number values D e ) τ f /τ osc > 1, where τ osc is the time constant of the boundary mechanical oscillations normal to the shear plane and τ f is the characteristic relaxation time for molecular flow and ordering processes in the confined region. A rate and state model generalized to include the effects of such oscillations is introduced, yielding results in close correspondence with the predictions of the atomistic simulations.
arXiv: Soft Condensed Matter, 2018
For partially wetting fluids, previous investigations of dynamic film formation by dip experiments have found that film thickness is independent of driving velocity. However, when flushing low viscosity aqueous bridges down hydrophobic tubes at high velocities, we find that the thickness of the deposited film strongly depends on driving conditions. We show that thickness is selected through meniscus curvature, and evidence a breakdown of the standard lubrication theory of triple line dynamics for low viscosity liquids at cm/s velocities, which we ascribe to inertial effects.
Unusual Contact-Line Dynamics of Thick Films and Drops
Journal of Colloid and Interface Science, 1999
We report several novel phenomena in contact-line and fingering dynamics of macroscopic spinning drops and gravity-driven films with dimensions larger than the capillary length. It is shown through experimental and theoretical analysis that such macroscopic films can exhibit various interfacial shapes, including multi valued ones, near the contact line due to a balance between the external body forces with capillarity. This rich variety of front shapes couples with the usual capillary, viscous, and intermolecular forces at the contact line to produce a rich and unexpected spectrum of contact-line dynamics. A single finger develops when part of the front becomes multivalued on a partially wetting macroscopic spinning drop in contrast to a different mechanism for microscopic drops of completely wetting fluids. Contrary to general expectation, we observe that, at high viscosity and low frequencies of rotation, the speed of a glycerine finger increases with increasing viscosity. Completely wetting Dow Corning 200 Fluid spreads faster over a dry inclined plane than a prewetted one. The presence of a thin prewetted film suppresses fingering both for gravity-driven flow and for spin coating. We analyze some of these unique phenomena in detail and offer qualitative physical explanations for the others.
Nonlinear Dynamics of Thin Films and Fluid Interfaces
2003
This five-day multidisciplinary workshop focussed on the mathematics of free-surface fluid flow. Building on theoretical and experimental developments of the last few years, the workshop brought together mathematicians and physicists at the forefront of research in experiments, analysis, computation, and modelling. The workshop yielded a rich exchange of ideas in the areas of thin liquid films, dynamic contact lines, slender jets, Hele-Shaw flow, and fluid interfaces.
Coating flows of non-Newtonian fluids: weakly and strongly elastic limits
Journal of Engineering Mathematics, 2008
This paper presents an asymptotic analysis of the thickness of the liquid film that coats a smooth solid substrate when it is withdrawn from a bath of non-Newtonian fluid, and compares the results with experimental measurements. The film thickness is, to a good approximation, uniform above the point where the film is withdrawn from the fluid bath, and depends on the rotation rate, the fluid properties and the substrate geometry. Theoretical predictions of the film thickness for a number of different substrate geometries (an inclined plate, roller and fiber) are presented, and are compared with experimental measurements in a single roller geometry. Results are obtained for two different limits of the Criminale–Ericksen–Filbey constitutive equation in which the fluid rheology is either weakly elastic and dominated by shear thinning, or strongly elastic and dominated by elastic stresses. A lubrication analysis yields a thin-film equation which characterizes the film thickness as a function of spatial position. The rheological properties of the test fluids are measured independently using steady and oscillatory shearing deformations. The viscometric parameters are then used, in conjunction with the governing thin-film equation, which is solved using matched asymptotics, to give a quantitative prediction of the thickness of the fluid coating. The onset of an instability which causes the film thickness to vary with axial position along the roller is also observed experimentally.