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.

Numerical simulation of extensional deformations of viscoelastic liquid bridges in filament stretching devices

Abstract: Large extensional deformations of viscoelastic fluid columns in filament stretching rheometers are studied through numerical simulations up to Hencky strains of greater than e=4. The time-dependent axisymmetric calculations incorporate the effects of viscoelasticity, surface tension, fluid inertia, plus a deformable free surface and provide quantitative descriptions of the evolution in the filament profile, the kinematics in the liquid column and the resulting dynamic evolution in the viscous and elastic contributions to the total stress. In addition to investigating the variation in the apparent Trouton ratio expected in experimental measurements using this new type of extensional rheometer, we also investigate the generic differences between the response of Newtonian and viscoelastic fluid filaments described by the Oldroyd-B model. For small strains, the fluid deformation is governed by the Newtonian solvent contribution to the stress and the filament evolution is very similar in both the Newtonian and viscoelastic cases. However, in the latter case at large strains and moderate Deborah numbers, elastic stresses dominate leading to strain-hardening in the axial mid-regions of the column and subsequent drainage of the quasi-static liquid reservoir that forms near both end-plates. These observations are in good qualitative agreement with experimental observations. For small initial aspect ratios and low strains, the non-homogeneous deformation predicted by numerical simulations is well described by a lubrication theory solution. At larger strains, the initial flow non-homogeneity leads to the growth of viscoelastic stress boundary layers near the free surface which can significantly affect the transient Trouton ratio measured in the device. Exploratory design calculations suggest that mechanical methods for modifying the boundary conditions at the rigid end-plates can reduce this non-homogeneity and lead to almost ideal uniaxial elongational flow kinematics.

An experimental study of rivulet instabilities in centrifugal spin coating of viscous Newtonian and non‐Newtonian fluids

Abstract: An experimental study on the onset and evolution of centrifugally driven rivulets is presented, which aims to investigate the influence on the instability of various experimental conditions (drop volume and rotational frequency), the wetting properties of the liquid (surface tension and contact angle), and fluid viscoelasticity. The apparatus allows continuous observation of the drop shapes following an impulsive spin‐up of the substrate, and these are analyzed by digital image analysis. The flows exhibit an onset time, or, equivalently, a critical radius, before which the drop spreads axisymmetrically. Data on drop spreading are compared with simple predictions of lubrication theory. The measured azimuthal wave number and growth rate of the instability are in good agreement with the linear stability analysis of Troian et al. [Europhys. Lett. 10, 25 (1989)], as long as the critical radius is taken from the experiment itself. The most unstable wavelength is found to be independent of both drop size and rotation speed in the range of parameters investigated, as observed previously by Melo et al. [Phys. Rev. Lett. 63, 1958 (1989)]. On the other hand, a change in the wetting properties of the liquid significantly modifies the critical radius, which, in turn, affects the number of fingers, with the nonwetting fluid exhibiting a smaller critical radius. This trend is in agreement with the mechanism of instability that is linked to the presence of a capillary ridge near the edge of the drop. No qualitative nor quantitative difference in behavior has been observed between a Boger fluid having a relaxation time of about 1 s, and its Newtonian solvent, in the experimental conditions considered.

Resistance functions for spherical particles, droplets and bubbles in cylindrical tubes

Abstract: Numerical computations are performed to evaluate the resistance functions for low Reynolds number flow past spherical particles, droplets and bubbles in cylindrical domains. Spheres of arbitrary radius a and radial position b move with arbitrary velocity U within a cylinder of radius R. The undisturbed fluid may be at rest, or subject to a pressure-driven flow with maximum velocity U 0 . The spectral boundary element method is employed to compute the resistance force for torque-free bodies in three cases : rigid solids, fluid droplets with viscosity ratio λ = 1, and bubbles with viscosity ratio λ = 0. A lubrication theory is developed to predict the limiting resistance of bodies near contact with the cylinder walls. Compact algebraic expressions are developed which accurately represent the numerical data over the entire range of particle positions 0 < b/(R-a) < 1 for all particle sizes in the range 0 < a/R < 0.9. The resistance functions are consistent with known analytical results and are presented in a form suitable for further studies of particle migration in cylindrical vessels.