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.

The energetics of the breakup of a sheet and of a rivulet on a vertical substrate in the presence of a uniform surface shear stress

Abstract: We use the lubrication approximation to obtain a complete description of the energetics of the breakup both of a fluid sheet of uniform thickness into a periodic array of infinitely many identical thin rivulets and of a single thin rivulet into one or more identical sub-rivulets on a vertical substrate in the presence of a prescribed uniform longitudinal shear stress at the free surface of the fluid by comparing the total energies of the different states. For both problems the situation when the volume flux is positive is relatively straightforward (and, in particular, qualitatively the same as that in the case of no prescribed shear stress), but when the volume flux is negative it is more complicated. However, whatever the value of the prescribed shear stress, there is always a critical thickness below which it is energetically favourable for a sheet to break up into rivulets and a critical semi-width below which it is energetically favourable for a rivulet to remain as a single rivulet, and a critical thickness above which it is energetically favourable for a sheet to remain as a sheet and a critical semi-width above which it is energetically favourable for a rivulet to break up into sub-rivulets.

Flow Structure and Transfer Jets in a Contra-Rotating Rigid-Roll Coating System

Abstract: A comprehensive analysis is presented of the internal flow structures that can arise in the coating bead of a twin roll coater, operating in forward mode, as inlet flux is varied seamlessly from a starved to a flooded condition. This is accomplished via the application of lubrication theory combined with the acquisition of accurate finite element solutions of the full two free surface flow problem. The former is used to map out associated control-space diagrams in terms of the non-dimensional quantities, roll speed ratio, inlet flux and Capillary number, and, further, to predict the distribution of eddies and liquid transfer paths as a function of the main operating parameters. The dynamic contact angle is predicted as a function of the operating conditions for both the computations and analysis. Detailed results are presented which: (i) provide a complete picture of attendant eddy structures; (ii) quantify the strengths of primary, secondary and asymmetric liquid transfer jets; (iii) reveal the presence of a weak secondary asymmetric transfer jet in the intermediate to flooded inlet flow regime; (iv) describe stagnation and free surface locations as a function of inlet flux and Capillary number; (v) demonstrate the unexpected coexistence of the primary and asymmetric jets in the low speed ratio meniscus regime.

Dynamics of air bearing sliders

Abstract: In this paper we present new results for the dynamics of a problem for the interaction of a compressible gas flow with a movable rigid surface. Compressible lubrication theory is applied to describe the dynamics of the vertical motion of air bearing sliders used in computer hard disk drives. In the limit of large bearing number we show this problem can be reduced to a nonlinear integrodifferential equation. Linear stability analysis and perturbation methods show that over the range of possible slider positions there is an infinite sequence of Hopf bifurcations yielding stable large amplitude periodic orbits. The dynamics of near-crash behavior and interaction with a moving disk surface are also addressed.