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.

A model for the human tear film with heating from within the eye

Abstract: A model for tear film dynamics and cooling during the interblink period is formulated that includes heat transfer from the interior of the eye. Lubrication theory is used to derive an equation for the thickness of the film; the nonlinear partial differential equation for the thickness is solved subject to either a fixed temperature at the substrate or with heat diffusion from within two different model rectangular domains. The model domains are simplified geometries that represent the anterior eye and that may include the cornea and some aqueous humor; one model domain is asymptotically thin (thin substrate) and the other has finite thickness (thick substrate). The thick substrate case captures temperature decreases that are observed in vivo, while the thin substrate and fixed temperature models do not. Parameters to reproduce observed temperature decreases are found.

Simulation of fluid flow in the step and flash imprint lithography process

Abstract: Step and Flash Imprint Lithography (SFIL) is a photolithography process in which the photoresist is dispensed onto the wafer in its liquid monomer form and then imprinted and cured into a desired pattern instead of using traditional optic systems. The mask used in the SFIL process is a template of the desired features that is made using electron beam writing. Several variable sized drops of monomer are dispensed onto the wafer for imprinting. The base layer thickness at the end of the imprinting process is typically about 50 nm, with an approximate imprint area of one square inch. This disparate length scale allows simulation of the fluid movement through the template-wafer channel by solving governing fluid equations that are simplified by lubrication theory. Capillary forces are also an important factor governing fluid movement; a dimensionless number known as the capillary number is used to describe these forces. This paper presents a simulation to model the flow and coalescence of the multiple fluid drops and the effect the number of drops dispensed has on final imprint time. The imprint time is shown to decrease with the use of increasing numbers of drops or with the use of an applied force on the template. Appropriate filling of features in the template is an important issue in SFIL, so a mechanism for handling the interface movement into features using a modified boundary condition is outlined and examples are. Fluid spreading outside of the mask edge is also an issue that is resolved by results from this study. The simulation is thus a useful predictive tool providing insight on the effect multiple drop configurations and applied force have on imprint time, as well as providing a means for predicting feature filling.

Limiting cases of gravitational drainage of a vertical free film for evaluating surfactants

Abstract: The evolution of the deforming free surface of a vertically oriented thin film draining under gravity is examined for the case when there is an insoluble surfactant monolayer on a viscous, incompressible, and free liquid film with finite surface viscosity. Three coupled nonlinear partial differential equations describing the free surface shape, the surface velocity, and surfactant transport are obtained. These equations are derived at leading order and do not have inertial effects. We examine the case where the film is nearly flat so that mean surface tension is negligible; this will be in good agreement with experimental data with respect to long-time behavior of film thickness. This will be shown both analytically and computationally.We will show that in the limit of large surface viscosity, the evolution of the free surface is that obtained for the tangentially immobile case. It is verified that increasing surface viscosity slows down film drainage, thereby enhancing film stability. The Marangoni effec...

Thin-film flows near isolated humps and interior corners

Abstract: This paper concerns the surface-tension-driven flow of a thin layer of viscous liquid following a sudden change in the shape of its substrate. It is assumed that the substrate either develops an isolated hump or bends to create an interior corner. The flow is modelled using an evolution equation derived from lubrication theory, extended in the case of a corner with fully nonlinear expressions for interfacial curvature and volume conservation. Numerical simulations and large-time asymptotics are used to describe the evolution of the film. Over long times the film typically forms a quasi-static puddle adjacent to the hump (or in the corner) and a wave-like disturbance propagates into the far field. For sufficiently large humps and sharp corners, the film pinches off to form an effective contact line at the edge of the puddle, at which the film height tends to zero as time tends to infinity; as long as the film does not rupture (which it cannot in the mathematical framework adopted), the effective contact line drifts slowly away from the hump towards a limiting position dictated by the transient dynamics. Flows off humps with maxima less than a critical height have a qualitatively different structure, captured by one of two possible branches of similarity solutions of the thin-film equation, whereby pinch-off does not occur.

Probing the Effect of Salinity and pH on Surface Interactions between Air Bubbles and Hydrophobic Solids: Implications for Colloidal Assembly at Air/Water Interfaces.

Abstract: In this work, a bubble probe atomic force microscope (AFM) was employed to quantify the interactions between two air bubbles and between an air bubble and an octadecyltrichlorosilane (OTS)-hydrophobized mica under various aqueous conditions. The key parameters (e.g., surface potentials, decay length of hydrophobic attraction) were obtained by analyzing the measured forces through a theoretical model based on Reynolds lubrication theory and an augmented Young-Laplace equation by including effect of disjoining pressure. The bubble-OTS hydrophobic attraction with a decay length of 1.0 nm was found to be independent of solution pH and salinity. These parameters were further used to predict the attachment of OTS-hydrophobized particles onto the air/water interface, demonstrating that particle attachment driven by hydrophobic attraction could be facilitated by suppressing electrical double-layer repulsion at low pH or high salinity condition. This facile methodology can be readily extended to quantify interactions of many other colloidal particles with gas/water and oil/water interfaces, with implications for colloidal assembly at different interfaces in many engineering applications.