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AuthorBreward, C. J. W. (1)Breward, C. J. W. (1)Bruna, M. (1)Duffy, B. R. (1)Howell, P. D. (1)View MoreJournalJournal of Fluid Mechanics (4)KAUST Grant NumberKUK-C1-013-04 (4)Publisher

Cambridge University Press (CUP) (4)

Subject
thin films (4)

capillary flows (3)lubrication theory (2)biomedical flows (1)contact lines (1)View MoreTypeArticle (4)Year (Issue Date)2014 (2)2013 (1)2012 (1)Item AvailabilityMetadata Only (4)

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Three-dimensional coating and rimming flow: a ring of fluid on a rotating horizontal cylinder

Leslie, G. A.; Wilson, S. K.; Duffy, B. R. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2013-01-29) [Article]

The steady three-dimensional flow of a thin, slowly varying ring of Newtonian fluid on either the outside or the inside of a uniformly rotating large horizontal cylinder is investigated. Specifically, we study 'full-ring' solutions, corresponding to a ring of continuous, finite and non-zero thickness that extends all of the way around the cylinder. In particular, it is found that there is a critical solution corresponding to either a critical load above which no full-ring solution exists (if the rotation speed is prescribed) or a critical rotation speed below which no full-ring solution exists (if the load is prescribed). We describe the behaviour of the critical solution and, in particular, show that the critical flux, the critical load, the critical semi-width and the critical ring profile are all increasing functions of the rotation speed. In the limit of small rotation speed, the critical flux is small and the critical ring is narrow and thin, leading to a small critical load. In the limit of large rotation speed, the critical flux is large and the critical ring is wide on the upper half of the cylinder and thick on the lower half of the cylinder, leading to a large critical load. We also describe the behaviour of the non-critical full-ring solution and, in particular, show that the semi-width and the ring profile are increasing functions of the load but, in general, non-monotonic functions of the rotation speed. In the limit of large rotation speed, the ring approaches a limiting non-uniform shape, whereas in the limit of small load, the ring is narrow and thin with a uniform parabolic profile. Finally, we show that, while for most values of the rotation speed and the load the azimuthal velocity is in the same direction as the rotation of the cylinder, there is a region of parameter space close to the critical solution for sufficiently small rotation speed in which backflow occurs in a small region on the upward-moving side of the cylinder. © 2013 Cambridge University Press.

The influence of non-polar lipids on tear film dynamics

Bruna, M.; Breward, C. J. W. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014-04-04) [Article]

© 2014 Cambridge University Press. In this paper we examine the effect that physiological non-polar lipids, residing on the surface of an aqueous tear film, have on the film evolution. In our model we track the evolution of the thickness of the non-polar lipid layer, the thickness of the aqueous layer and the concentration of polar lipids which reside at the interface between the two. We also utilise a force balance in the non-polar lipid layer in order to determine its velocity. We show how to obtain previous models in the literature from our model by making particular choices of the parameters. We see the formation of boundary layers in some of these submodels, across which the concentration of polar lipid and the non-polar lipid velocity and film thickness vary. We solve our model numerically for physically realistic parameter values, and we find that the evolution of the aqueous layer and the polar lipid layer are similar to that described by previous authors. However, there are interesting dynamics for the non-polar lipid layer. The effects of altering the key parameters are highlighted and discussed. In particular, we see that the Marangoni number plays a key role in determining how far over the eye the non-polar lipid spreads.

Boundary conditions for free surface inlet and outlet problems

Taroni, M.; Breward, C. J. W.; Howell, P. D.; Oliver, J. M. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2012-08-10) [Article]

We investigate and compare the boundary conditions that are to be applied to free-surface problems involving inlet and outlets of Newtonian fluid, typically found in coating processes. The flux of fluid is a priori known at an inlet, but unknown at an outlet, where it is governed by the local behaviour near the film-forming meniscus. In the limit of vanishing capillary number Ca it is well known that the flux scales with Ca 2/3, but this classical result is non-uniform as the contact angle approaches π. By examining this limit we find a solution that is uniformly valid for all contact angles. Furthermore, by considering the far-field behaviour of the free surface we show that there exists a critical capillary number above which the problem at an inlet becomes over-determined. The implications of this result for the modelling of coating flows are discussed. © 2012 Cambridge University Press.

A pinned or free-floating rigid plate on a thin viscous film

Trinh, Philippe H.; Wilson, Stephen K.; Stone, Howard A. (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014-11-11) [Article]

© 2014 Cambridge University Press. A pinned or free-floating rigid plate lying on the free surface of a thin film of viscous fluid, which itself lies on top of a horizontal substrate that is moving to the right at a constant speed is considered. The focus of the present work is to describe how the competing effects of the speed of the substrate, surface tension, viscosity, and, in the case of a pinned plate, the prescribed pressure in the reservoir of fluid at its upstream end, determine the possible equilibrium positions of the plate, the free surface, and the flow within the film. The present problems are of interest both in their own right as paradigms for a range of fluid-structure interaction problems in which viscosity and surface tension both play an important role, and as a first step towards the study of elastic effects.

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