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AuthorVella, Dominic (2)Breward, C. J. W. (1)Breward, C. J. W. (1)Bruna, M. (1)Howell, P. D. (1)View MoreJournalJournal of Fluid Mechanics (5)KAUST Grant Number

KUK-C1-013-04 (5)

PublisherCambridge University Press (CUP) (5)Subject
capillary flows (5)

lubrication theory (4)thin films (3)MEMS/NEMS (2)biomedical flows (1)View MoreTypeArticle (5)Year (Issue Date)2014 (3)2012 (2)Item AvailabilityMetadata Only (5)

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A fluid-mechanical model of elastocapillary coalescence

Singh, Kiran; Lister, John R.; Vella, Dominic (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014-03-25) [Article]

© 2014 Cambridge University Press. We present a fluid-mechanical model of the coalescence of a number of elastic objects due to surface tension. We consider an array of spring-block elements separated by thin liquid films, whose dynamics are modelled using lubrication theory. With this simplified model of elastocapillary coalescence, we present the results of numerical simulations for a large number of elements, N = O(10<sup>4</sup>). A linear stability analysis shows that pairwise coalescence is always the most unstable mode of deformation. However, the numerical simulations show that the cluster sizes actually produced by coalescence from a small white-noise perturbation have a distribution that depends on the relative strength of surface tension and elasticity, as measured by an elastocapillary number K. Both the maximum cluster size and the mean cluster size scale like K<sup>-1/2</sup> for small K. An analytical solution for the response of the system to a localized perturbation shows that such perturbations generate propagating disturbance fronts, which leave behind 'frozen-in' clusters of a predictable size that also depends on K. A good quantitative comparison between the cluster-size statistics from noisy perturbations and this 'frozen-in' cluster size suggests that propagating fronts may play a crucial role in the dynamics of coalescence.

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.

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.

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.

Multiple equilibria in a simple elastocapillary system

Taroni, Michele; Vella, Dominic (Journal of Fluid Mechanics, Cambridge University Press (CUP), 2012-09-28) [Article]

We consider the elastocapillary interaction of a liquid drop placed between two elastic beams, which are both clamped at one end to a rigid substrate. This is a simple model system relevant to the problem of surface-tension-induced collapse of flexible micro-channels that has been observed in the manufacture of microelectromechanical systems (MEMS). We determine the conditions under which the beams remain separated, touch at a point, or stick along a portion of their length. Surprisingly, we show that in many circumstances multiple equilibrium states are possible. We develop a lubrication-type model for the flow of liquid out of equilibrium and thereby investigate the stability of the multiple equilibria. We demonstrate that for given material properties two stable equilibria may exist, and show via numerical solutions of the dynamic model that it is the initial state of the system that determines which stable equilibrium is ultimately reached. © 2012 Cambridge University Press.

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