The thinning of the liquid layer over a probe in two-phase flow

The draining of the thin water film that is formed between a two dimensional, infinite, initially flat oil-water interface and a smooth, symmetric probe, as the interface is advected by a steady and uniform flow parallel to the probe axis, is modelled using classical fluid dynamics. The governing equations are nondimensionalised using values appropriate to the oil extraction industry. The bulk flow is driven by inertia and, in some extremes, surface tension while the viscous effects are initially confined to thin boundary layers on the probe and the interface. The flow in the thin water film is dominated by surface tension, and passes through a series of asymptotic regimes in which inertial forces are gradually overtaken by viscous forces. For each of these regimes, and for those concerning the earlier stages of approach, possible solution strategies are discussed and relevant literature reviewed. Consideration is given to the drainage mechanism around a probe which protrudes a fixed specified distance into the oil. A lubrication analysis of the thin water film may be matched into a capillary-static solution for the outer geometry using a slender transition region if, and only if, the pressure gradient in the film is negative as it meets the static meniscus. The remarkable result is that, in practice, there is a race between rupture in the transition region and rupture at the tip. The analysis is applicable to the case of a very slow far field flow and offers significant insight into the non-static case. Finally, a similar approach is applied to study the motion of the thin water film in the fully inviscid approximation, with surface tension and a density contrast between the fluids

Dynamic wetting and spreading and the role of topography

Hoffman-de Gennes law, which relates the edge speed, ve, to the dynamic and equilibrium contact angles q and qe by ve µq(q2 -qe 2 ). When the liquid wets the surface completely and the equilibrium contact angle vanishes, the edge speed is proportional to the cube of the dynamic contact angle. When the droplets are non-volatile this law gives rise to simple power laws with time for the contact angle and other parameters in both the capillary and gravity dominated regimes. On a textured surface the equilibrium state of a droplet is strongly modified due to the amplification of the surface chemistry induced tendencies by the topography. The most common example is the conversion of hydrophobicity into superhydrophobicity. However, when the surface chemistry favors partial wetting, topography can result in a droplet spreading completely. A further, frequently over-looked consequence of topography is that the rate at which an out-of-equilibrium droplet spreads should also be modified. In this report, we review ideas related to the idea of topography induced wetting and consider how this may relate to dynamic wetting and the rate of droplet spreading. We consider the effect of the Wenzel and Cassie-Baxter equations on the driving forces and discuss how these may modify power-laws for spreading. We relate the ideas to both the hydrodynamic viscous dissipation model and the molecular-kinetic theory of spreading. This suggests roughness and solid surface fraction modified Hoffman-de Gennes laws relating the edge speed to the dynamic and equilibrium contact angle

Tear film thickness variations and the role of the tear meniscus

A mathematical model is developed to investigate the two-dimensional variations in the thickness of tear fluid deposited on the eye surface during a blink. Such variations can become greatly enhanced as the tears evaporate during the interblink period.\ud The four mechanisms considered are: i) the deposition of the tear film from the upper eyelid meniscus, ii) the flow of tear fluid from under the eyelid as it is retracted and from the lacrimal gland, iii) the flow of tear fluid around the eye within the meniscus and iv) the drainage of tear fluid into the canaliculi through the inferior and superior puncta.\ud There are two main insights from the modelling. First is that the amount of fluid within the tear meniscus is much greater than previously employed in models and this significantly changes the predicted distribution of tears. Secondly the uniformity of the tear film for a single blink is: i) primarily dictated by the storage in the meniscus, ii) quite sensitive to the speed of the blink and the ratio of the viscosity to the surface tension iii) less sensitive to the precise puncta behaviour, the flow under the eyelids or the specific distribution of fluid along the meniscus at the start of the blink. The modelling briefly examines the flow into the puncta which interact strongly with the meniscus and acts to control the meniscus volume. In addition it considers flow from the lacrimal glands which appears to occurs continue even during the interblink period when the eyelids are stationary

Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell

We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.Comment: 42 pages, 5 figures, added references, minor changes, to appear in Int. J. Mod. Phys. B (1998

Bio-nanotechnology application in wastewater treatment

The nanoparticles have received high interest in the field of medicine and water purification, however, the nanomaterials produced by chemical and physical methods are considered hazardous, expensive, and leave behind harmful substances to the environment. This chapter aimed to focus on green-synthesized nanoparticles and their medical applications. Moreover, the chapter highlighted the applicability of the metallic nanoparticles (MNPs) in the inactivation of microbial cells due to their high surface and small particle size. Modifying nanomaterials produced by green-methods is safe, inexpensive, and easy. Therefore, the control and modification of nanoparticles and their properties were also discussed

Revisiting Hele-Shaw dynamics to better understand beach evolution

Wave action, particularly during storms, drives the evo lution of beaches. Beach evolution by non-linear break ing waves is poorly understood due to its three-dimensional character, the range of scales involved, and our limited understanding of particle-wave interactions. We show how a novel, three-phase extension to the classic “Hele-Shaw” laboratory experiment can be designed that creates beach morphologies with breaking waves in a quasi-two-dimensional setting. Our thin Hele-Shaw cell simplifies the inherent complexity of three-phase dynamics: all dynamics become clearly visible and measurable. We show that beaches can be created in tens of minutes by several types of breaking waves, with about one-second periods. Quasi-steady beach morphologies emerge as function of initial water depth, at-rest bed level and wave-maker frequency. These are classified mathematically and lead to beaches, berms and sand bars

Breaking waves on a dynamic Hele-Shaw beach

We report the formation of quasi-steady beaches and dunes via breaking waves in our tabletop ‘Hele-Shaw’ beach experiment. Breaking waves are generated by a wave maker, and zeolite particles act as sand. The tank is narrow, just over one-particle diameter wide, creating a quasi-2D set-up. Classical breaker types are observed on a time-scale of about a second. Beach formation under breakers occurs on a longer time-scale, and is a matter of minutes for a range of mono-chromatic wave frequencies. Alternating the wave maker motion between two frequencies generally leads to beach formation but occasionally to formation of a stable dune with water on either side. Finally, the Hele-Shaw configuration explored here experimentally lends itself to multi-scale modeling of beach dynamics