Wetting of prototypical one- and two-dimensional systems: Thermodynamics and density functional theory.

Consider a two-dimensional capped capillary pore formed by capping two parallel planar walls with a third wall orthogonal to the two planar walls. This system reduces to a slit pore sufficiently far from the capping wall and to a single planar wall when the side walls are far apart. Not surprisingly, wetting of capped capillaries is related to wetting of slit pores and planar walls. For example, the wetting temperature of the capped capillary provides the boundary between first-order and continuous transitions to condensation. We present a numerical investigation of adsorption in capped capillaries of mesoscopic widths based on density functional theory. The fluid-fluid and fluid-substrate interactions are given by the pairwise Lennard-Jones potential. We also perform a parametric study of wetting in capped capillaries by a liquid phase by varying the applied chemical potential, temperature, and pore width. This allows us to construct surface phase diagrams and investigate the complicated interplay of wetting mechanisms specific to each system, in particular, the dependence of capillary wetting temperature on the pore width

On the moving contact line singularity: Asymptotics of a diffuse-interface model

The behaviour of a solid-liquid-gas system near the three-phase contact line is considered using a diffuse-interface model with no-slip at the solid and where the fluid phase is specified by a continuous density field. Relaxation of the classical approach of a sharp liquid-gas interface and careful examination of the asymptotic behaviour as the contact line is approached is shown to resolve the stress and pressure singularities associated with the moving contact line problem. Various features of the model are scrutinised, alongside extensions to incorporate slip, finite-time relaxation of the chemical potential, or a precursor film at the wall.Comment: 14 pages, 3 figure

A comparison of slip, disjoining pressure, and interface formation models for contact line motion through asymptotic analysis of thin two-dimensional droplet spreading

The motion of a contact line is examined, and comparisons drawn, for a variety of models proposed in the literature. Pressure and stress behaviours at the contact line are examined in the prototype system of quasistatic spreading of a thin two-dimensional droplet on a planar substrate. The models analysed include three disjoining pressure models based on van der Waals interactions, a model introduced for polar fluids, and a liquid-gas diffuse-interface model; Navier-slip and two non-linear slip models are investigated, with three microscopic contact angle boundary conditions imposed (two of these contact angle conditions having a contact line velocity dependence); and the interface formation model is also considered. In certain parameter regimes it is shown that all of the models predict the same quasistatic droplet spreading behaviour.Comment: 29 pages, 3 figures, J. Eng. Math. 201

The contact line behaviour of solid-liquid-gas diffuse-interface models

A solid-liquid-gas moving contact line is considered through a diffuse-interface model with the classical boundary condition of no-slip at the solid surface. Examination of the asymptotic behaviour as the contact line is approached shows that the relaxation of the classical model of a sharp liquid-gas interface, whilst retaining the no-slip condition, resolves the stress and pressure singularities associated with the moving contact line problem while the fluid velocity is well defined (not multi-valued). The moving contact line behaviour is analysed for a general problem relevant for any density dependent dynamic viscosity and volume viscosity, and for general microscopic contact angle and double well free-energy forms. Away from the contact line, analysis of the diffuse-interface model shows that the Navier--Stokes equations and classical interfacial boundary conditions are obtained at leading order in the sharp-interface limit, justifying the creeping flow problem imposed in an intermediate region in the seminal work of Seppecher [Int. J. Eng. Sci. 34, 977--992 (1996)]. Corrections to Seppecher's work are given, as an incorrect solution form was originally used.Comment: 33 pages, 3 figure

Dynamic Pricing in the Presence of Social Learning and Strategic Consumers

When a product of uncertain quality is first introduced, consumers may choose to strategically delay their purchasing decisions in anticipation of the product reviews of their peers. This paper investigates how the presence of social learning affects the strategic interaction between a dynamic-pricing monopolist and a forward-looking consumer population, within a simple two-period model. Our analysis yields three main insights. First, we find that the presence of social learning has significant structural implications for optimal pricing policies: In the absence of social learning, decreasing price plans are always preferred by the firm; by contrast, in the presence of social learning we find that (i) if the firm commits to a price path ex ante (preannounced pricing), an increasing price plan is typically announced, whereas (ii) if the firm adjusts price dynamically (responsive pricing), prices are initially low and may either rise or decline over time. Second, we establish that under both preannounced and responsive pricing, even though the social learning process exacerbates strategic consumer behavior (i.e., increases strategic purchasing delays), its presence results in an increase in expected firm profit. Third, we illustrate that, contrary to results reported in existing literature on strategic consumer behavior, in settings where social learning is significantly influential, preannounced pricing policies are generally not beneficial for the firm

A review of the healthcare-management (modeling) literature published at Manufacturing and Service Operations Management

Healthcare systems throughout the world are under pressure to widen access, improve efficiency and quality of care, and reduce inequity. Achieving these conflicting goals requires innovative approaches, utilizing new technologies, data analytics, and process improvements. The operations management community has taken on this challenge: more than 10% of articles published in M&SOM in the period from 2009 to 2018 has developed analytical models that aim to inform healthcare operational decisions and improve medical decision-making. This article presents a review of the research published in M&SOM on healthcare management since its inception 20 years ago and reflects on opportunities for further research

Asymptotic analysis of evaporating droplets

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.We consider the evaporation dynamics of a two-dimensional, partially-wetting sessile droplet of a volatile liquid in its pure vapour, which is supported on a smooth horizontal superheated substrate. Assuming that the liquid properties remain unchanged, we utilise a one-sided lubrication-type model for the evolution of the droplet thickness, which accounts for the effects of evaporation, capillarity, slip and the kinetic resistance to evaporation. We follow an asymptotic approach, which yields a set of coupled evolution equations for the droplet radius and area, estimating analytically the evaporation-modified apparent angle when evaporation effects are weak. The validity of our matching procedure is verified by numerical experiments, obtaining also an estimate for the evaporation time

Density functional study of condensation in capped capillaries.

We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at $T\leqslant {{T}_{\text{cw}}}$ ) or continuous (at $T\gt {{T}_{\text{cw}}}$ ), where ${{T}_{\text{cw}}}$ is the capillary wetting temperature. At $T \gt {{T}_{\text{cw}}}$ , the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies