A mathematical model of three-dimensional flow in a scraped-surface heat exchanger

We present a simple mathematical model of fluid flow in a Scraped-Surface Heat Exchanger (SSHE). Specifically we consider steady isothermal flow of a Newtonian fluid around a periodic array of pivoted scraper blades in a channel with one stationary and one moving wall, when there is an applied pressure gradient in a direction perpendicular to the wall motion. The flow is fully three-dimensional, but decomposes naturally into a two-dimensional transverse flow driven by the boundary motion and a longitudinal pressure-driven flow

Travelling-wave similarity solutions for an unsteady shear-stress-driven dry patch in a flowing film

We investigate unsteady flow of a thin film of Newtonian fluid around a symmetric slender dry patch moving with constant velocity on an inclined planar substrate, the flow being driven by a prescribed constant shear stress at the free surface of the film (which would be of uniform thickness in the absence of the dry patch). We obtain a novel unsteady travelling-wave similarity solution which predicts that the dry patch has a parabolic shape and that the film thickness increases monotonically away from the dry patch

Rivulet flow down a slippery substrate

A detailed analysis of small-scale locally unidirectional gravity-driven rivulet flow with prescribed volume flux down an inclined slippery substrate for a rivulet with either constant width (i.e., pinned contact lines) or constant contact angle is undertaken. In particular, we determine the effect of varying the Navier slip length λ (i.e., the strength of the slip at the solid-fluid interface) on the rivulet. The present analysis shows that the shape and size of the rivulet and the velocity within it depend strongly on the value of λ. Increasing the value of λ reduces the viscous resistance at the substrate and, hence, leads to a larger velocity within the rivulet, and so the prescribed flux is achieved with a smaller rivulet. In particular, in the limit of strong slip, λ → ∞, for a rivulet of a perfectly wetting fluid and a rivulet with constant width, the velocity becomes large and plug-like like O(λ1/2) ≫ 1, and the rivulet becomes shallow like O(λ-1/2) ≪ 1, while for a rivulet with positive constant contact angle, the velocity becomes large and plug-like like O(λ2/3) ≫ 1, and the rivulet becomes narrow like O(λ-1/3) ≪ 1 and shallow like O(λ-1/3) ≪ 1

ANIMA OBSCURA

This technical paper presents the results of the past three years research and development work by an interdisciplinary team of artists, scholars, disability empowerment experts, engineers, computer scientists and medical doctors, working together to invent new cutting edge technologies for real people’s needs. The group has called itself SPIRITlevel (see www.smartlabcentre.com) and has aimed to harness and share the power of technology when invented by and for people with unlimited imaginations despite physical limitations. The project discussed is ‘ANIMA OBSCURA’: a showcase performance designed to demonstrate the empowering abilities of new technology in the performing arts, where bio-affective feedback systems and motion tracking technologies can be usefully (and invisibly) combined with live performance by disabled and able-bodied dancers, to allow every person to dance, move, and bring an augmented world to life. The showcase has broadcastable elements and scaleable format that makes it suitable for demonstration in hospital settings, rehabilitation units, art galleries, museums, and main stages. It can be utilised by individuals for personal therapy and healing, or used collaboratively in online game-playing between hospital beds or, in the ‘mainstream’, through webcast and broadcast formats

Rivulet flow over and through a permeable membrane

Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a rivulet of fluid with finite width over and through a permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semiwidth or fixed contact angle is determined, and it is shown how the length, base area, and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system. In particular, whereas there is a physically realizable pendant rivulet solution only if the semiwidth does not exceed a critical value, there are physically realizable sessile and vertical rivulet solutions for all values of the semiwidth; moreover, a sessile rivulet with fixed semiwidth has a finite maximum possible length which is attained in the limit of a wide rivulet

Competitive evaporation of multiple sessile droplets

An asymptotic model is derived for the competitive diffusion-limited evaporation of multiple thin sessile droplets under the assumption that the droplets are well separated. Exact solutions of the model are obtained for a pair of and for a polygonal array of identical droplets, and the model is found to perform well even outside its formal range of validity, up to and including the limit of touching droplets. The shielding effect of droplets on each other is demonstrated, and the model is used to investigate the effect of this shielding on droplet evolutions and lifetimes, as well as on the coffee-ring effect. The theoretical predictions of the model are found to be in good agreement with recent experimental results for seven relatively closely-spaced droplets, suggesting that the model could be a useful tool for studying a wide range of other droplet configurations

The shear-driven Rayleigh problem for generalised Newtonian fluids

We consider a variant of the classical ‘Rayleigh problem’ (‘Stokes’s first problem’) in which a semi-infinite region of initially quiescent fluid is mobilised by a shear stress applied suddenly to its boundary. We show that self-similar solutions for the fluid velocity are available for any generalised Newtonian fluid, regardless of its constitutive law. We demonstrate how these solutions may be used to provide insight into some generic questions about the behaviour of unsteady, non-Newtonian boundary layers, and in particular the effect of shear thinning or thickening on the thickness of a boundary layer

Coating flow on a rotating cylinder in the presence of an irrotational airflow with circulation

A detailed analysis of steady coating flow of a thin film of a viscous fluid on the outside of a uniformly rotating horizontal circular cylinder in the absence of surface-tension effects but in the presence of a non-uniform pressure distribution due to an irrotational airflow with circulation shows that the presence of the airflow can result in qualitatively different behaviour of the fluid film from that in classical coating flow. Full-film solutions corresponding to a continuous film of fluid covering the entire cylinder are possible only when the flux and mass of fluid do not exceed critical values, which are determined in terms of the non-dimensional parameters F and K representing the speed of the far-field airflow and the circulation of the airflow, respectively. The qualitative changes in the behaviour of the film thickness as F and K are varied are described. In particular, the film thickness can have as many as four stationary points and, in general, has neither top-to-bottom nor right-to-left symmetry. In addition, when the circulation of the airflow is in the same direction as the rotation of the cylinder the maximum mass of fluid that can be supported on the cylinder is always less than that in classical coating flow, whereas when the circulation is in the opposite direction the maximum mass of fluid can be greater than that in classical coating flow

Asymptotic and numerical analysis of a simple model for blade coating

Motivated by the industrial process of blade coating, the two-dimensional flow of a thin film of Newtonian fluid on a horizontal substrate moving parallel to itself with constant speed under a fixed blade of finite length in which the flows upstream and downstream of the blade are coupled via the flow under the blade is analysed. A combination of asymptotic and numerical methods is used to investigate the number and nature of the steady solutions that exist. Specially, it is found that in the presence of gravity there is always at least one, and (depending on the parameter values) possibly as many as three, steady solutions, and that when multiple solutions occur they are identical under and downstream of the blade, but differ upstream of it. The stability of these solutions is investigated, and their asymptotic behaviour in the limits of large and small flux and weak and strong gravity effects, respectively, determined

Tick-, mosquito-, and rodent-borne parasite sampling designs for the National Ecological Observatory Network

Parasites and pathogens are increasingly recognized as significant drivers of ecological and evolutionary change in natural ecosystems. Concurrently, transmission of infectious agents among human, livestock, and wildlife populations represents a growing threat to veterinary and human health. In light of these trends and the scarcity of long-term time series data on infection rates among vectors and reservoirs, the National Ecological Observatory Network (NEON) will collect measurements and samples of a suite of tick-, mosquito-, and rodent-borne parasites through a continental-scale surveillance program. Here, we describe the sampling designs for these efforts, highlighting sampling priorities, field and analytical methods, and the data as well as archived samples to be made available to the research community. Insights generated by this sampling will advance current understanding of and ability to predict changes in infection and disease dynamics in novel, interdisciplinary, and collaborative ways