Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers

Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of O(1). The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect

Surface tension driven flow of blood in a rectangular microfluidic channel: Effect of erythrocyte aggregation

Microfluidic platforms have increasingly been explored for in vitro blood diagnostics and for studying complex microvascular processes. The perfusion of blood in such devices is typically achieved through pressure driven set-ups. Surface tension driven blood flow provides an alternative flow delivery option, and various studies in the literature have examined the behaviour of blood flow in such fluidic devices. In such flows, the influence of red blood cell (RBC) aggregation, the phenomenon majorly responsible for the non-Newtonian nature of blood, requires particular attention. In the present work, we examine differences in the surface tension driven flow of aggregating, non-aggregating RBC, and Newtonian suspensions, in a rectangular micro channel. The velocity fields were obtained using microPIV techniques. The analytical solution for blood velocity in the channel is developed utilising the power law model for blood viscosity. The results showed that RBC aggregation has an impact at the late stages of the flow, observed mainly in the bluntness of the velocity profiles. At the initial stages of the flow the shearing conditions are found moderately elevated, preventing intense RBC aggregate formation. As the flow decelerates in the channel RBC aggregation increases, affecting the flow characteristics

Developed liquid film passing a trailing edge under the action of gravity and capillarity

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge

Dissolution and sorption processes on the surface of calcite in the presence of high Co2+ concentration

The interaction of the calcite surface with Co2+-rich aqueous solutions ([Co2+aq]initial = 1000 ppm, i.e., ca. 17 mM) was investigated by means of macroscopic experiments and surface spectroscopic techniques. In the case of the macroscopic experiments, calcite powder and monocrystals were immersed into solutions for different time periods (from 1 min to one month). The Ca concentrations in the filtrates was measured by means of atomic absorption spectrometry (AAS) while the interacted solids were studied using a combination of X-ray photoelectron spectroscopy (XPS) and 12C-rutherford backscattering spectrometry (12C-RBS). The macroscopic data showed a characteristic surface dissolution process, in parallel to the surface sorption processes. Adsorption and co-precipitation were seen for almost the entire immersion period for both calcite powder and monocrystals. The surface study by XPS (analyzed at a depth of approximately 12 nm) suggested that adsorption takes place in the first hour of the interaction, followed by incorporation of Co2+ into calcite surface layers, leading to the formation of a Co2+-bearing surface (co)precipitate, which occurs over a period of hours and days. The 12C-RBS measurements on calcite { 10 1 ¯ 4 } indicated that the thickness of this surface co-precipitate was 270 nm after one day and then stabilized at 320 nm after more than a week

Inequities in energy-balance related behaviours and family environmental determinants in European children : baseline results of the prospective EPHE evaluation study

Background: Tackling inequalities in overweight, obesity and related determinants has become a top priority for the European research and policy agendas. Although it has been established that such inequalities accumulate from early childhood onward, they have not been studied extensively in children. The current article discusses the results of an explorative analysis for the identification of inequalities in behaviours and their determinants between groups with high and low socio-economic status. Methods: This study is part of the Epode for the Promotion of Health Equity (EPHE) evaluation study, the overall aim of which is to assess the impact and sustainability of EPODE methodology to diminish inequalities in childhood obesity and overweight. Seven community-based programmes from different European countries (Belgium, Bulgaria, France, Greece, Portugal, Romania, The Netherlands) participate in the EPHE study. In each of the communities, children aged 6-8 years participated, resulting in a total sample of 1266 children and their families. A parental self-administrated questionnaire was disseminated in order to assess the socio-economic status of the household, selected energy balance-related behaviours (1. fruit and vegetable consumption; 2. soft drink/fruit juices and water consumption; 3. screen time and 4. sleep duration) of the children and associated family environmental determinants. The Mann-Whitney U test and Pearson's chi-square test were used to test differences between the low and high education groups. The country-specific median was chosen as the cut-off point to determine the educational level, given the different average educational level in every country. Results: Children with mothers of relatively high educational level consumed fruits and vegetables more frequently than their peers of low socio-economic status. The latter group of children had a higher intake of fruit juices and/or soft drinks and had higher screen time. Parental rules and home availability were consistently different between the two socio-economic groups in our study in all countries. However we did not find a common pattern for all behaviours and the variability across the countries was large. Conclusions: Our findings are indicative of socio-economic inequalities in our samples, although the variability across the countries was large. The effectiveness of interventions aimed at chancing parental rules and behaviour on health inequalities should be studied

Choking and hydraulic jumps in laminar flow

The viscous hydraulic jump still represents research in progress rather than a finalised edifice. The existing rigorous approaches show how this phenomenon is tied in with a bifurcation of the upstream flow adjacent to the guiding rigid plate of finite length, aligned perpendicularly to the direction of gravity. Here, this together with the upstream influence by the detached flow triggers transition from super‐ to subcritical flow (sensing its susceptibility to the upstream propagation of small disturbances). We present recent advances in the self‐consistent theory of single‐layer jumps continued as free shear layers

Surface tension driven flow of blood in a rectangular microfluidic channel: Effect of erythrocyte aggregation

Microfluidic platforms have increasingly been explored for in vitro blood diagnostics and for studying complex microvascular processes. The perfusion of blood in such devices is typically achieved through pressure-driven setups. Surface tension driven blood flow provides an alternative flow delivery option, and various studies in the literature have examined the behavior of blood flow in such fluidic devices. In such flows, the influence of red blood cell (RBC) aggregation, the phenomenon majorly responsible for the non-Newtonian nature of blood, requires particular attention. In the present work, we examine differences in the surface tension driven flow of aggregating and non-aggregating RBC and Newtonian suspensions, in a rectangular microchannel. The velocity fields were obtained using micro-PIV techniques. The analytical solution for blood velocity in the channel is developed utilizing the power law model for blood viscosity. The results showed that RBC aggregation has an impact at the late stages of the flow, observed mainly in the bluntness of the velocity profiles. At the initial stages of the flow, the shearing conditions are found moderately elevated, preventing intense RBC aggregate formation. As the flow decelerates in the channel, RBC aggregation increases, affecting the flow characteristics

Determination of As in particulate matter using Se as an internal standard by multi-element electrothermal atomic absorption spectrometry

In this study Se has been evaluated as a potential internal standard for the determination of As in particulate matter using multi-element electrothermal atomic absorption spectrometry. The use of Se reduced matrix interferences improving the recoveries and method precision, especially at concentration levels near the limit of quantification. Moreover, a better linearity was achieved. The detection limits with and without the use of Se were 1.88 μg L-1or 1.13 ng m-3and 2.88 μg L-1or 1.73 ng m-3, respectively. The calculated recoveries ranged from 98.9% to 110% rather than 41.5% to 114% without Se. In both cases, with and without the use of Se, the method uncertainty was calculated based on Monte Carlo analysis. The results showed that the uncertainty reduced at the lower concentration levels, near the limit of quantification, while it increased at the higher ones. The method was applied to determine As in PM10 samples from an industrial area near Athens. The mean annual concentration of As was found to be 5.69 ng m-3, lower than the air quality limit set by the European Council. This journal is © the Partner Organisations 2014