How valid is Taylor dispersion formula in slugs?

In a landmark paper, Taylor predicted that shear flow increases the effective diffusivity of species [Taylor, Proc. Roy. Soc. A, 219:186-203,1953]. This paper focused on Poiseuille flow in a circular pipe and predicted the existence of an effective species diffusion much greater than molecular diffusion. The ratio between the effective and molecular diffusion was shown to scale with the square of the Peclet number (product of the pipe diameter with the mean flow velocity divided by the molecular diffusivity). Taylor's study assumed two infinite columns of miscible fluids initially juxtaposed in a pipe and transported by the flow. A question of high practical interest is how valid this prediction is when a finite-sized slug is considered instead of an infinite fluid column. This paper sheds light on the finite-size effects on the mixing of two miscible fluids in a slug and quantifies how accurate Taylor's prediction is for finite length liquid columns. 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Measurement of differential cross sections and W + /W − cross-section ratios for W boson production in association with jets at √s =8 TeV with the ATLAS detector

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The topic researched for this thesis pertains to the transport and mixing of liquids in the micro-scale. With microfluidic applications in mind, the aim of this research is to further understand and investigate the role of surface tension gradient in the behavior of liquid droplets and slugs. Various platforms that offer differing air-liquid interface exposure, as well as the influence of gravity, have been studied in this research. First, the work pertaining to the uphill climb of a water droplet due to the presence of an adjacent volatile droplet is presented. The experimental results from this novel method of propulsion were confirmed through numerical simulations that accounted for two-phase flows and the transport of diluted species. Second, the mixing of two miscible liquid droplets, of which one is varied by concentration, was investigated. The results provide a clear contrast between the mixing rates resulting from two systems: one with the influence of surface tension gradient, and the other with only molecular diffusion. The numerical simulations carried out confirmed that mixing rate is improved when a surface tension gradient is present. Third, the actuation of droplets in a partially-enclosed setup known as a Hele-Shaw cell was investigated. Sandwiched in between two parallel plates, the actuation of a water droplet was observed upon the introduction of a volatile droplet adjacent to it. The Marangoni and dissipative forces were estimated through both analytical and numerical approaches, where close agreement was found. Lastly, a numerical model was developed to estimate the resistive force for a water slug in a capillary tube. Compared to the first three works investigated, the setup for the capillary tube is different in that it is fully-enclosed. In the numerical approach, the experimental parameters previously published by our group were used and a range of body force values were incorporated to estimate the forces. As a result, numerical results for Marangoni force that agrees well with analytical values were obtained. A second dimensionless model built allowed for the study of mixing time through altering only the Reynolds and Peclet number. The work undertaken for this research has shown the feasibility of liquid self-propulsion in various setups. Additional parametric studies performed serve as a valuable contribution to this thesis. The numerical models built enable the understanding of the effects of parameters that are otherwise difficult to achieve experimentally. The works presented in this thesis, both experimental and numerical, provide insight into droplet actuation or coalescence through surface tension gradient, which could serve as a basis for future work in the similar context

Integration of vapor-solid grown ZnO nanowires through dielectrophoresis

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