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Continuous InkJet (CIJ) printing is a common 2-Dimensional printing technique that creates jets of ink that breakup into drops as they are propelled towards a substrate to create a print. Inkjet printing has been used not only to print on paper, but to manufacture a variety of devices including OLEDs, solar cells and microfluidic devices. In many cases, the ‘ink’ consists of a polymer dissolved in a volatile solvent. As this ink is sprayed on to the substrate, the solvent evaporates, leaving the polymer behind as the print. The addition of the polymer alters the physics of the problem significantly enough that it varies greatly from jetting only a fluid with nothing dissolved in it. Polymers impart viscoelasticity to the solution, creating ink jets that are long-lived and difficult to break into droplets. In order to maintain the formation of drops in a repeatable, uniform fashion, a disturbance of known magnitude is imposed upon the jet. While jetting a liquid with no additives in it, this disturbance governed jet breakup leads to the formation of satellite drops, smaller drops of fluid in-between the main jet drops. Satellite drops are an undesirable occurrence in inkjet printing because of their unpredictable behavior and potential to affect the quality of the print. However, the addition of polymers to the liquid can control and potentially suppress the formation of these satellite drops, greatly improving the print quality. The elasticity of iv the polymer and its ability to influence the jet behavior and formation of satellite drops is highly dependent on multiple factors including the backbone rigidity, molecular weight and the concentration in which it is present in the fluid. Strongly viscoelastic effects have a marked effect on the jet and their presence can be quantified quite easily. However, some polymers show weak viscoelastic behavior while present in the ink fluids and may or may not affect the jetting process. The objective of this study is to examine such a class of polymeric fluids that are weakly viscoelastic in the context of inkjet printing and satellite drop formation. Firstly, the fluids are tested in an extensional rheology setup called Capillary Breakup Extensional Rheometry – Drop-on-Substrate (CaBER-DoS) to quantify their extensional properties. Then, they are tested in an emulated inkjet printing setup. The goal is to quantify the impact of the aforementioned factors on jetting and using satellite drop behavior as a guiding metric to understanding viscoelastic behavior in inkjet printing fluids.

The asymptotic behavior of the wave functions of three charged particles has been investigated. There are two different types of three-body scattering wave functions. The first type of scattering wave function evolves from the incident three-body wave of three charged particles in the continuum. The second type of scattering wave function evolves from the initial two-body incident wave. In this work the asymptotic three-body incident wave has been derived in the asymptotic regions where two particles are close to each other and far away from the third particle. This wave function satisfies the Schrodinger equation up to terms O(1/3pa), where pa is the distance between the center of mass of two particles and the third particle. The derived asymptotic three-body incident wave transforms smoothly into Redmond’s asymptotic incident wave in the asymptotic region where all three particles are well separated. For the scattering wave function of the second type the asymptotic threebody scattered wave has been derived in all the asymptotic regions. In the asymptotic region where all three particles well separated, the derived asymptotic scattered wave coincides with the Peterkop asymptotic wave. In the asymptotic regions where two particles are close to each other and far away from the third one, this is a new expression which is free of the logarithmically diverging phase factors that appeared in the Peterkop approach. The derived asymptotic scattered wave resolves a long-standing phase-amplitude ambiguity. Based on these results the expressions for the exact prior and post breakup amplitudes have been obtained. The post breakup amplitude for charged particles has not been known and has been derived for the first time directly from the prior form. It turns out that the post form of the breakup amplitude is given by a surface integral in the six dimensional hyperspace, rather than a volume integral, with the transition operator expressed in terms of the interaction potentials. We also show how to derive a generalized distorted-wave-Born approximation amplitude (DWBA) from the exact prior form of the breakup amplitude. It is impossible to derive the DWBA amplitude from the post form. The three-body Coulomb incident wave is used to calculate the reaction rates of 7Be(ep, e)8B and 7Be(pp, p)8B nonradiative triple collisions in stellar environments.

This work is an extension to the spray model of Watkins and Jones (2010). In their model, the spray is characterized by evaluating the three moments Q_2, Q_3 and Q_4 of general gamma number size distribution from their transport equations. The sub-models of drop drag, drop break-up and drop collisions were simulated in terms of gamma distributions. The model is considered as non-vaporising and compared with cases which have low ambient gas temperature and also is strict to a particular set of sub-models for drop drag and break up which they are applicable to produce integrable functions. In this work the model is adjusted to allow a variety of sub-models to be implemented. Three models (TAB, ETAB, DDB) are considered for drop breakup which have been basically introduced to be used with the Droplet Discrete Method (DDM) approach. So in order to implement these models with the model of Watkins and Jones the source terms of the breakup are calculated by grouping the droplets in each cell into parcels which contain a certain number of droplets with similar physical properties (size, velocity, temperature ...). The source terms of each parcel are calculated and multiplied by the number of droplets in these parcels and a numerical integration is then used to obtain the resultant effect of the drop breakup in each cell. The number of drops in each cell is determined from the gamma size distribution. Also three hybrid breakup models (KH-RT, Turb-KH-RT, Turb-TAB) which include two distinct steps: primary and secondary break up model are implemented. The Kelvin- Helmholtz (KH) and the turbulence induced breakup (Turb) models were used to predict the primary break up of the intact liquid core of a liquid jet while the secondary break up is modelled using the TAB model and competition between the KH and the RT models. Both models are allowed to work simultaneously. However it is assumed that if the disintegration occurs due to the RT the KH break up does not occur. In case of drag sub-model, a dynamic drag model is introduced which accounts for the effects of drop distortion and oscillation due to the effects of high relative velocity between the liquid and the surrounding gas. In this model the drag coefficient is empirically related to the magnitude of the drop deformation. The magnitude of drop deformation was calculated by using the TAB model. In this work, the effects of mass and heat transfer on the spray are modelled. An additional equation for the energy of the liquid is solved. The mass transfer rate is evaluated using the model of Godsave (1953) and Spalding (1953) while the Faeth correlation (1983) is used to model heat transfer between the two phases. For all equations of heat and mass transfer between phases, the drop Nusselt and Sherwood number are calculated by using the correlation of Ranz and Marshall. In this model also the liquid surface-average temperature T_l2 which is calculated by Watkins (2007) is used to determine the heat and mass transfer between phases instead of liquid volume-average temperature. It was derived by assuming a parabolic temperature profile within individual drops. All the equations are treated in Eulerian framework using the finite volume method. The model has been applied to a wide range of sprays and compared to a number of experiments with different operating conditions including high liquid injection pressure and high ambient gas density and temperature. A reasonable agreement is found by the ETAB model with most of the data while the TAB and the DDB models continually underestimate the penetration and drop sizes of the spray. The hybrid breakup models perform well and show better agreement with the available experimental data than the single breakup models. In term of high temperature cases, the model correctly captures the effect of evaporation on the different spray properties especially with hybrid break up model.

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This study examined models of self and other as they relate to attachment, forgiveness, emotional and cognitive reactions to a breakup, relationship variables, and positive and negative feelings toward the self and former partner after a romantic relationship is ended. This study also tested how these variables change over time. Data were collected over a period of five weeks from 130 undergraduates who had experienced a breakup within the two weeks prior to beginning the study. Data were analyzed with a series of univariate and multivariate analyses of variance. Results found that there were differences in how participants reacted to the relationship breakup based on attachment style. There were some changes over time in the variables for all the attachment styles, and there was only one interaction between time and attachment style. Results are discussed in terms of previous research findings. Limitations of the current study are discussed and suggestions for future research are presented.

River ice breakup and associated flooding are realities for many northern communities. This is certainly the case in Hay River, NWT, which is located at the junction of the Hay River and Great Slave Lake. Hay River experiences a wide range of spring river ice scenarios; from docile thermal melt outs, to severe ice jams resulting in life-threatening, disastrous flooding. This study involved the analysis of five seasons of aerial and time-lapse photographs, water level measurements and hydrometeorologic data. This work also compiled an extended historical record of breakup in the Hay River delta, which was compared against the field data gathered for this study; combining local, experiential knowledge with scientific observation into a cohesive description of breakup. This will be used to advise the non-technical flood watch community on the patterns of timing and sequencing of breakup, which is critical for evacuation planning. / Water Resources Engineering

Many flow regimes in Nuclear Reactor Safety Research are characterized by multiphase flows, with one phase being a continuous liquid and the other phase consisting of gas or vapour of the liquid phase. In dependence on the void fraction of the gaseous phase the flow regimes e.g. in vertical pipes are varying from bubbly flows with low and higher volume fraction of bubbles to slug flow, churn turbulent flow, annular flow and finally to droplet flow. In the regime of bubbly and slug flow the multiphase flow shows a spectrum of different bubble sizes. While disperse bubbly flows with low gas volume fraction are mostly mono-disperse, an increase of the gas volume fraction leads to a broader bubble size distribution due to breakup and coalescence of bubbles. Bubbles of different sizes are subject to lateral migration due to forces acting in lateral direction different from the main drag force direction. The bubble lift force was found to change the sign dependent on the bubble size. Consequently this lateral migration leads to a de-mixing of small and large bubbles and to further coalescence of large bubbles migrating towards the pipe center into even larger Taylor bubbles or slugs. An adequate modeling has to consider all these phenomena. A Multi Bubble Size Class Test Solver has been developed to investigate these effects and test the influence of different model approaches. Basing on the results of these investigations a generalized inhomogeneous Multiple Size Group (MUSIG) Model based on the Eulerian modeling framework has been proposed and was finally implemented into the CFD code CFX. Within this model the dispersed gaseous phase is divided into N inhomogeneous velocity groups (phases) and each of these groups is subdivided into Mj bubble size classes. Bubble breakup and coalescence processes between all bubble size classes Mj are taken into account by appropriate models. The inhomogeneous MUSIG model has been validated against experimental data from the TOPFLOW test facility.