Thin, binary liquid droplets, containing polymer: An investigation of the parameters controlling film shape

For the fabrication of P-OLED displays, using inkjet printing, it is important to control the final shape resulting from evaporation of droplets containing polymer. Due to peripheral pinning and consequent outward capillary flow, a ring-like final shape is typically observed. This is often undesirable, with a spatially uniform film usually required. Several experimental studies have shown that binary liquid inks can prevent ring formation. There is no consensus of opinion on the mechanism behind this improvement. We have developed a model for the drying of thin, binary liquid droplets, based on thin-film lubrication theory, and we solve the governing equations to predict the final shape. White-light interferometry experiments are conducted to verify the findings. In addition, we present the results of a linear stability analysis that identifies the onset of an instability driven by a difference in surface tension. If the more volatile liquid is more abundant, an instability becomes increasingly likely.This research has been funded by the Engineering & Physical Sciences Research Council, UK and CASE studentship funding from Cambridge Display Technology Ltd., UK. We thank Dr Mark Dowling of Cambridge Display Technology Ltd., for help with the experimental setup.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.16

Thin, binary liquid droplets, containing polymer: an investigation of the parameters controlling film shape

For the fabrication of P-OLED displays, using inkjet printing, it is important to control the final shape resulting from evaporation of droplets containing polymer. Due to peripheral pinning and consequent outward capillary flow, a ring-like final shape is typically observed. This is often undesirable, with a spatially uniform film usually required. Several experimental studies have shown that binary liquid inks can prevent ring formation. There is no consensus of opinion on the mechanism behind this improvement. We have developed a model for the drying of thin, binary liquid droplets, based on thin-film lubrication theory and solve the governing equations to predict the final shape. White light interferometry experiments are conducted to verify the findings. In addition, we present the results of a linear stability analysis that identifies the onset of a surface tension differential driven instability. If the more volatile liquid is more abundant, an instability becomes increasingly likely.This research has been funded by the Engineering & Physical Sciences Research Council, UK and CASE studentship funding from Cambridge Display Technology Ltd., UK. We thank Dr Mark Dowling of Cambridge Display Technology Ltd., for help with the experimental setup.This is the author accepted manuscript. The final version is available from Cambridge University Press via http://dx.doi.org/10.1017/jfm.2016.16

Performance modelling of the Cambridge Fast Ring protocol

The Cambridge Fast Ring is high-speed slotted ring. The features that make it suitable for use at very large transmission rates are the synchronous transmission, the simplicity of the medium-access-control protocol, and the possibility of immediate retransmission of erroneous packets. A novel analytical model of the Cambridge Fast Ring with normal slots is presented. The model is shown to be accurate and usable over wide range of parameters. A performance analysis based on this model is presented

Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and Lambda-Transitions

We use a free-energy minimization approach to describe the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e. ``spontaneous breaking'' of the topology) of the original object on a secular time scale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems.Comment: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in Ap

Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.Comment: 10 pages, 8 figure

A Tale of Two Distributions: From Few To Many Vortices In Quasi-Two-Dimensional Bose-Einstein Condensates

Motivated by the recent successes of particle models in capturing the precession and interactions of vortex structures in quasi-two-dimensional Bose-Einstein condensates, we revisit the relevant systems of ordinary differential equations. We consider the number of vortices $N$ as a parameter and explore the prototypical configurations ("ground states") that arise in the case of few or many vortices. In the case of few vortices, we modify the classical result of Havelock [Phil. Mag. ${\bf 11}$, 617 (1931)] illustrating that vortex polygons in the form of a ring are unstable for $N \geq7$. Additionally, we reconcile this modification with the recent identification of symmetry breaking bifurcations for the cases of $N=2,\dots,5$. We also briefly discuss the case of a ring of vortices surrounding a central vortex (so-called $N+1$ configuration). We finally examine the opposite limit of large $N$ and illustrate how a coarse-graining, continuum approach enables the accurate identification of the radial distribution of vortices in that limit.Comment: 15 pages, 2 figure

Multiple Components in Narrow Planetary Rings

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with two degrees of freedom respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.Comment: 4 pages, 7 figures (some in colors