Theory of Drop Formation

We consider the motion of an axisymmetric column of Navier-Stokes fluid with a free surface. Due to surface tension, the thickness of the fluid neck goes to zero in finite time. After the singularity, the fluid consists of two halves, which constitute a unique continuation of the Navier-Stokes equation through the singular point. We calculate the asymptotic solutions of the Navier-Stokes equation, both before and after the singularity. The solutions have scaling form, characterized by universal exponents as well as universal scaling functions, which we compute without adjustable parameters

Experiments in free shear flows: Status and needs for the future

Experiments in free turbulent flows are recommended with the primary concern placed on classical flows in order to augment understanding and for model building. Five classes of experiments dealing with classical free turbulent flows are outlined and proposed as being of particular significance for the near future. These classes include the following: (1) Experiments clarifying the effect of density variation owing to use of different gases, with and without the additional effect of density variation due to high Mach number or other effects; (2) experiments clarifying the role and importance of various parameters which determine the behavior of the near field as well as the condictions under which any of these parameters can be neglected; (3) experiments determining the cumulative effect of initial conditions in terms of distance to fully established flow; (4) experiments for cases where two layers of distinctly different initial turbulence structure flow side by side at the same mean speed; and (5) experiment using contemporary experimental techniques to study structure in free turbulent shear flows in order to compliment and support contemporary work on boundary layers

One-Dimensional Approximation of Viscous Flows

Attention has been paid to the similarity and duality between the Gregory-Laflamme instability of black strings and the Rayleigh-Plateau instability of extended fluids. In this paper, we derive a set of simple (1+1)-dimensional equations from the Navier-Stokes equations describing thin flows of (non-relativistic and incompressible) viscous fluids. This formulation, a generalization of the theory of drop formation by Eggers and his collaborators, would make it possible to examine the final fate of Rayleigh-Plateau instability, its dimensional dependence, and possible self-similar behaviors before and after the drop formation, in the context of fluid/gravity correspondence.Comment: 17 pages, 3 figures; v2: refs & comments adde

Air entrainment through free-surface cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow space inside the cusp destroys its stationary shape when the walls of the cusp come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations

Sociodemographic factors and patient perceptions are associated with attitudes to kidney transplantation among haemodialysis patients

Background. Treatment decisions made by patients with chronic kidney disease are crucial in the renal transplantation process. These decisions are influenced, amongst other factors, by attitudes towards different treatment options, which are modulated by knowledge and perceptions about the disease and its treatment and many other subjective factors. Here we study the attitude of dialysis patients to renal transplantation and the association of sociodemographic characteristics, patient perceptions and experiences with this attitude. Methods. In a cross-sectional study, all patients from eight dialysis units in Budapest, Hungary, who were on haemodialysis for at least 3 months were approached to complete a self-administered questionnaire. Data collected from 459 patients younger than 70 years were analysed in this manuscript. Results. Mean age of the study population was 53 +/- 12 years, 54% were male and the prevalence of diabetes was 22%. Patients with positive attitude to renal transplantation were younger (51 +/- 11 versus 58 +/- 11 years), better educated, more likely to be employed (11% versus 4%) and had prior transplantation (15% versus 7%)(P < 0.05 for all). In a multivariate model, negative patient perceptions about transplantation, negative expectations about health outcomes after transplantation and the presence of fears about the transplant surgery were associated, in addition to incre- asing age, with unwillingness to consider transplantation. Conclusions. Negative attitudes to renal transplantation are associated with potentially modifiable factors. Based on this we suggest that it would be necessary to develop standardized, comprehensible patient information systems and personalized decision support to facilitate modality selection and to enable patients to make fully informed treatment decisions

Theory of the collapsing axisymmetric cavity

We investigate the collapse of an axisymmetric cavity or bubble inside a fluid of small viscosity, like water. Any effects of the gas inside the cavity as well as of the fluid viscosity are neglected. Using a slender-body description, we show that the minimum radius of the cavity scales like $h_0 \propto t'^{\alpha}$, where $t'$ is the time from collapse. The exponent $\alpha$ very slowly approaches a universal value according to $\alpha=1/2 + 1/(4\sqrt{-\ln(t')})$. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single non-trivial scaling exponent. Our predictions are confirmed by numerical simulations

The Two Fluid Drop Snap-off Problem: Experiments and Theory

We address the dynamics of a drop with viscosity $\lambda \eta$ breaking up inside another fluid of viscosity $\eta$. For $\lambda=1$, a scaling theory predicts the time evolution of the drop shape near the point of snap-off which is in excellent agreement with experiment and previous simulations of Lister and Stone. We also investigate the $\lambda$ dependence of the shape and breaking rate.Comment: 4 pages, 3 figure

Hydrodynamic theory of de-wetting

A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, de-wetting case, a critical speed exists above which a stationary contact line is no longer sustainable and a liquid film is being deposited on the solid. Demonstrating this behavior to be a hydrodynamic instability close to the contact line, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid