Inertial and dimensional effects on the instability of a thin film

We consider here the effects of inertia on the instability of a flat liquid film under the effects of capillary and intermolecular forces (van der Waals interaction). Firstly, we perform the linear stability analysis within the long wave approximation, which shows that the inclusion of inertia does not produce new regions of instability other than the one previously known from the usual lubrication case. The wavelength, $\lambda_m$, corresponding to he maximum growth, $\omega_m$, and the critical (marginal) wavelength do not change at all. The most affected feature of the instability under an increase of the Laplace number is the noticeable decrease of the growth rates of the unstable modes. In order to put in evidence the effects of the bidimensional aspects of the flow (neglected in the long wave approximation), we also calculate the dispersion relation of the instability from the linearized version of the complete Navier-Stokes (N-S) equation. Unlike the long wave approximation, the bidimensional model shows that $\lambda_m$ can vary significantly with inertia when the aspect ratio of the film is not sufficiently small. We also perform numerical simulations of the nonlinear N-S equations and analyze to which extent the linear predictions can be applied depending on both the amount of inertia involved and the aspect ratio of the film

Thin film instability with thermal noise

We study the effects of stochastic thermal fluctuations on the instability of the free surface of a flat liquid film upon a solid substrate. These fluctuations are represented as a standard Brownian motion that can be added to the deterministic equation for the film thickness within the lubrication approximation. Here, we consider that while the noise term is white in time, it is coloured in space. This allows for the introduction of a finite correlation length in the description of the randomized intermolecular interaction. Together with the expected spatial periodicity of the flow, we find a dimensionless parameter, $\beta$, that accounts for the relative importance of the spatial correlation. We perform here the linear stability analysis (LSA) of the film under the influence of both terms, and find the corresponding power spectra for the amplitudes of the normal modes of the instability. We compare this theoretical result with the numerical simulations of the complete non-linear problem, and find a good agreement for early times. For late times, we find that the stochastic LSA predictions on the dominant wavelength remains basically valid. We also use the theoretical spectra to fit experimental data from a nanometric melted copper film, and find the corresponding times of the evolution as well as the values of the parameter, $\beta$

Drops with non-circular footprints

In this paper we study the morphology of drops formed on partially wetting substrates, whose footprint is not circular. This type of drops is a consequence of the breakup processes occurring in thin films when anisotropic contact line motions take place. The anisotropy is basically due to hysteresis effects of the contact angle since some parts of the contact line are wetting, while others are dewetting. Here, we obtain a peculiar drop shape from the rupture of a long liquid filament sitting on a solid substrate, and analyze its shape and contact angles by means of goniometric and refractive techniques. We also find a non--trivial steady state solution for the drop shape within the long wave approximation (lubrication theory), and compare most of its features with experimental data. This solution is presented both in Cartesian and polar coordinates, whose constants must be determined by a certain group of measured parameters. Besides, we obtain the dynamics of the drop generation from numerical simulations of the full Navier--Stokes equation, where we emulate the hysteretic effects with an appropriate spatial distribution of the static contact angle over the substrate

Thin films dewetting with phase separation: Dependence of surface tension and Hamaker constant on concentration

We study the instability of a thin film composed of two miscible fluids (binary fluid) placed on a solid planar surface. We include the fact that both the free surface and wetting energies depend on the mixture concentration. By assuming a linear relationship between these energies and both the bulk and surface concentrations, we analyze their effect on the phase separation of the constituent fluids. The problem is formulated within the gradient dynamics formulation applied to the thin film limit of the Cahn-Hilliard Navier-Stokes equations. The dependence of the free surface energy on concentration leads to a Marangoni type of effect, while the wetting energy resulting from fluid--solid interaction between the film and the substrate is described by a concentration dependent Hamaker constant. The linear stability analysis uncovers that both monotonous and oscillatory evolution is possible. While our problem formulation applies to any binary mixture that can be consistently modeled via the presented approach, a particular interpretation of the results is provided for the case of liquid metal alloy films on nanoscale. In this context, we find that rich dynamics is possible, including the evolution that may lead to formation of drops of the Janus--type as well as of core-shell configurations

Riemann Surfaces of genus g with an automorphism of order p prime and p>g

The present work completes the classification of the compact Riemann surfaces of genus g with an analytic automorphism of order p (prime number) and p > g. More precisely, we construct a parameteriza- tion space for them, we compute their groups of uniformization and we compute their full automorphism groups. Also, we give affine equations for special cases and some implications on the components of the singular locus of the moduli space of smooth curves of genus g.Comment: 28 pages, 5 figure

On the uniqueness of (p,h)(p,h)-gonal automorphisms of Riemann surfaces

Let $X$ be a compact Riemann surface of genus $g\geq 2$. A cyclic subgroup of prime order $p$ of $Aut(X)$ is called properly $(p,h)$-gonal if it has a fixed point and the quotient surface has genus $h$. We show that if $p>6h+6$, then a properly $(p,h)$-gonal subgroup of $Aut(X)$ is unique. We also discuss some related results.Comment: final version, 9 pages, minor improvements, added 2 reference

Automatic Visual Acuity Estimation by Means of Computational Vascularity Biomarkers Using Oct Angiographies

[Abstract] Optical Coherence Tomography Angiography (OCTA) constitutes a new non-invasive ophthalmic image modality that allows the precise visualization of the micro-retinal vascularity that is commonly used to analyze the foveal region. Given that there are many systemic and eye diseases that affect the eye fundus and its vascularity, the analysis of that region is crucial to diagnose and estimate the vision loss. The Visual Acuity (VA) is typically measured manually, implying an exhaustive and time-consuming procedure. In this work, we propose a method that exploits the information of the OCTA images to automatically estimate the VA with an accurate error of 0.1713.Instituto de Salud Carlos III; DTS18/00136Ministerio de Economía y Competitividad; DPI2015-69948-RXunta de Galicia; ED431G/01Xunta de Galicia; ED431C 2016-047Ministerio de Ciencia, Innovación y Universidades; RTI2018-095894-B-I0

Competition between collapse and breakup in nanometer-sized thin rings using molecular dynamics and continuum modeling

We consider nanometer-sized fluid annuli (rings) deposited on a solid substrate and ask whether these rings break up into droplets due to the instability of Rayleigh-Plateau-type modified by the presence of the substrate, or collapse to a central drop due to the presence of azimuthal curvature. The analysis is carried out by a combination of atomistic molecular dynamics simulations and a continuum model based on a long-wave limit of Navier-Stokes equations. We find consistent results between the two approaches, and demonstrate characteristic dimension regimes which dictate the assembly dynamics.Fil: Nguyen, Trung Dac. Oak Ridge National Laboratory; Estados UnidosFil: Fuentes-Cabrera, Miguel. Oak Ridge National Laboratory; Estados UnidosFil: Fowlkes, Jason D.. Oak Ridge National Laboratory; Estados UnidosFil: Diez, Javier Alberto. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Instituto de Física Arroyo Seco; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: González, Alejandro G.. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Exactas. Instituto de Física Arroyo Seco; ArgentinaFil: Kondic, Lou. New Jersey Institute Of Technology; Estados UnidosFil: Rack, Philip D.. Oak Ridge National Laboratory; Estados Unido

The Latin American Dialysis and Renal Transplantation Registry: report 2019

Background Chronic kidney disease (CKD) in Latin America (LA) continues to represent a challenge due to the burden of disease it causes and the difficulty in accessing treatment. LA has a total population of 652 million people living in 20 countries that occupy an area of 19.2 million km2. The Latin American Dialysis and Renal Transplantation Registry (LADRTR), founded in 1991, has collected data and reports on patients receiving kidney replacement therapy (KRT) since 1993. This article summarizes the registry data for 2019. Methods Participating countries complete an annual survey collecting aggregated data on incident and prevalent patients on KRT in all modalities. The different treatment modalities considered were hemodialysis (HD), peritoneal dialysis (PD) and living functioning kidney graft (LFG). National gross domestic product per capita (GDP, expressed in US dollars) and life expectancy at birth (LEB) corresponding to the year 2019 were collected from the World Bank Data Bank. Prevalence and incidence were compared with previous years and were also correlated with GDP and LEB. Results On 31 December 2019 a total of 432 610 patients were in KRT in LA, corresponding to an overall unadjusted prevalence of 866 per million population (pmp). Regarding treatment modality, 66.7% of the prevalent patients were treated with HD and 9.3% with PD while 24% of the patients had an LFG. A total of 85 224 patients started KRT in LA, representing a total unadjusted incidence rate of 168 pmp. Diabetic nephropathy as a cause of CKD continues to be a relevant percentage (36%) and five countries reported CKD of nontraditional causes. The kidney transplant rate in the region was 22 pmp, varying from 1 to >60 pmp. The total prevalence of KRT correlated positively with GDP per capita (r2 = 0.6, P < 0.01) and LEB (r2 = 0.23, P < 0.05). The overall incidence rate also significantly correlated with GDP (r2 = 0.307, P < 0.05). The overall unadjusted mortality rate was 13%. Conclusion Accessibility to KRT is still limited in LA. It is necessary to continue the efforts made by each country and the Latin American Society of Nephrology and Hypertension to guarantee equal access to treatment