Meniscus effects on the frequency and damping of capillary-gravity waves in a brimful circular cylinder

We study the effects of a meniscus on the oscillations of a viscous liquid filling a right circular cylindrical container by using the natural viscous complex eigenfunctions of the problem. The free surface of the liquid is assumed to have a pinned contact line. By projecting the governing equations onto an appropriate basis, a nonlinear eigenvalue problem for the complex frequencies is obtained. This is then solved to13; obtain the modal frequencies as a function of the contact angle $\theta_c$, the Reynolds and Bond numbers Re and Bo and the liquid depth h. At shallow depths, the13; effect of the meniscus is, in general, to increase the modal frequency and decrease the damping rate with increasing $\theta_c$. At large depths and for higher modes, the13; damping rate monotonically decreases with increasing $\theta_c$ while the frequency attains13; a maximum in the neighbourhood of $90^0$. However, there are parameter values for13; which the meniscus results in anomalous behaviours in the damping rate. Extensive13; comparison with experimental and computational results for the $\theta_c = 90^0$ case is13; very good; comparison with the one available experimental result for $\theta_c = 62^0$ is also13; very good. Extensive results for a variety of contact angles have been tabulated for13; Reynolds and Bond numbers for which experimental results exist in the flat interface13; case, for comparison with future experimental results that may be obtained with13; curved menisci

The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Is the subharmonic threshold always lower than the fundamental one in plane Poiseuille flow.

We revisit the secondary instability of a Tollmein-Schlichting wave in plane Poiseuille flow at Re = 5000 and find that the fundamental threshold can be lower than the subharmonic one in the wavenumber space, in contrast to the prevalent view in the literature that only instability of subharmonic modes occurs at very low disturbance amplitudes and fundamental modes need a higher disturbance amplitude to become unstable. This is because of overlooking the even class of fundamental modes, which happen to produce the lower threshold at those wavenumbers. Published by AIP Publishing

Boundary Integral Equations for the Laplace-Beltrami Operator

We present a boundary integral method, and an accompanying boundary element discretization, for solving boundary-value problems for the Laplace-Beltrami operator on the surface of the unit sphere $\S$ in $\mathbb{R}^3$. We consider a closed curve ${\cal C}$ on ${\cal S}$ which divides ${\cal S}$ into two parts ${\cal S}_1$ and ${\cal S}_2$. In particular, ${\cal C} = \partial {\cal S}_1$ is the boundary curve of ${\cal S}_1$. We are interested in solving a boundary value problem for the Laplace-Beltrami operator in $\S_2$, with boundary data prescribed on \C

Collapse of three vortices on a sphere

The self-similar collapse of three point vortices moving on the surface of a sphere of radius R is analysed and compared with known results from the corresponding planar problem described in (AREF H., Motion of three vortices, Phys. Fluids, 22 (1979) 393-400; NOVIKOV E. A., Dynamics and statistics of a system of vortices, Sov. Phys. JETP, 41 (1975) 937-943; NOVIKOV E. A. and SEDOV Y., Vortex collapse, Sov. Phys. JETP, 50 (1979) 297-301; SYNGE J. L., On the motion of three vortices, Can. J. Math., 1 (1949) 257-270). An important conserved quantity is the center of vorticity vector c4(!i41 3 Gi xi )O!i41 3 Gi, which must have length R for collapse to occur. Collapse trajectories occur in pairs, called “partner states”, which have two distinct collapse times t2Et1. The collapse time that is achieved for a given configuration depends on the sign of the parallelpiped volume formed by the vortex position vectors, hence depends on whether the vortices (G1 , G2 , G3 ) are arranged in a right-handed or left-handed sense. From a given collapsing configuration, one can obtain the partner state by reversing the signs of the Gi’s, or, alternatively, by using a discrete symmetry associated with the initial configuration that leaves all relative distances unchanged, but reverses the sign of the parallelepiped volume. In the plane, there is only one collapse time associated with a given configuration—the partner state is one that expands self-similarly (AREF H., Motion of three vortices, Phys. Fluids, 22 (1979) 393-400). Formulas for the collapsing trajectories are derived and compared with the planar formulas. The collapse trajectories are then projected onto the stereographic plane where a new Hamiltonian system is derived governing the vortex motion. In this projected plane, the solutions are not self-similar. In the last section, the collapse process is studied using tri-linear coordinates, which reduces the system to a planar one

Graphene-based ultrathin flat lenses

Flat lenses when compared to curved surface lenses have the advantages of being aberration free and they offer a compact design necessary for a myriad of electro-optical applications. In this paper we present flat and ultra-thin lenses based on graphene, the world’s thinnest known material. Monolayers and low number multilayers of graphene were fabricated into Fresnel zones to produce Fresnel zone plates which utilize the reflection and transmission properties of graphene for their operation. The working of the lens and their performance in the visible and terahertz regimes was analyzed computationally. Experimental measurements were also performed to characterize the lens in the visible regime and a good agreement was obtained with the simulations. The work demonstrates the principle of atom thick graphene-based lenses, with perspectives for ultra-compact integration.HB would like to thank The Leverhulme Trust for the research funding. QD is supported by Bureau of International Cooperation, Chinese Academy of Sciences (121D11KYSB20130013).This is the accepted manuscript. The final version is available from ACS at http://pubs.acs.org/doi/abs/10.1021/ph500197j

Binder free three-dimensional sulphur/few-layer graphene foam cathode with enhanced high-rate capability for rechargeable lithium sulphur batteries.

A novel ultra-lightweight three-dimensional (3-D) cathode system for lithium sulphur (Li-S) batteries has been synthesised by loading sulphur on to an interconnected 3-D network of few-layered graphene (FLG) via a sulphur solution infiltration method. A free-standing FLG monolithic network foam was formed as a negative of a Ni metallic foam template by CVD followed by etching away of Ni. The FLG foam offers excellent electrical conductivity, an appropriate hierarchical pore structure for containing the electro-active sulphur and facilitates rapid electron/ion transport. This cathode system does not require any additional binding agents, conductive additives or a separate metallic current collector thus decreasing the weight of the cathode by typically ∼20-30 wt%. A Li-S battery with the sulphur-FLG foam cathode shows good electrochemical stability and high rate discharge capacity retention for up to 400 discharge/charge cycles at a high current density of 3200 mA g(-1). Even after 400 cycles the capacity decay is only ∼0.064% per cycle relative to the early (e.g. the 5th cycle) discharge capacity, while yielding an average columbic efficiency of ∼96.2%. Our results indicate the potential suitability of graphene foam for efficient, ultra-light and high-performance batteries.Kai Xi thanks the Cambridge Overseas Trust. P.R.K. acknowledges funding from the Cambridge Commonwealth Trust. S.H. acknowledges funding from ERC grant InsituNANO (no. 279342), EPSRC under grant GRAPHTED (project reference EP/K016636/1) and Grant EP/H047565/1. This research was partially supported by the EU FP7 Work Programme under grant GRAFOL (project reference 285275). XP and CD acknowledge funding from the ERC under grant number 259619 PHOTO EM.This is the accepted manuscript. The final version is available from RSC at http://pubs.rsc.org/en/Content/ArticleLanding/2014/NR/C4NR00326H#!divAbstract

Time Evolution of the Wettability of Supported Graphene under Ambient Air Exposure.

The wettability of graphene is both fundamental and crucial for interfacing in most applications, but a detailed understanding of its time evolution remains elusive. Here we systematically investigate the wettability of metal-supported, chemical vapor deposited graphene films as a function of ambient air exposure time using water and various other test liquids with widely different surface tensions. The wettability of graphene is not constant, but varies with substrate interactions and air exposure time. The substrate interactions affect the initial graphene wettability, where, for instance, water contact angles of ∼85 and ∼61° were measured for Ni and Cu supported graphene, respectively, after just minutes of air exposure. Analysis of the surface free energy components indicates that the substrate interactions strongly influence the Lewis acid-base component of supported graphene, which is considerably weaker for Ni supported graphene than for Cu supported graphene, suggesting that the classical van der Waals interaction theory alone is insufficient to describe the wettability of graphene. For prolonged air exposure, the effect of physisorption of airborne contaminants becomes increasingly dominant, resulting in an increase of water contact angle that follows a universal linear-logarithmic relationship with exposure time, until saturating at a maximum value of 92-98°. The adsorbed contaminants render all supported graphene samples increasingly nonpolar, although their total surface free energy decreases only by 10-16% to about 37-41 mJ/m2. Our finding shows that failure to account for the air exposure time may lead to widely different wettability values and contradicting arguments about the wetting transparency of graphene.We acknowledge funding from EPSRC (Grant No. EP/K016636/1, GRAPHTED) and ERC (Grant No. 279342, InsituNANO). P.R. Kidambi acknowledges the Lindemann Trust Fellowship. R.S. Weatherup acknowledges a Research Fellowship from St. John’s College, Cambridge and a EU Marie Skłodowska-Curie Individual Fellowship under grant ARTIST (no. 656870) from the European Union’s Horizon 2020 research and innovation programme.This is the final version of the article. It first appeared from the American Chemical Society via https://doi.org/10.1021/acs.jpcc.5b1049