Inviscid coalescence of drops

We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than $\ell_{\nu} = \rho\nu^2/\sigma$, which is $10 nm$ for water. Using a high-precision boundary integral method, we show that the walls of the thin retracting sheet of air between the drops reconnect in finite time to form a toroidal enclosure. After the initial reconnection, retraction starts again, leading to a rapid sequence of enclosures. Averaging over the discrete events, we find the minimum radius of the liquid bridge connecting the two drops to scale like $r_b \propto t^{1/2}$

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

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A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath.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

Contact line motion for partially wetting fluids

We study the flow close to an advancing contact line in the limit of small capillary number. To take into account wetting effects, both long and short-ranged contributions to the disjoining pressure are taken into account. In front of the contact line, there is a microscopic film corresponding to a minimum of the interaction potential. We compute the parameters of the contact line solution relevant to the matching to a macroscopic problem, for example a spreading droplet. The result closely resembles previous results obtained with a slip model

Simulation of a Dripping Faucet

We present a simulation of a dripping faucet system. A new algorithm based on Lagrangian description is introduced. The shape of drop falling from a faucet obtained by the present algorithm agrees quite well with experimental observations. Long-term behavior of the simulation can reproduce period-one, period-two, intermittent and chaotic oscillations widely observed in experiments. Possible routes to chaos are discussed.Comment: 20 pages, 15 figures, J. Phys. Soc. Jpn. (in press

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

Identification of structure in condensed matter with the topological cluster classification

We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with $m\leq13$ particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.Comment: 28 pages, 28 figure

Interactions between the ice algae Fragillariopsis cylindrus and microplastics in sea ice

High concentrations of microplastics have been found in sea ice but the mechanisms by which they get captured into the ice and which role ice algae might play in this process remain unknown. Similarly, we do not know how the presence of microplastics might impact the colonization of sea ice by ice algae. To estimate the ecological impact of microplastics for Polar ecosystems, it is essential to understand their behaviour during ice formation and possible interactions with organisms inhabiting sea ice. In this study we tested the interaction between the ice algae Fragillariopsis cylindrus and microplastic beads with and without sea ice present and, in a third experiment, during the process of ice formation. With sea ice present, we found significantly less algae cells in the ice when incubated together with microplastics compared to the incubation without microplastics. However, during ice formation, the presence of microplastics did not impact the colonisation of the ice by F. cylindrus cells. Further, we observed a strong correlation between salinity and the relative amount of beads in the water and ice. With increasing salinity of the water, the relative amount of beads in the water decreased significantly. At the same time, the relative amount of beads in the ice increased significantly with increasing ice salinity. Both processes were not influenced by the presence of F. cylindrus. Also, we found indications that the presence of algae can affect the amount of microplastic beads sticking to the container walls. This could indicate that EPS produced by ice algae plays a significant role in surface binding properties of microplastics. Overall, our results highlight that the interactions between algae and microplastics have an influence on the uptake of microplastics into sea ice with possible implications for the sea ice food web

Modeling and Observations of High-silica Magmatic Systems on Earth and Mars

On Earth, evolved felsic crust is commonly associated with plate tectonics, specifically subduction zones, and the role of water in modulating melting conditions and phase equilibria in the mantle and crust. As Mars lacks evidence of both plate tectonics and extensive water, felsic rock is unexpected there. However, new studies via remote sensing and in situ observation indicate a wider range of primary rock compositions on Mars, suggesting an incomplete understanding of how these materials form. Nili Patera, a caldera on the Syrtis Major shield volcano, has been a locus of compositional research on Mars, including the first detection of bedrock spectrally consistent with evolved felsic material. Using visible/near-infrared data from the CRISM instrument aboard the Mars Reconnaissance Orbiter, the extent of this feldspathic terrane in Nili Patera is mapped and its relation to surrounding mafic units is investigated. This provides important controls such as the areal extent (a proxy for volume) and relative age that can be used to constrain its magmatic formation history. A high-silica magma system on Earth, the Laguna del Maule volcanic field in Chile, is also studied. A stochastic magmatic model unifying dynamics and compositional understanding of magma system evolution is used to generate numerous realizations using known Laguna del Maule conditions and exploring a range of unknown magmatic fluxes in the crust. Forward models are developed and used to transform the magmatic model outputs to observable geophysical signals in gravity, magnetotellurics, and seismic velocity, which are evaluated against field measurements to determine a probable history of the Laguna del Maule magmatic system and investigate current arguments about the structure and supports of shallow, silicic systems. Together, these studies elucidate our understanding of how high-silica systems can form and evolve in disparate conditions.Ph.D

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