Fragmentation instabilities of a drop as it falls in a miscible fluid

We review here a series of experiments on the fragmentation instabilities that a liquid drop undergoes as it falls inside a fluid with which it is miscible, so called the solvent. Motivated by the original experiments initiated by Thomson and Newall in 1885, we started to investigate this subject more than one decade ago, encountering up to date a number of challenging problems in hydrodynamical instabilities, complicated by the presence of transient interfaces between the drop and the solvent. In particular, we have shown that when a drop of liquid is deposited over the surface of the same liquid, it falls down inside the solvent because the energy associated to its surface tension against air is instantaneously converted into kinetic energy. As a consequence, a very fast fluid injection takes place as the drop touches the free surface of the solvent and the drop enters inside the solvent. Due to the hydrodynamical instabilities related to the large velocity gradients, it develops into a ring that expands radially. The ring continues to go downwards inside the solvent until it stops at a certain height due to viscous dissipation. In the first stages of the ring expansion, a fluid membrane remains attached to the ring, so-called “turban" for its shape, which is concave or convex depending on the sign of the density difference between the drop and the solvent. When a small density difference is introduced between the drop and the solvent, the ring becomes unstable because of density gradients and it fragments into smaller droplets. On their turn, the secondary droplets may undergo the same instability and may fragment again, so that a cascade of fragmentation takes place. If the density difference is positive, that is, the drop is heavier than the solvent, the secondary droplets continue to go down deeper inside the solvent, until the whole process is washed out by the slow diffusion of the concentration gradients. When the density difference between the drop and the solvent is negative, then the secondary droplets rise up to the free surface of the solvent, where they are distorted by the equivalent of an impact with a rigid wall. Universal scaling laws for the cascade of fragmentation and for the dynamical behavior of the drop have been derived and accompany the experimental observations.     

Surface properties of liquid In-Zn alloys

The measurements of surface tension and density of zinc, indium and liquid In-Zn alloys containing 0.9, 0.85, 0.75, 0.70, 0.60, 0.40, 0.25 and 0.10 mole fraction of In were carried out using the method of maximum pressure in gaseous bubbles (MBP) as well as dilatometric technique. The technique of sessile drop was additionally applied in the measurements of surface tension for pure indium and zinc. The measurements were performed at temperature range 474-1151 K. The isotherms of surface tension calculated based on Butler's equation at 700 and 1100 K corresponded well with the experimental values for zinc content lower than 0.6 mole fraction. The surface tension calculated for alloys of higher zinc concentrations (0.6 < X_Zn < 0.95) had a positive value of the surface tension temperature coefficient (dσ/dT), which did not coincide with the experimental results. The density as well as molar volume of liquid In-Zn alloys showed almost identical behaviour like the ideal solutions. The observed little deviations were contained within assessed experimental errors.     

Stability of a deposited liquid cluster

The fragmentation of silver liquid clusters deposited onto a silicon surface is observed after heating the clusters to 1073 K and subsequent annealing with the exposition time 3 min. This contradicts macroscopic models of a liquid drop deposited on a surface if we use critical parameters of bulk silver. Some versions are analyzed that are based on cluster properties and may explain the phenomenon of cluster fragmentation. An experiment is suggested for clarifying the nature of the cluster fragmentation phenomenon and cluster critical phenomena.     

Effect of an alternating field on the relaxation of effect of an alternating field on the relaxation of magnetic flux in a Josephson medium

We establish how trapped magnetic flux depends on the frequency and amplitude of an alternating field and how such a field affects the relaxation rate of the flux. We find that the nature of the flux creep changes in the process and that relaxation of the flux stops after the external field is switched off. We examine the dynamics of flux relaxation in a ring in the approximation in which the current density is assumed homogeneous, for various density dependences of the effective vortex activation energy. The critical current density and the vortex activation energy are obtained as functions of the external field strength. Finally, we explain the observed behavior in terms of the different field profiles emerging in the rings. Zh. éksp. Teor. Fiz. 111, 1047–1056 (March 1997)     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

Possible observation of coulomb blockade at room temperature

We have studied the (I–V) characteristics of the tunnel junction formed between the tip and the substrate in an STM at room temperature. We find that in such an arrangement it may be possible to get a junction capacitance ⋍10⁻¹⁹ F and junction conductance <1μs. When the junction conductance is <1μs strong nonlinearity is observed in the (I–V) characteristics. We explain this nonlinearity as onset of coulomb blockade of tunneling electrons.     

Elastic and thermodynamic properties in CdO at high pressures from first-principles calculations

In this study, we report first-principles calculations of the elastic and thermodynamic properties for CdO in both the B1 (rocksalt) phase and B2 (cesium chloride) phase. The calculations are performed within the framework of density functional theory, using the pseudopotential plane-wave method. From the theoretical results, we find that the high pressure structural phase transition of CdO from B1 structure to B2 structure is 90.31 GPa. The calculated values are, generally speaking, in good agreement with experiments and with similar theoretical calculations. According to the quasi-harmonic Debye model, we investigate the sound velocity and Debye temperature of CdO under pressures in the range of 0<P<150 GPa.     

Benchmarking vdW‐DF first‐principles predictions against Coupled Electron–Ion Monte Carlo for high‐pressure liquid hydrogen

We report first‐principles results for the nuclear structure and optical responses of high‐pressure liquid hydrogen along two isotherms in the region of molecular dissociation. We employ density functional theory with the vdW‐DF approximation (vdW) and benchmark the results against existing predictions from Coupled Electron–Ion Monte Carlo (CEIMC). At fixed density and temperature, we find that the pressure obtained from vdW is higher than that from CEIMC by about 10 GPa in the molecular insulating phase and about 20 GPa in the dissociated metallic phase. Molecules are found to be over‐stabilized using vdW, with a slightly shorter bond length and with a stronger resistance to compression. As a consequence, pressure dissociation along isotherms using vdW is more progressive than that computed with CEIMC. Below the critical point, the liquid–liquid phase transition is observed with both theories in the same density region, but the one predicted by vdW has a smaller density discontinuity, i.e. a smaller first‐order character. The optical conductivity computed using Kubo–Greenwood formulation is rather similar for the two systems and reflects the slightly more pronounced molecular character of vdW.     

Bound States in Coulomb Systems ‐ Old Problems and New Solutions

We analyze the quantum statistical treatment of bound states in Hydrogen considered as a system of electrons and protons. Within this physical picture we calculate analytically isotherms of pressure for Hydrogen in a broad density region and compare to some results from the chemical picture. Our study is restricted to the range of intermediate temperatures 10⁴K < T < 10⁵K and not too high densities n < 10²⁴ protons per cm³, the formation of molecules is neglected. First we resume in detail the two transitions along isotherms: (i) formation of bound states occurring by increasing the density from low to moderate values, (ii) the destruction of bound states in the high density region, modelled here by Pauli‐Fock effects. Avoiding chemical models we will show, why bound states according to a discrete part of the spectra occur only in a valley in the T‐p plane. First we study virial expansions in the canonical ensemble and then in the grand canonical ensemble. We show that in fugacity representations the population of bound states saturates at higher density and that a combination of both representations provides quickly converging equations of state. In the case of degenerate systems we calculated first the density‐dependent energy levels, and find the pressure in Hartree‐Fock‐Wigner approximation showing the prominent role of Pauli blocking and Fock effects in the selfenergy (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral linewidth of light quasi-elastically scattered from xenon along the coexistence curve near the critical point

We have measured the linewidth of the central component of light scattered from xenon in both the liquid and vapor phases from 1 to 900 mK below the critical point, and compared our results with the predictions of the mode-mode coupling theory. By taking proper account of the “noncritical” background, using independent measurements of all parameters in both the singular and background parts of the theoretical linewidth, we find satisfactory agreement for 0.03<qξ<6.     

A study of the evaporative deposition process: Pipes and truncated transport dynamics

We consider contact line deposition of an evaporating thin drop. Following Dupont’s proposal (unpublished), we focus on transport dynamics truncated by a maximal concentration as the single deposition mechanism. The truncated transport process, formalized as the “pipe model”, admits a characteristic shock front that has a robust functional form and depends only on local hydrodynamic properties. By applying the pipe model, we solve the density profile in different asymptotic regimes. In particular, we find that near the contact line the density profile follows a scaling law that is proportional to the square root of the concentration ratio defined as the initial solute volume concentration divided by the maximal concentration. The maximal deposit density occurs at about 2/3 of the total drying time for uniform evaporation and 1/2 for diffusion-controlled evaporation. Away from the contact line, areal density decays exponentially with the radial distance to the power of -3 for the uniform evaporation and -7 for the diffusion-controlled evaporation.     

沉积在液体衬底上连续铝薄膜的微观结构

研究了沉积在硅油衬底表面的连续铝薄膜的微结构及其表面形貌.与沉积在单晶硅表面的铝薄膜相比,两种铝薄膜均属颗粒结构,但硅油表面的铝薄膜具有颗粒尺寸较小、大小不均匀,表面起伏较大等特点,而且在该铝薄膜边缘的下表面,有一明显的波纹状楔型结构,其斜率仅为10^-4—10^-5.实验结果表明：这一现象是由于液体衬底的热膨胀行为引起的.此外对样品的晶态也进行了研究. 关键词： 铝薄膜 液体衬底 微观结构     

Drop deformation in polymer blends during elongational flow

An original method for measuring droplet deformation in polymer melts during uniaxial elongational flow has been developed. It is based on the observation of a limited number of drops, before and after elongation in the melt. The shape of the elongated drops was frozen by fast quenching. Two PS samples for the continuous phase, plus two HDPE, and one PMMA for the drops, allowed a wide range of viscosity ratios (0.0046 < p < 13). Experiments at high capillary number (Ca) values were in good agreement with Taylor's linear newtonian theory up to deformations of about λ = 4: viscous drops (p > 1) deform less than the surrounding matrix, whereas the opposite is observed for low viscosity drops (p < 1) with a limiting ratio of drop vs. matrix deformation of 5/3 at vanishing drop viscosity. Experiments carried out at Ca values of the order of unity showed that the drop deformation increases linearly with their initial radius in agreement with the linear theory. In some cases, the agreement with the data could be improved by using Palierne's theory for viscoelastic systems. Analytical expressions could be obtained for maxwellian fluids and high capillary numbers.     

Brane singularities with mixtures in the bulk

By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five‐dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of perfect fluid (with a density and pressure depending on the extra coordinate) and a massless scalar field. The two bulk components interact by exchanging energy so that the total energy is conserved. In a particular range of the interaction parameters, we find flat brane general solutions avoiding the singularity at finite distance from the brane, in the same region of the equation of state constant parameter γ = P/ρ that we found previously in the absence of the bulk scalar field (‐1 < γ < ‐1/2).     

Testing “microscopic” theories of glass-forming liquids

We assess the validity of “microscopic” approaches of glass-forming liquids based on the sole knowledge of the static pair density correlations. To do so, we apply them to a benchmark provided by two liquid models that share very similar static pair density correlation functions while displaying distinct temperature evolutions of their relaxation times. We find that the approaches are unsuccessful in describing the difference in the dynamical behavior of the two models. Our study is not exhaustive, and we have not tested the effect of adding corrections by including, for instance, three-body density correlations. Yet, our results appear strong enough to challenge the claim that the slowdown of relaxation in glass-forming liquids, for which it is well established that the changes of the static structure factor with temperature are small, can be explained by “microscopic” approaches only requiring the static pair density correlations as nontrivial input.     

On a moving liquid film and its instability on textured surfaces

Recently, two regimes of viscous friction on textured surfaces were proposed in the context of penetration of liquid film into the texture (EPL 79, 56005 (2007)): the Poiseuille and Stokes regimes. With this idea on viscous friction, we theoretically discuss instabilities on a liquid film on textured surfaces when the film is forced to move with external forces. When a film recedes due to a pressure drop, we find scaling laws for instabilities to be checked in future experiments. When a circular film expands due to centrifugal force we find that the expanding film is stable against rim fluctuations (within the linear stability analysis) with its radius determined by a simple equation. Our discussion sheds light on the curvature of the front of the moving liquid film on textured surfaces and how the film thickness is kept fixed to the texture height on textured surfaces, aspects which have not been discussed in previous studies.     

Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment

Currently, both the g factor measurement of the muon as well as the Lamb shift 2S–2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both “muonic” discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.