Spherical Interface Research Articles

Spontaneous Two-Dimensional Spherical Colloidal Structures

Two-dimensional spherical crystalline colloidal structures are formed at the interface between water and oil as the result of spontaneous emulsification and colloidal self-assembly. When water droplets are introduced in oil containing a lipophilic surfactant, smaller water droplets of uniform size are spontaneously produced at the spherical interface. Initially of submicrometer size, the small droplets at the interface self-assemble, forming ordered structures, and grow uniformly with time until they reach a size of a few micrometers, maintaining the crystalline structure.

Response to “Comment on ‘Theoretical analysis of numerical aperture increasing lens microscopy’” [J. Appl. Phys. 97, 053105 (2005)

We have identified that there is a small error in the original paper by Ippolito et al. [J. Appl. Phys. 97, 053105 (2005)] and we express our thanks to the authors of the comment for bringing it to our attention. However, the comment by Sheppard and Huat [J. Appl. Phys. 100, 086108 (2006)] has misinterpretations that lead to erroneous conclusions. We disagree with the statement of the comment that the conclusions on planar interface would carry through to the case of a numerical aperture increasing lens (NAIL). Our model calculates the wave aberration and provides valuable insight to the limitations of spatial resolution in the case of NAIL imaging and its dependence on various parameters, whereas angular spectrum method is not applicable to a spherical interface. The only significant error by Ippolito et al. is limited to an incorrect plot of Φ040 although the correct equation is given in the article.

Thermal Radiative Transport Enhancement via Electromagnetic Surface Modes in Microscale Spherical Regions Bounded by Silicon Carbide

A Green function approach is used with the fluctuation-dissipation theorem to develop a qualitative theoretical model of radiation heat transfer across an evacuated microscale spherical geometry bounded by silicon carbide. The appropriate scalar Green function is presented by employing an impedance boundary condition to describe the electromagnetic spherical interface condition and thus capture the surface modes. This work shows that the spherical boundary can result in spectral conditions for surface mode excitation that depend not only on the dielectric function, but on the sphere radius as well. The surface modes are shown to enhance the radiation significantly and are attributed to surface phonon polariton modes excited at the interface, and surface modes excited by the mechanism of total internal reflection.

Adsorption of colloidal particles to curved interfaces

As a simple model for a Pickering emulsion droplet, we consider the adsorption of spherical particles to a spherical liquid-liquid interface in order to investigate the curvature effect on the particle adsorption. By taking into account both the surface and the volume energies due to the presence of a particle, we show that the equilibrium contact angle is determined by the classical Young's equation although the adsorption energy depends on the curvature. We also calculate the partitioning of the colloidal particles among the two liquids and the interface. The distribution of colloidal particles is expressed in terms of the interfacial curvature as well as the relative wettability of the particle.

Evolution and impedance operators of spherically symmetric bianisotropic media

An operator method, which was developed earlier for bianisotropic layered media with plane and cylindrical interfaces, is generalized to solve spherically symmetric problems: determination of eigenmodes of spherical waveguides, investigation of surface waves, calculation of light scattering cross-section by multi-layer spherical particles. Analytical results are applied to obtain the modes of the negative-refractive-index waveguide, to determine dispersion curves of the waves at the spherical interface between isotropic and bianisotropic media, to reveal the regularities of electromagnetic wave scattering by spherical dielectric particles.

Comprehensive study of the vapour–liquid coexistence of the truncated and shifted Lennard–Jones fluid including planar and spherical interface properties

Vapour–liquid equilibria of the Lennard–Jones potential, truncated and shifted at 2.5σ, are studied using molecular dynamics simulations, an attractive option for studying inhomogeneous systems. Comprehensive simulation data are reported for three cases: no interface, a planar interface, and a spherical interface between the coexisting phases, covering a wide range of temperatures. Spherical droplets are also studied for a range of radii between 5 and 16σ. The size dependence of the surface tension, based on the Irving–Kirkwood pressure tensor, and other properties is quantified for spherical interfaces. All simulation results are correlated with a consistent set of empirical equations. A comparison with the results of other authors as well as with experimental data for noble gases and methane is also presented.

Bell-Plesset effects for an accelerating interface with contiguous density gradients

A Plesset-type treatment [M. S. Plesset, J. Appl. Phys. 25, 96 (1954)] is used to assess the effects of contiguous density gradients at an accelerating spherical classical interface on Rayleigh-Taylor and Bell-Plesset perturbation growth. Analytic expressions are obtained that describe enhanced Rayleigh-Taylor instability growth from contiguous density gradients aligned with the acceleration and which increase the effective Atwood number of the perturbed interface. A new pathway for geometric amplification of surface perturbations on an accelerating interface with contiguous density gradients is identified. A resonance condition between the density-gradient scale length and the radius of the interface is also predicted based on a linearized analysis of Bernoulli’s equation, potentially leading to enhanced perturbation growth. Comparison of the analytic treatment with detailed two-dimensional single-mode growth-factor simulations shows good agreement for low-mode numbers where the effects of spherical geometry are most manifested.

Charge Renormalization in Planar and Spherical Charged Lipidic Aqueous Interfaces

The charge renormalization in planar and spherical charged lipidic aqueous interfaces has been investigated by means of thermodynamic and electrokinetic measurements. We analyzed the behavior of mixed DOTAP/DOPE monolayers at the air-electrolyte solution interface and DOTAP/DOPE liposomes 100 nm in size dispersed in an aqueous phase of varying ionic strength. For the two systems, we have compared the "effective" surface charge derived from the measurements of surface potential and zeta-potential to the "bare" charge based on the stoichiometry of the lipid mixture investigated. The results confirm that a strong charge renormalization occurs, whose strength depends on the geometry of the mesoscopic system. The dependence of the "effective" charge on the "bare" charge is discussed in light of an analytical approximation based on the Poisson-Boltzmann equation recently proposed.

球形ユーザ・インタフェース・デバイスの開発と移動ロボットへの応用

球形ユーザ・インタフェース・デバイスの開発と移動ロボットへの応用

Interfacial tension of magnetic fluids in the mean spherical approximation

The interfacial tension coefficient for a plane and spherical interface between weakly and highly concentrate phases of magnetic fluid was evaluated in square-gradient expansion for the mean spherical approximation of dipole–dipole interaction. The method based on the minimization of free energy functional was used for solution. The density profile in the interface layer, the influence factor, Tolman length and the interfacial tension coefficient were calculated as functions of temperature and concentration using the tail of pair correlation function. The anisotropy of interfacial tension for a plane interface was calculated far from critical point in weak magnetic field. The estimations for arbitrary angles between magnetic field and interface normal were made for interfacial tension. It was shown that dependence of the interfacial tension on radius of macrodrop is negligible. Giving the expression for interfacial tension coefficient is possible and can be presented as functions of physical measured parameters: magnetic susceptibility, density and compressibility. That opens up the possibility of using these expressions for description of polydisperse magnetic fluids. The theoretical results agree well with experimental estimations.

Thermocapillary transport of energy during water evaporation

When evaporation occurs at a spherical water-vapor interface maintained at the circular mouth of a small funnel, studies of the energy transport have indicated that thermal conduction alone does not provide enough energy to evaporate the liquid at the observed rate. If the Gibbs model of the interface is adopted and the "surface-thermal capacity" is assigned a value of 30.6+/-0.8 kJ/(m2 K), then for evaporation experiments with the interfacial temperature in the range -10 degrees C< or =TLV< or =3.5 degrees C and Marangoni number (Ma) in the range 100<Ma<22,000, it was found that if energy transport by both thermocapillary convection and thermal conduction were taken into account, conservation of energy was fully satisfied. The question addressed herein is whether the assigned value of the surface-thermal capacity is an ad hoc empirical parameter or a property of the water-vapor interface that can be used in other circumstances. Accordingly, a series of experiments has been conducted in which water evaporated at cylindrical interfaces that were, on average, 4.4 times larger in area than that of the spherical interfaces used to measure the surface-thermal capacity initially. It is shown that using the value of the surface-thermal capacity determined at a spherical interface, the energy transported by thermocapillary convection and thermal conduction at a cylindrical interface is sufficient to evaporate the liquid at the observed rate. Knowing the value of the surface-thermal capacity also allows the local evaporation flux to be calculated from the measured temperature profiles in the liquid and vapor phases. The calculated local evaporation flux can then be used with statistical rate theory to calculate the vapor-phase pressure along the interface. The predicted mean vapor-phase pressure is in close agreement with that measured, and the predicted pressure gradient is consistent with that expected when thermocapillary convection is present.

Spectroscopic properties of a two-level atom interacting with a complex spherical nanoshell

Frequency shifts, radiative decay rates, the Ohmic loss contribution to the nonradiative decay rates, fluorescence yield, and photobleaching of a two-level atom radiating anywhere inside or outside a complex spherical nanoshell, i.e., a stratified sphere consisting of alternating silica and gold concentric spherical shells, are studied. The changes in the spectroscopic properties of an atom interacting with complex nanoshells are significantly enhanced, often more than two orders of magnitude, compared to the same atom interacting with a homogeneous dielectric sphere. The detected fluorescence intensity can be enhanced by 5 or more orders of magnitude. The changes strongly depend on the nanoshell parameters and the atom position. When an atom approaches a metal shell, decay rates are strongly enhanced yet fluorescence yield exhibits a well-known quenching. Rather contra-intuitively, the Ohmic loss contribution to the nonradiative decay rates for an atomic dipole within the silica core of larger nanoshells may be decreasing when the silica core–inner gold shell interface is approached. The quasi-static result that the radial frequency shift in a close proximity of a spherical shell interface is approximately twice as large as the tangential frequency shift appears to apply also for complex nanoshells. Significantly modified spectroscopic properties (see computer program available at http://www.wave-scattering.com) can be observed in a broad band comprising all (nonresonant) optical and near-infrared wavelengths.

Brookite → rutile phase transformation of TiO 2 studied with monodispersed particles

TiO 2 is a polymorphic material (anatase, brookite, and rutile) of current interest for a variety of technological applications. Though the anatase → rutile transformation has been studied extensively, the brookite transition has rarely been addressed up to date due to the difficulties encountered in obtaining phase-pure brookite. The brookite → rutile transformation has been studied in this work using monodispersed quasi-spherical particles (∼154 nm, composed of phase-pure brookite nanocrystals of ∼25 nm) as a starting material. The transition mainly proceeds within the individual particles in the temperature range 500–600 °C, without the positive detection of the anatase polymorph. The transformation kinetics are best expressed by the “contracting spherical interface” model in the studied temperature range, from which an apparent activation energy of 143.4 ± 1.2 kJ/mol was derived. The rate parameter for the phase transition may be expressed as k = 1.28 × 10 4 exp ( - 17248 ± 144 / T ) s - 1 .

Non-axisymmetric spherical interface dynamos

A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo with a solar-like internal differential rotation and a single-cell meridional circulation is investigated. There are four regions in our interface dynamo model: a uniformly rotating core, a thin differentially rotating tachocline, a turbulent convection zone and a nearly insulating exterior. The different regions are coupled by the electric and magnetic matching conditions at the interfaces. For the first time, non-axisymmetric spherical nonlinear interface dynamos are found. When the magnetic Reynolds number based on the differential rotation is small or when the effect of the meridional circulation is substantial, we show that the spherical interface dynamos are non-axisymmetric even though the a-distribution, differential rotation and meridional circulation are all axisymmetric. Implication of the results for the solar dynamo is discussed.

Analysis of electromagnetic scattering by a plasma anisotropic sphere

An analytical solution of electromagnetic fields in homogeneous plasma anisotropic media is obtained in this paper. In the source‐free plasma anisotropic media, the source‐free Maxwell's equations are utilized, where the expansion of plane wave factors is made in terms of the spherical vector wave functions in isotropic media, and the Fourier transformation is then applied. As a result, the field expressions represented using eigenfunctions are obtained in spectral domain. Applying boundary conditions on the spherical interface between air and plasma anisotropy, the electromagnetic fields of the plane wave scattered by a plasma anisotropic sphere are derived. Numerical results for the very general plasma dielectric material media are obtained, and those in a special case are compared between the present method and the Method of Moments (MoM) speeded up with the Conjugate‐Gradient Fast‐Fourier‐Transform (CG‐FFT) approach. The formulations in this paper can be generalized to those of more complex cases, such as layered plasma anisotropic sphere, plasma sheath, as well as plasma anisotropic material coated conducting sphere.

Simulation of light propagation by local spherical interface approximation.

A new local elementary interface approximation is introduced for the modeling of wave propagation through interfaces between homogeneous media. The incident wave and the surface profile are approximated locally by a spherical wave and a spherical surface, respectively. The wave field travels through the modulated structure according to the laws of geometrical optics, being refracted by the surface and propagating to the output plane locally as a geometric spherical wave. Diffraction theory is applied to propagate the field from the output plane onwards. We provide comparisons of the method with the thin-element approximation, the local plane-wave and interface approach, and rigorous diffraction theory using a sinusoidal surface-relief grating as an example. We illustrate the power of the new method by applying it to the analysis of a diffractive beam splitter.

Distortion of a Spherical Gaseous Interface Accelerated by a Plane Shock Wave

The evolution of a spherical gaseous interface accelerated by a plane weak shock wave has been investigated in a square cross section shock tube via a multiple exposure shadowgraph diagnostic. Different gaseous bubbles, i.e., helium, nitrogen, and krypton, were introduced in air at atmospheric pressure in order to study the Richtmyer-Meshkov instability in the spherical geometry for negative, close to zero, and positive initial density jumps across the interface. We show that the bubble distortion is strongly different for the three cases and we present the experimental velocity and volume of the developed vortical structures. We prove that at late times the bubble velocities reach constant values which are in good agreement with previous calculations. Finally, we point out that, in our flow conditions, the gaseous bubble motion and shape are mainly influenced by vorticity and aerodynamic forces.

A Three‐dimensional Spherical Nonlinear Interface Dynamo

A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo is investigated using a finite-element method based on the three-dimensional tetrahedralization of the spherical system. The spherical interface dynamo model consists of four zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a uniformly rotating turbulent convection envelope, and a nearly insulating exterior. The four regions are coupled magnetically through matching conditions at the interfaces. Without the effect of a tachocline, the conventional nonlinear α2 dynamo is always stationary, axisymmetric, and equatorially antisymmetric even though numerical simulations are always fully three-dimensional and time dependent. When there is no tachocline, the azimuthal field is confined to the convection zone while the poloidal magnetic field penetrates into the radiative core. The effects of an interface dynamo with a tachocline having a purely axisymmetric toroidal velocity field are as follows: (1) the action of the steady tachocline always gives rise to an oscillatory dynamo with a period of about 2 magnetic diffusion units, or about 20 yr if the magnetic diffusivity in the convection zone is 108 m2 s-1; (2) the interface dynamo solution is always axisymmetric, selects dipolar symmetry, and propagates equatorward (for the assumed form of α) although the simulation is fully three-dimensional; (3) the generated magnetic field mainly concentrates in the vicinity of the interface between the tachocline and the convection zone; and (4) the strength of the toroidal magnetic field is dramatically amplified by the effect of the tachocline. Extensions of Cowling's theorem and the toroidal flow theorem to multilayer spherical shell regions with radially discontinuous magnetic diffusivities are presented.

Linearized stability analysis of accelerated planar and spherical fluid interfaces with slow compression.

We present linearized stability analyses of the effect of slow anisotropic compression or expansion on the growth of perturbations at accelerated fluid interfaces in both planar and spherical geometries. The interface separates two fluids with different densities, compressibilities, and compression rates. We show that a perturbation of large mode number on a spherical interface grows at precisely the same rate as a similar perturbation on a planar interface subjected to the same normal and transverse compression rates.

Transient elastic wave propagation in a spherically symmetric bimaterial medium modeling the thorax

The transient response resulting from an impact wave on an elastic bimaterial, made out of a “hard” medium and a “soft” medium, welded at a spherical interface, have been investigated by using an integral transform technique. This technique permits isolation of the pressure and shear waves contributions to the wave field. The method of solution makes use of the generalized ray/Cagniard-de Hoop (GR/CdH) method associated with a “flattening approximation” (FA) technique, similar to the Earth flattening transformation used in geophysics. The GR/CdH method and the FA technique are briefly presented, together with their numerical implementations. The FA has proved to be useful in geophysical application, however, as far as the authors know, it has never been investigated for other applications. For the purpose of this paper, numerous tests of the method have been performed in order to check that the FA is appropriate to compute transient responses in the special case presented here. We could determine appropriate values for some parameters involved in the FA. This paper follows Grimal et al. [Int. J. Solid Struct. 39 (2002) 5345] in which we investigated the same bimaterial with a plane––instead of spherical––interface. Numerical examples are concerned with the propagation of an impact wave in the thorax modeled as a bimaterial (thoracic wall-lung). In addition to the effects of the weak coupling of the two media already observed in our previous study, we found that, for interface curvatures characteristic of those measured in the thorax, focalization of energy is manifest.