Spherical Interface Research Articles

Encapsulated Microbubble Fiber-Tip Fabry-Perot Cavity With Tunable Bandwidth for Sensitive Acoustic Detection

A photothermally generated microbubble on a single-mode fiber tip with tunable frequency bandwidth was demonstrated for sensitive detection of acoustic waves. The microbubble with spherical gas-water interface formed a flexible Fabry-Pérot cavity at the fiber tip and detected the acoustic waves by interferometric readout of the bubble deformation. To work in different liquids besides water, the sensor was encapsulated into a water-filled tube and the effects of the encapsulation process on the optical and acoustic characteristics of the sensor were investigated. A 40 μm-diameter microbubble based sensor exhibited a noise-equivalent pressure level of ∼1.0 mPa/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1/2</sup> at the frequency of ∼100 kHz. The bubble diameter was photothermally changed from 20 μm to 60 μm, which enabled online tuning of the sensor resonant frequency from 100 kHz to 300 kHz. This tunable feature is attractive to applications that requires the detection of acoustic waves covering different frequency bands. The encapsulated microbubble sensor with advantages of high sensitivity, tunable bandwidth and low-cost would be interesting for applications in biomedical and industrial areas involving various liquid environments.

A study on the asymptotic approximation for surfactant adsorption onto a spherical air-water interface

The asymptotic approximation equation was derived as a simple means for determining the adsorption mechanism and estimating surfactant diffusivity for surfactant adsorption onto a clean, spherical air-water interface (Makievski et al., 1999). However, the applicability of this approximation is yet to be examined. In this study, a theoretical simulation was conducted to better understand its applicability and validity. The diffusion-controlled adsorption of a nonionic surfactant onto a clean spherical interface (with radius = 0.03, 0.1, 0.5, and ∞ cm) was considered, and theoretical dynamic surface tension (γ) profiles were generated using the Langmuir adsorption isotherm. The initial region of γ(t1/2) profiles was best-fitted with asymptotic approximation with only one unknown parameter, the surfactant diffusivity. The initial region of the γ(t1/2) profiles could be well-described by the asymptotic approximation (a parabolic equation), but a notable deviation was observed on the diffusivity obtained from the fitting. This deviation was dependent on the bulk concentration and the duration of the initial region fitted; whilst being only slightly dependent on bubble radius. Although the results demonstrated the viability of this approximation, there existed a possibility of obtaining multiple values of diffusivity by choosing different initial regions of a γ(t1/2) profile.

Influence of initial particle configuration upon sphericity of shock loaded density interface in SPH modelling of Richtmyer-Meshkov instability

The Richtmyer-Meshkov Instability (RMI) occurs when a perturbed interface between two fluids of different densities undergoes impulsive acceleration by, for example, a shock wave. Its study is important for gaining better understanding of processes governing inertial confinement fusion where a spherical solid deuterium-tritium (DT) capsule filled with the DT gas is compressed by a powerful laser [1]. The imploding shock moving to the center of the spherical shell causes the RMI to form on its inner surface due to a large density difference between solid and gaseous DT phases, which leads to a rapid growth of initially present randomperturbations. Usually, the density interface consists of random perturbations (e.g., surface roughness, machining inaccuracies, etc.) which initially grow linearly before nonlinear effects emerge. To improve reliability of shock-driven flow simulations, it is necessary to understand the factors which inuence the RMI growth. Our work aims to find the best initial particle configuration that does not introduce artificial perturbations of the spherical density interface. The shocked interface must preserve spherical symmetry if no perturbations are applied. In order to reduce the number of simulated particles in calculation, it is necessary to adapt spatial resolution, i.e., to increase the concentration of particles in target regions.

The effect of surfactant on the drag and wall correction factor of a drop in a bounded medium

Abstract In the present article, the analytical solution for creeping motion of a drop/bubble characterized by insoluble surfactant is examined at the instant it passes the center of a spherical container filled with Newtonian fluid at low Reynolds number. The presence of surfactant characterizes the interfacial region by an axisymmetric interfacial tension gradient and coefficient of surface dilatational viscosity. Under the assumption of the small capillary number, the deformation of spherical phase interface is not taken into account. The computations not only yield information on drag force and wall correction factor, but also on interfacial velocity and flow field for different values of surface tension gradient and surface dilatational viscosity. In the limiting cases, the analytical solutions describing the drag force and wall correction factor for a drop in a bounded medium reduces to expressions previously stated by other authors in literature. The results reveal the strong influence of the surface dilatational viscosity and surface tension gradient on the motion of drop/bubble. Increasing the surface tension gradient and surface dilatational viscosity, results in linear variation of drag force. When the surface tension gradient increases, the drag force for unbounded medium increases more as compared to the bounded medium hence wall correction factor decreases with increase in surface tension gradient whereas it increases with increase in surface dilatational viscosity.

Hierarchical Microphase Behaviors of Chiral Block Copolymers under Kinetic and Thermodynamic Control

Hierarchical Microphase Behaviors of Chiral Block Copolymers under Kinetic and Thermodynamic Control

A quasi complex-lamellar solution for a hemispherically bounded cyclonic flowfield

This work describes an inviscid solution for a cyclonic flowfield evolving in a hemispherical chamber configuration. In this context, a vigorously swirling motion is triggered by a gaseous stream that is introduced tangentially to the inner circumference of the chamber's equatorial plane. The resulting updraft spirals around while sweeping the chamber wall, reverses direction while approaching the headend, and then tunnels itself out through the inner core portion of the chamber. Our analysis proceeds from the Bragg–Hawthorne formulation, which proves effective in the treatment of steady, incompressible, and axisymmetric motions. Then using appropriate boundary conditions, we are able to obtain a closed-form expression for the Stokes streamfunction in both spherical and cylindrical coordinates. Other properties of interest are subsequently deduced, and these include the principal velocities and pressure distributions, vorticity, swirl intensity, helicity density, crossflow velocity, and the location of the axial mantle; the latter separates the outer annular updraft from the inner, centralized downdraft. Due in large part to the overarching spherical curvature, the cyclonic motion also exhibits a polar mantle across which the flow becomes entirely radial inward. Along this lower and shorter spherical interface, the polar velocity vanishes while switching angular direction. Interestingly, both polar and axial mantles coincide in the exit plane where the ideal outlet size, prescribed by the mantle position, is found to be approximately 70.7% of the chamber radius. We thus recover the same mantle fraction of the cyclonic flow analog in a right-cylindrical chamber where an essentially complex-lamellar motion is established.

Long range corrections for inhomogeneous fluids containing a droplet or a bubble

ABSTRACT Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monatomic Lennard–Jones fluid. The method is generalised to the Mie potential and arbitrary molecular structures, employing a numerically efficient centre of mass cut-off scheme. The results are validated by a series of droplet simulations for one-centre and two-centre Lennard–Jones fluids with different cut-off radii r c . Systems with provide a check of self-consistence. Further, a system containing a bubble is investigated for the one-centre Lennard–Jones fluid. The equilibrium properties are almost completely independent on the cut-off radius. In comparison with vapour–liquid equilibrium data for systems without a curved interface, all properties show the expected behaviour. Simulation data are used to approximate the surface tension, which is in good agreement with the findings for planar interfaces, thus verifying the present corrections.

Long range corrections for inhomogeneous fluids containing a droplet or a bubble

Long range corrections for molecular simulations of inhomogeneous fluids with a spherical interface are presented. Correction terms for potential energy, force and virial are derived for the monato...

Assessment of the statistical rate theory expression for evaporation mass flux

A series of 72 steady-state evaporation experiments in which water evaporated from a spherical liquid-vapor interface have been conducted. In each experiment, the interfacial temperatures, the temperature profile across the liquid-vapor interface, and the pressure in the vapor phase were measured. When the interfacial parameters were used in the statistical rate theory (SRT) expression for evaporation flux, the vapor-phase pressure could be predicted to a reasonable degree of accuracy in all experiments. In all 72 experiments, the interfacial temperature of the vapor was always higher than that of the liquid phase and in certain cases, the difference was measured to be 7.1 K. Measurement of the vapor-phase pressure near the cool liquid-vapor interface and far from the interface did not show a significant difference, indicating that the density (concentration) in the bulk vapor phase may not be uniform.

On the stress analysis around a nanoinhomogeneity embedded in a half-space with the account of Steigmann–Ogden interface effects

This paper examines the interface elasticity between an elastic half-space and a spherical nanoinhomogeneity subjected to a unidirectional far-field tension that is parallel to the half-space plane boundary. The spherical interface is modeled by the full version of Steigmann–Ogden interface theory. Due to their marginal significance, the effects of half-space plane boundary are neglected. The problem is solved by decomposing the unidirectional load into an all-around and an equal-but-opposite traction field. Benefitting from the property of axial symmetry, the former subproblem is solved by the sole use of Boussinesq displacement potentials. The latter condition is addressed by six harmonic functions extracting from Boussinesq, Papkovich–Neuber and Dougall displacement potentials. The relations between cylindrical and spherical harmonic functions are employed to clear the tractions along the half-space plane boundary and to satisfy the nonclassical traction equilibrium conditions across the matrix/nanoinhomogeneity interface. Truncating the resultant infinite series and equating the coefficients preceding Legendre polynomials, associated Legendre functions as well as their derivatives lead to a system of algebraic equations with respect to the dimensionless unknown parameters in displacement potentials. Extensive parametric studies are further performed in order to analyze the importance of interface tension, interface Lamé constants, interface flexural rigidities, shear moduli ratio and nanoinhomogeneity radius-to-depth ratio on stress distributions and stress concentrations. Comparisons against both the classical and the Gurtin–Murdoch solutions help to clarify the separate effects of individual interface material properties. Stresses inside a soft nanoinhomogeneity is most affected by the additional incorporation of interface flexural rigidities. In addition, the deviatoric component of the interface curvature change tensor is found to be more important than the mean part for the proposed nanoinhomogeneity problem.

An exact irrotational solution for a hemispherically bounded cyclonic flowfield

This study focuses on the development of an internal potential flow solution in the context of a hemispherically bounded cyclonic chamber. The analysis proceeds from the Bragg–Hawthorne equation, which is quite effective in the treatment of steady, inviscid, and axisymmetric flows when expressed in terms of the streamfunction. Once the streamfunction is obtained, other flow properties are readily deduced; these include the principal velocity and pressure distributions, swirl intensity, crossflow velocity, and mantle location. Furthermore, given the overarching spherical geometry, two different types of mantles are identified and related to the coexistence of axially bidirectional and circularly bipolar regions. The first, axial mantle, which is traditionally used in the analysis of cylindrical and conical cyclone separators, consists of a rotating, non-translating interfacial layer along which the axial velocity vanishes. It thus separates the outer, vertical updraft, from the inner, swirling downdraft. The second, polar mantle, which arises in the context of a hemispherical flow configuration, coincides with the spherical interface along which the polar velocity vanishes. It hence partitions the flow domain into a much larger outer region, where the flow direction remains strictly counterclockwise, and a proportionally smaller inner region, where the outflow becomes clockwise. Despite their dissimilar structures, both axial and polar mantles meet in the exit plane at a fractional radius of 1/e2 or 13.53%. In this study, the unique characteristics of the resulting irrotational motion, which reduces to a continuously looping, hemispherically cyclonic potential vortex, are evaluated and discussed.

Surface tensions at elevated pressure depend strongly on bulk phase saturation

HypothesisUnderstanding interfacial phenomena at elevated pressure is crucial to the design of a variety of processes, modeling important systems, and interpreting interfacial thermodynamics. While many previous studies have offered insight into these areas, current techniques have inherent drawbacks that limit equilibrium measurements. ExperimentsIn this work, we adapt the ambient microtensiometer of Alvarez and co-workers into a high pressure microtensiometer (HPMT) capable of experimentally quantifying a wide range of interfacial phenomena at elevated pressures. Particularly, the HPMT uses a microscale spherical interface pinned to the tip of a capillary to directly measure surface tension via the Laplace equation. The stream of microscale bubbles used to pressurize the system ensures quick saturation of the bulk phases prior to conducting measurements. The HPMT is validated by measuring the surface tension of air–water as a function of pressure. We then measure the surface tension of CO2 vapor and water as a function of pressure, finding lower equilibrium surface tension values than originally reported in the literature. FindingsThis work both introduces further development of a useful experimental technique for probing interfacial phenomena at elevated pressures and demonstrates the importance of establishing bulk equilibrium to measure surface tension. The true equilibrium state of the CO2-water surface has a lower tension than previously reported. We hypothesize that this discrepancy is likely due to the long diffusion timescales required to ensure saturation of the bulk fluids using traditional tensiometry. Thus we argue that previously reported elevated pressure measurements were performed at non-equilibrium conditions, putting to rest a long standing discrepancy in the literature. Our measurements establish an equilibrium pressure isotherm for the pure CO2-water surface that will be essential in analyzing surfactant transport at elevated pressures.

A consistent and parallelized height function based scheme for applying contact angle to 3D volume-of-fluid simulations

A height function based numerical scheme has been developed to apply contact angle in the parallel computational framework of 3D volume-of-fluid method. Given that most of the reported height function methods are implemented in 2D, the differences between the implementations of 2D and 3D height function methods are first focused. Then, a novel scheme is proposed to preserve the accuracy and consistency of height function for the calculation of interface curvature near the contact line. Finally, the extension to parallel computation is presented in details because it is not a trivial task as it appears, e.g., the information transmission among the cells neighboring two intersecting boundaries requires careful treatment. Numerical tests reveal that with the proposed scheme, accurate estimations of interface curvature and normal vector are obtained for a spherical interface, and such a numerical strategy allows the spurious currents to decrease to machine accuracy for a 3D stationary droplet. Moreover, by simulating a droplet spreading on a solid wall with 3D Cartesian grid, either from a static state driven by capillary force or with an initial impact velocity, the numerical results verify that the contact line can maintain an axi-symmetric shape during the dynamic spreading.

On spherical nanoinhomogeneity embedded in a half-space analyzed with Steigmann–Ogden surface and interface models

This paper determines the elastic fields in a positive half-space embedded with a spherical inhomogeneity under the context of Steigmann–Ogden surface/interface mechanical model. The half-space is loaded by an equal-biaxial far-field tension applied at infinity. While bulk domains are treated as linearly isotropic elastic solids, both the half-space plane boundary and the matrix/inhomogeneity interface are modeled by the Steigmann–Ogden theory. The well-developed method of Boussinesq displacement potentials is used to solve the elastostatic Navier’s equations of equilibrium. In view of the geometry and loading configurations, four sets of cylindrical and spherical harmonic potentials are carefully proposed to solve the problem. Implementation of the nonclassical Steigmann–Ogden boundary conditions at both the half-space free surface and the spherical interface results in a semianalytical solution in the form of infinite Legendre series. Extensive parametric studies are performed with respect to the surface and interface Steigmann–Ogden material parameters, shear moduli ratio between the spherical inhomogeneity and its surrounding matrix, and the inhomogeneity radius-to-depth ratio. Comparison and contrast with the well known Gurtin–Murdoch model reveals the significance of surface flexural rigidities at both boundaries of the considered mechanical model. When compared with the effects of matrix/inhomogeneity interface, the surface tension, Lamé constants and flexural rigidities at the half-space plane boundary are of secondary importance. This work is able to shed some lights on the modeling of self-organized adatoms and islands that is essential in the semiconductor industry.

Spherical Array System for High-Precision Transcranial Ultrasound Stimulation and Optoacoustic Imaging in Rodents.

Ultrasound can be delivered transcranially to ablate brain tissue, open the blood-brain barrier, or affect neural activity. Transcranial focused ultrasound in small rodents is typically done with low-frequency single-element transducers, which results in unspecific targeting and impedes the concurrent use of fast neuroimaging methods. In this article, we devised a wide-angle spherical array bidirectional interface for high-resolution parallelized optoacoustic imaging and transcranial ultrasound (POTUS) delivery in the same target regions. The system operates between 3 and 9 MHz, allowing to generate and steer focal spots with widths down to [Formula: see text] across a field of view covering the entire mouse brain, while the same array is used to capture high-resolution 3-D optoacoustic data in real time. We showcase the system's versatile beam-forming capacities as well as volumetric optoacoustic imaging capabilities and discuss its potential to noninvasively monitor brain activity and various effects of ultrasound emission.

Kinetic modelling of evaporation and condensation phenomena around a spherical droplet

The steady evaporation and condensation phenomena around a spherical droplet of the condensed phase of a vapor are investigated with basis on a kinetic model to the linearized Boltzmann equation. The kinetic equation is solved via a discrete velocity method which takes into account the discontinuity of the distribution function of molecular velocities on the spherical interface. The calculations are carried out in a wide range of the gas rarefaction and evaporation-condensation coefficient. The results obtained via solution of the linearized Navier-Stokes equations with temperature and pressure jump boundary conditions are also presented and compared to those obtained via kinetic equation. A comparison between the linearized and non-linear solutions of the kinetic model is also presented to show the limit of applicability of the linearized approach.

Phase-field lattice Boltzmann model for interface tracking of a binary fluid system based on the Allen-Cahn equation.

A lattice Boltzmann (LB) model is proposed to track the interface of binary fluid system based on the conservative-form Allen-Cahn (A-C) equation for phase field. Utilizing an equilibrium distribution function and a modified LB equation, this model is able to correctly recover the conservative A-C equation through the Chapman-Enskog analysis. A series of two-dimensional (2D) and three-dimensional (3D) phase-capturing benchmark tests have been conducted for validation, which include the diagonal translation of a circular interface, the rigid-body rotation of a Zalesak disk, and the deformation of 2D circular interface and 3D spherical interface in shear flows, all illustrating better accuracy and stability of the proposed model than the previous models tested. By coupling the incompressible hydrodynamic equation, a stationary droplet, a spinodal decomposition, and the Rayleigh-Taylor instability are simulated as well, showing the satisfying performance of the model in dealing with complex interfaces of binary fluid systems.

Rayleigh-Taylor instability in a spherical configuration: A viscous potential flow approach

In this paper, Rayleigh-Taylor (RT) instability at the spherical interface is analyzed through the potential flow theory of viscous fluids. The linear stability theory is utilized including normal mode procedure. The viscous, incompressible fluids are confined in the spherical shell and the interface distortion is expressed in terms of spherical harmonic functions. We achieve a quadratic equation for the illustration of instability/stability criterion. We also compute the highest growth of perturbations and corresponding mode. The Plane configuration results are recovered when the mode of perturbations is very large. Viscosity is found to stabilize the interface while the Weber number and Reynolds number have destabilizing nature.

Scalable and integrated flow synthesis of triple-responsive nano-motors via microfluidic Pickering emulsification

Artificial micro-/nano-motors are tiny machines as newly emerging tools capable of achieving numerous tasks. In principle, the self-phoretic motions require asymmetric structures in geometry and chemistry. However, conventional production techniques suffered from complex and time consuming multi-step process in low uniformity, and difficult to endow multi-functions into motors. This work disclosed a continuous-flow synthesis of triple-responsive (thermophoretic, chemical and magnetic movement) nano-motors (m-SiO2/Fe3O4-Pdop/Pt) via microfluidic Pickering emulsification in a process of integrated and scalable manner. The droplet microfluidic process allows efficient self-assembly of the silica nanoparticles surrounding the spherical interface of resin droplet, rendering excellent Pickering efficiency and reproducibility, and followed by anisotropic decoration of polydopamine (Pdop) and Pt catalyst in a serial flow process. The obtained Janus nanoparticles reveal double- or triple-responsive self-propulsions with synergic mobility by combining thermophoresis powered by light, catalytic driven motion in H2O2 or magnetic movement by magnet. Further, a non-metallic polydopamine based thermophoretic motion as well as an automated nano-cleaner for rapid water purification by dye removal are convincingly functioned. Finally, this novel integrated flow strategy proves a scalable manufacturing production (> 0.7 g hr−1) of the nano-motors using inexpensive single microreactor, fulfilling quantitative and qualitative needs for versatile applications.

Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface

Through the computation of the most-unstable modes, we perform a systematic analysis of the linear Rayleigh–Taylor instability at a spherical interface separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration over the entire parameter space. Using the growth rate as the dependent variable, the parameter space is spanned by the spherical harmonic degree n and three dimensionless variables: the Atwood number A, the viscosity ratio s, and the dimensionless variable B=(aRρ22/μ22)1/3R, where aR, ρ2, and μ2 are the local radial acceleration at the interface and the density and viscosity of the denser overlying fluid, respectively. To understand the effect of the various parameters on the instability behavior and to identify similarities and differences between the planar and spherical configurations, we compare the most-unstable growth rates αP* (planar) and αS* (spherical) under homologous driving conditions. For all A, when s ≪ 1, the planar configuration is more unstable than the spherical (αP*&amp;gt;αS*) within the interval 0 &amp;lt; B &amp;lt; ∞. However, as s increases to O(1), there is a region for small values of B where αS*&amp;gt;αP*, whereas for larger values of B, αP*&amp;gt;αS* once again. When s ∼ 2, the maximum of αS* for the n = 1 mode is greater than αS* for any other mode (n ≥ 2). For s∼O(10), αS*&amp;gt;αP* for all A within 0 &amp;lt; B &amp;lt; ∞. We find that the instability behavior between the planar and spherical systems departs from each other for s ≳ 2 and diverges considerably for s ≫ 1. In the limit when s → ∞, the planar configuration reduces to the trivial solution αP*≡0 for all B and A, whereas αS* has a non-zero limiting value for the n = 1 mode but vanishes for all the other modes (n ≥ 2). We derive an equation for αS* in this limit and obtain closed form solutions for the maximum of αS* and the value of B at which this occurs. Finally, we compare the most-unstable growth rates between the exact dispersion relation and three different approximations to highlight their strengths and weaknesses.