Spherical Interface Research Articles

Influence of interface on nondeformable micropolar drop migration

Abstract In this article, an analytical approach is considered to study the issue of specifying Stokesian motion due to a micropolar sphere drop translating at a concentric instantaneous position within a spherical fluid-fluid interface that divides two immiscible fluids, one of which is bounded and the other is unbounded. Here, the focus is on the situation where there are two microstructure-related fluid phases (micropolar fluids) out of the three. The motion is considered to have low Reynolds numbers; thus, the drop's surface and fluid-fluid interface have insignificant deformation. For both the components of the microrotation and velocity, general solutions to the slow axisymmetric motion of the micropolar/viscous fluid in a spherical coordinate system are obtained based on a concentric position. Boundary conditions are fulfilled at the drop's surface and the fluid-fluid interface. Especially, the boundary condition for the microrotation-vorticity is utilised at the fluid-fluid interface; while the continuity of tangential couple stress and microrotation are also utilised at the drop's surface. Findings indicate that the normalised hydrodynamic force increases monotonically as the droplet-to-interface radius ratio increases, acting on a moving micropolar sphere droplet and becoming unlimited when the drop's surface touches the fluid-fluid interface. The numerical findings for the normalised force operating on the micropolar sphere droplet at different values of the suitable parameters are introduced in both graphical and tabular form. Our numerical findings are compared with the suitable data for the special cases stated in the literature. This current investigation is significant within the domains of industrial, biological, medicinal, and natural processes, for example, liquid-liquid extraction, raindrop formation, blood cells moving through a vein or artery, suspension rheology, sedimentation, and coagulation.

Viscous Rayleigh–Taylor instability at a dynamic interface in spherical geometry

In their study, Terrones et al. [“Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface,” Phys. Fluids 32, 094105 (2020)] elucidated that investigations into the viscous Rayleigh–Taylor instability (RTI) in spherical geometry at a quiescent interface yield significant physical insights. Yet, the complexity amplifies when addressing a dynamic spherical interface pertinent to engineering and scientific inquiries. The dynamics of RTI, particularly when influenced by the Bell–Plesset effects at such interfaces, offers a rich tapestry for understanding perturbation growth. The evolution of this instability is describable by a coupled set of equations, allowing numerical resolution to trace the radius evolution and instability characteristics of a bubble akin to the implosion scenario of a fusion pellet in inertial confinement fusion scenarios. The investigation encompasses the impact of viscosity, external pressure, discrete mode, and a surface-tension-like force on the interfacial instability. In general, the oscillation of the bubble radius exhibits a decay rate that diminishes with increasing Reynolds number (Re). It is important to note that the growth of the perturbed amplitude is not only solely determined by the mechanical properties of the fluid but also by the dynamics of the interface. The low-order modal (n<20) disturbance is dominant with relatively high Reynolds numbers. There is a specific mode corresponding the maximum in amplitude of perturbation in the linear phase, and the mode decreases as the Re decreases. The application of external pressure noticeably accelerates the bubble's oscillation and impedes its shrinkage, thereby preventing the bubble from collapsing completely. The increase in external pressure also promotes the transition from the first peak to the trough of the disturbance. At higher-order modes, the fluctuation of the disturbance curve tends to be uniform. The ultrahigh-order modes require a strong enough pressure to be excited. In addition, the smaller Weber number (We) helps to accelerate the bubble oscillation and promote the fluctuation of the disturbance amplitude, but has no significant effect on the time of the disturbance peak. These findings contribute to a deeper understanding of interfacial instabilities in the context of spherical bubbles and, especially, for the dynamics of fusion capsules in inertial confinement fusion.

Construction of spherical heterogeneous interface on ZnFe2O4@C composite nanofibers for highly efficient microwave absorption

Enriching the electromagnetic wave loss mechanism and improving the impedance matching are the keys to improve the electromagnetic wave absorption performance of carbon fibers. In this study, beaded ZnFe2O4@C absorbing composite fibers (ZFCF) with synergistic effects of magnetic loss and dielectric loss was prepared by electrospinning and heat treatment. ZnFe2O4 magnetic particles effectively improve the impedance matching and increase the loss mechanism of carbon nanofibers. The optimal ZFCF composite has excellent absorption performance, with a minimum reflection loss of −53.6 dB at 2.64 mm and the widest effective absorption bandwidth of 4.32 GHz. The excellent absorption performance is attributed to significant magnetic losses from eddy currents and magnetic resonance generated by ZnFe2O4, and strong interfacial polarization from the numerous heterogeneous interfaces. Additionally, the one-dimensional carbon nanofibers create a conductive network and structural defects that enhance conductive loss and dipole polarization effects. Moreover, the RCS of ZFCF composite was significantly reduced by −32.85 dBm2. The combination of simulation technology and material design is of great significance for the study of electromagnetic wave absorption mechanism and the rational design of electromagnetic wave absorbing coatings.

Strategy for a high thermal conductivity and low thermal resistance under compression of oriented carbon fiber with spherical alumina thermal interface material

Thermal pads prepared with pitch-based carbon fibre (CF) orientation have garnered widespread attention due to their generally higher through-plane thermal conductivity. However, these thermal pads must undergo compression during the assembly process. When the compression exceeds a certain threshold, the orientation degree of the CFs inside the thermal pad can change, leading to a reduction in thermal conductivity. In this study, spherical alumina and CF were utilized to optimize thermal transfer stability under compression. The results demonstrate that the composites can still maintain efficient and stable heat transfer even when compressed by 25 %, which represents a more than 60 % improvement compared to pure CF-oriented composites. Furthermore, the relative motion between spherical alumina and CF, driven by their significant morphological differences, enhances the degree of CF orientation during the orientation process. With only 11.8 wt% CF loading, the composite achieved an impressive through-plane thermal conductivity of up to 20.4 W·m−1·K−1.

Extending Finch-Skea isotropic model to anisotropic domain in modified f(, T ) gravity

This paper considers the Finch-Skea isotropic solution and extends its domain to three different anisotropic interiors by using the gravitational decoupling strategy in the context of f(R,T) gravitational theory. For this, we consider that a static spherical spacetime is initially coupled with the perfect matter distribution. We then introduce a Lagrangian corresponding to a new gravitating source by keeping in mind that this new source produces the effect of pressure anisotropy in the parent fluid source. After calculating the field equations for the total matter setup, we apply a transformation on the radial component, ultimately providing two different systems of equations. These two sets are solved independently through different constraints that lead to some new solutions. Further, we consider an exterior spacetime to calculate three constants engaged in the seed Finch-Skea solution at the spherical interface. The estimated radius and mass of a star candidate LMC X-4 are utilized to perform the graphical analysis of the developed models. It is concluded that only the first two resulting models are physically relevant in this modified theory for all the considered parametric choices.

Unmasking quantum effects in the surface thermodynamics of fluid nanodrops.

The focus of our study is an in-depth investigation of the quantum effects associated with the surface tension and other thermodynamic properties of nanoscopic liquid drops. The behavior of drops of quantum Lennard-Jones fluids is investigated with path-integral Monte Carlo simulations, and the test-area method is used to determine the surface tension of the spherical vapor-liquid interface. As the thermal de Broglie wavelength, λB, becomes more significant, the average density of the liquid drop decreases, with the drop becoming mechanically unstable at large wavelengths. As a consequence, the surface tension is found to decrease monotonically with λB, vanishing altogether for dominant quantum interactions. Quantum effects can be significant, leading to values that are notably lower than the classical thermodynamic limit, particularly for smaller drops. For planar interfaces (with infinite periodicity in the direction parallel to the interface), quantum effects are much less significant with the same values of λB but are, nevertheless, consequential for values representative of hydrogen or helium-4 at low temperatures corresponding to vapor-liquid coexistence. Large quantum effects are found for small drops of molecules with quantum interactions corresponding to water, ethane, methanol, and carbon dioxide, even at ambient conditions. The notable decrease in the density and tension has important consequences in reducing the Gibbs free-energy barrier of a nucleating cluster, enhancing the nucleation kinetics of liquid drops and of bubble formation. This implies that drops would form at a much greater rate than is predicted by classical nucleation theory.

Imaging Deep Haemorrhage and Ischaemia in Preterm Infants' Heads with Time-Domain Near-Infrared Optical Tomography: Phantom Study.

The occurrence of brain lesions in preterm infants is common and can result in lasting disabilities. To prevent these and to safeguard the brain through therapeutic measures or neuroprotective treatments, it is important to identify cerebral ischaemia/hypoxia and haemorrhage at an early stage. For this purpose, we have successfully developed a cutting-edge time-domain near-infrared optical tomography (TD-NIROT) system, which offers diagnostic imaging for neonatal brain oxygenation. Our objective is to validate the effectiveness of the TD-NIROT in detecting deep ischaemia/hypoxia and haemorrhages through phantom experiments. Spherical silicone phantoms were fabricated to replicate the head of preterm infant. To simulate the lesions, we made two head phantoms and embedded small inclusions mimicking ischaemia and haemorrhage at the depth of 30 mm. Additionally, a spherical interface was constructed to connect the spherical phantom to the imaging system, allowing us to collect time-domain data. Following the data acquisition, we proceeded with image reconstruction. Dice similarity was used as an indicator of the accuracy and similarity between the reconstructed images and the ground truth. The resulting images exhibited an accurate location of haemorrhage and detected the ischaemia with a slightly shifted position with Dice similarity of 0.47 and 0.27. Our experiment validates the capability of our TD-NIROT system in successfully detecting deep haemorrhages and ischaemia within the phantom model. The achieved results suggest a promising level of accuracy in the imaging process. These findings are encouraging to continue this work to ultimately achieve clinical application of the TD-NIROT system in diagnosing and monitoring neonatal brain injuries.

Impact of a spherical interface on a concentrical spherical droplet

<p>In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature.</p>

Recovery of Cu2+ from acid mine drainage by bentonite-carbide slag composite particle through spontaneous film formation-crystal self-growth-fixed mineralization

In this study, a novel bentonite-carbide slag composite particle (BCS) with endogenetic crystal ion of OH− was prepared by using bentonite and carbide slag as raw materials to treat acid mine drainage containing Cu2+. Macroexperiment, microtest, and theoretical analysis were adopted to reveal the characteristics and mechanism of BCS for the recovery of heavy metal ions from acid mine drainage (AMD). The results showed that the solution around the BCS can spontaneously form a spherical colloid film interface layer, and Cu2+ can be recovered by self-growth film formation and fixed mineralization through the synergistic effect of adsorption, precipitation, induced crystallization, and self-growth mineralization. Two stages, including liquid film formation and self-growth mineralization, existed in the formation and mineralization of mineralized films. This study provided a new treatment perspective for the removal and fixed mineralization recovery of heavy metal ions in AMD. It also provides a scientific theoretical basis for the spontaneous film formation, crystallization, self-growth, and fixed mineralization recovery of heavy metal ions in AMD by the endogenetic crystal ion of OH− in BCS.

Influence of Sphericity on Surface Termination of Icosahedral Colloidal Clusters.

Colloids self-organize into icosahedral clusters composed of a Mackay core and an anti-Mackay shell under spherical confinement to minimize the free energy. This study explores the variation of surface arrangements of colloids in icosahedral clusters, focusing on the determining factors behind the surface arrangement. To efficiently assemble particles in emulsion droplets, droplet-to-droplet osmotic extraction from particle-laden droplets to salt-containing droplets is used, where the droplets are microfluidically prepared to guarantee a high size uniformity. The icosahedral clusters are optimally produced during a 24-h consolidation period at a 0.04m salt concentration. The findings reveal an increase in the number of particle layers from 10 to 15 in the icosahedral clusters as the average number of particles increases from 3300 to 11 000. Intriguingly, the number of layers in the anti-Mackay shells, or surface termination, appears to more strongly depend on the sphericity of the clusters than on the deviation in the particle count from an ideal icosahedral cluster. This result suggests that the sphericity of the outermost layer, formed by the late-stage rearrangement of particles to form an anti-Mackay shell near the droplet interface, may play a pivotal role in determining the surface morphology to accommodate a spherical interface.

Pressure dynamics of an internal shock wave emission inside a water droplet and potential cavitation

Shock reflected by a spherical interface is involved in shock-droplet interaction. Here, we investigate the pressure dynamics of an internal spherical shock wave and the potential cavitation inside a spherical water droplet. We conduct hydrodynamic simulation and employ the linear geometrical acoustics approximation to analyze the negative pressure and the wavefront at different intervals d between the source point of the shock and the droplet surface. Studies indicate that the negative pressure at a very large d is primarily attributed to the focusing effect of the droplet surface, whereas the collision of the reflected waves contributes to negative pressure at a small d. The caustic, which is the locus of the cusps (singular points) on the shock wavefront is determined by the parametric equations. Notably, the caustic also has singular points owing to the off-axis reflection. Finally, we evaluate the cavitation inside the droplet. Cavitation occurs on the opposite side of the droplet and moves away from the surface with d increasing, which agrees with previous experimental results. Additionally, we demonstrate that cavitation can occur with less damage to the droplet compared to a planar shock impact on a water droplet.

Stability analysis of spherical viscous fluid-Oldroyd B viscoelastic fluid interface: A viscous potential flow approach

The present study investigates the stability of a spherical interface formed by a combination of a viscous fluid and an Oldroyd B viscoelastic fluid using the linear stability analysis. The spherical geometry consists of a viscous fluid occupying the inner sphere, while the outer sphere is filled with the viscoelastic fluid. The governing equations are derived based on the viscous-viscoelastic irrotational theory, and their solutions are obtained using mathematical methods. The analysis results in a third-degree polynomial equation that describes the growth of perturbations, which is then evaluated numerically. It is found that the perturbations grow more rapidly at the interface between the viscoelastic and viscous fluids than at the interface between the viscous fluid and the surrounding medium. The instability of the interface increases with an increase in the Weissenberg number, which is a dimensionless parameter that characterizes the viscoelasticity of the fluid.

Scattering of a Plane Sound Wave by a Spherical Interface of Two Media with Sound Absorption in the Acoustic Boundary Layer

Scattering of a Plane Sound Wave by a Spherical Interface of Two Media with Sound Absorption in the Acoustic Boundary Layer

Curvature and shape relaxation in surface-viscous domains.

The mechanics of curved, heterogeneous, surfactant-laden surfaces and interfaces are important to a variety of engineering and biological applications. To date, most models of rheologically complex interfaces have focused on homogeneous systems of planar or fixed curvature. In this study, we investigate a simple, dynamical model of a two-phase surface fluid on a curved interface: a condensed, surface-viscous domain embedded within a surface-inviscid, spherical interface of time-varying radius of curvature. Our aim is to understand how changes in surface curvature generate two-dimensional Stokes flows inside the domain, thereby resisting curvature deformation and distorting the domain shape. We model the surface stress within the domain using the classical Boussinesq-Scriven constitutive equation, simplified for a near-spherical cap undergoing a small-amplitude curvature deformation. We then analyze the frequency-dependent dynamics of the surface stress and curvature within the domain when the pressure difference across the surface is sinusoidally oscillated. We find that the curvature relaxes diffusively, and thus define a Peclet number (Pe) relating the rate of diffusion to the oscillation frequency. At small enough Pe, the surface deforms quasi-statically, whereas at high Pe, the curvature varies sharply within a thin boundary layer adjacent to the domain border. Consequently, the curvature of the domain appears discontinuous from the rest of the surface under rapid oscillation. We then examine the linear stability of the domain shape to small, non-axisymmetric perturbations when the surface is steadily compressed (i.e., the pressure difference across it is increased). While the line tension at the domain border tends to maintain circular symmetry, surface-viscous stresses generated by surface compression tend to destabilize the perimeter. A shape instability arises above a critical surface capillary number (Ca) relating surface-viscous stresses to line tension. Moreover, we show that the mechanism of instability is distinct from that of the famous Saffman-Taylor fingering instability. Various extensions of our model are discussed, including materials with finite dilatational surface viscosity, linear and nonlinear (visco)elasticity, and large-amplitude deformations.

Scattering of a Plane Sound Wave by a Spherical Interface of Two Media with Sound Absorption in the Acoustic Boundary Layer

The scattering of a plane sound wave by a spherical interface between two liquid or gaseous media is simulated. The influence of heat conductivity and viscosity is taken into account; the results of G. Kirchhoff’s classical work on sound propagation in a viscous and heat-conducting medium are used. A spherical surface can have any wave dimension. The results are compared with the field scattered by a solid sphere, which is an ideal heat conductor.

Size-dependent effective shear modulus in a three-phase sphere model incorporating Steigmann-Ogden surface elasticity

We derive a solution for the size-dependent effective shear modulus of a three-phase sphere model incorporating Steigmann-Ogden surface elasticity under a uniform remote deviatoric load. In the three-phase model, the internal spherical inhomogeneity, the intermediate spherical annulus of the matrix and the surrounding infinite region of equivalent homogeneous material are bonded through an inner spherical interface endowed with Steigmann-Ogden surface elasticity (with vanishing surface tension) and an outer perfect spherical interface. The value of the effective shear modulus is equal to that of the matrix for any volume fraction when the three size-dependent interface parameters satisfy a single condition. Furthermore, the neutrality of the composite sphere to a prescribed uniform deviatoric stress field for any volume fraction is accomplished when the three size-dependent interface parameters satisfy two particular conditions. The neutrality is valid only for a Steigmann-Ogden interface and not for a Gurtin-Murdoch interface.

Stability analysis of water-alumina nanofluid film at the spherical interface

The interface of a viscous fluid and [Formula: see text]-water nanofluid is analyzed through linear instability analysis in a spherical configuration. The viscous fluid lies inside the sphere while the outside region contains nanofluid. In this model, the viscosity of the nanofluid is considered a function of the base fluid viscosity, nanoparticles volume fraction, fractal aggregates, and nanoparticles shape. The perturbed flow is taken as irrotational, and the linear perturbation equations are solved through viscous irrotational theory. The perturbations growth rate can be computed through a 2-degree polynomial and the coefficients of this polynomial are the functions of the Atwood number, Richardson number, Weber number, Reynolds number, etc. The nanofluid interface is found more stable than the viscous fluid interface. The density of nanofluids raises the amplitude of disturbances while the nanofluid's viscosity has a reverse effect.

Position controlled lasing threshold of the acceptor emission in a dynamic twin droplet system made using a microfluidic chip

We demonstrate low threshold acceptor lasing consequent to the efficient coupling and radiative energy transfer between the donor and acceptor droplets in a dynamic array of coupled droplets named twin droplets, made using a microfluidic chip. The ability of the microdroplet to focus the incoming plane wave internally along the principle diameter, by virtue of its spherical interface and higher refractive index than the background medium, is recognized as the prime cause of observed acceptor lasing in the coupled droplet system. This is confirmed by observing only acceptor fluorescence when the refractive index of the donor droplet falls below that of the background. By flipping the position of the acceptor in the twin droplets, we further show that the threshold of the acceptor lasing is dependent on the acceptor position and, hence, the coupling direction. Using the emission polarization measurements from the twin droplets, we also show that the acceptor emission is highly polarized and follows the pump laser polarization.

Concentration–Capillary Convection when Transferring Mass through a Spherical Interface while Extracting a Liquid

Concentration–Capillary Convection when Transferring Mass through a Spherical Interface while Extracting a Liquid

Position controlled lasing threshold of the acceptor emission in a dynamic twin droplet system made using a microfluidic chip

We demonstrate low threshold acceptor lasing consequent to the efficient coupling and radiative energy transfer between the donor and acceptor droplets in a dynamic array of coupled droplets named twin droplets, made using a microfluidic chip. The ability of the microdroplet to focus the incoming plane wave internally along the principle diameter, by virtue of its spherical interface and higher refractive index than the background medium, is recognized as the prime cause of observed acceptor lasing in the coupled droplet system. This is confirmed by observing only acceptor fluorescence when the refractive index of the donor droplet falls below that of the background. By flipping the position of the acceptor in the twin droplets, we further show that the threshold of the acceptor lasing is dependent on the acceptor position and, hence, the coupling direction. Using the emission polarization measurements from the twin droplets, we also show that the acceptor emission is highly polarized and follows the pump laser polarization.