Spherical Cavity Research Articles

Excitation of Electromagnetic Field Inside Rotating Spherical Cavity

Excitation of Electromagnetic Field Inside Rotating Spherical Cavity

Millimeter-wave dielectric characterization of liquids-in-flow using spherical cavity resonator

Millimeter-wave dielectric characterization of liquids-in-flow using spherical cavity resonator

Effects of a spherical slip cavity filled with micropolar fluid on a spherical micropolar droplet

In this work, a two-fluid phase flow problem involving an axisymmetrical quasi-steady motion of a spherical micropolar droplet translating at a concentric point in a second non-mixable micropolar fluid within a spherical impermeable cavity with a slip surface is analysed under low Reynolds numbers. The two fluid phases that have a microstructure (micropolar fluid) are the case that is being focused on. The Stokes equations are solved inside and outside the droplet for the velocity fields. In addition, based on the concentric position, general solutions in terms of spherical coordinates are obtained. In this case, tangential couple stress and continuity of microrotation are used. For different cases, the normalised drag forces acting on the droplet are represented via graphs for different values of relative viscosity, droplet-to-cavity radii ratio, and the parameter that connects the tangential couple stress with microrotation. The normalised drag force is found to be a monotonically increasing function of the drop-to-cavity radii ratio. It is found that when the droplet-to-cavity radii ratio approaches zero, there is a very strong interaction between the droplet and the cavity. When comparing a solid sphere to a gas bubble, the normalised drag force is larger. Additionally, the results showed that permitting spin and slip at the cavity’s interior surface improved the wall correction factor influencing the droplet. The present study is important in the fields of natural, industrial, and biomedical processes such as raindrop formation, liquid–liquid extraction, suspension rheology, sedimentation, coagulation, and the motion of blood cells in an artery or vein.

Survival probabilities and first-passage distributions of self-propelled particles in spherical cavities.

A model of self-propelled motion in a closed compartment containing simple or complex fluids is formulated in this paper in terms of the dynamics of a point particle moving in a spherical cavity under the action of random thermal forces and exponentially correlated noise. The particle's time evolution is governed by a generalized Langevin equation (GLE) in which the memory function, connected to the thermal forces by a fluctuation-dissipation relation, is described by Jeffrey's model of viscoelasticity (which reduces to a model of ordinary viscous dynamics in a suitable limit). The GLE is transformed exactly to a Fokker-Planck equation that in spherical polar coordinates is in turn found to admit of an exact solution for the particle's probability density function under absorbing boundary conditions at the surface of the sphere. The solution is used to derive an expression (that is also exact) for the survival probability of the particle in the sphere, starting from its center, which is then used to calculate the distribution of the particle's first-passage times to the boundary. The behavior of these quantities is investigated as a function of the Péclet number and the persistence time of the athermal forces, providing insight into the effects of nonequilibrium fluctuations on confined particle motion in three dimensions.

Analysis of high-speed water entry in semi-sealed cylindrical shells: Cavity formation and self-disturbance characteristics

The high-speed water entry of a semi-sealed cylindrical shell is a complex unsteady process involving the multiphase flow. In order to study the influence of special structure of the semi-sealed cylindrical shell, the fluid-structure interaction method based on Star-CCM+ and ABAQUS is adopted. The results show that semi-sealed cylindrical shells with different structures all form nested cavities, among which the shell with a shorter length forms a nearly spherical cavity, while the shell with a smaller diameter forms a cavity that is close to a long strip shape. When the Mach number of the initial impact velocity is lower than 0.16, the top wall of the shell can be completely restored as the jet leaves the top wall. The von Mises stress at the top wall of the shell is higher than that at the side wall position. The deformation at the top of shells with larger diameter, shorter length, and smaller thickness is greater. The high-speed vertical water entry process of the semi-sealed cylindrical shell exhibits unique self disturbance characteristics, indicating that shells with thicker thickness and a longer length will exhibit obvious deflection after the self-jet phenomenon occurs.

Studying the influence of a gyrostatic moment on the motion of a charged rigid body containing a viscous incompressible liquid

The rotational motion of a charged rigid body (RB) is examined. The RB has a spherical cavity that contains an incompressible viscous liquid. The influence of a gyrostatic moment (GM), constant torques at the body-connected axes, and the action of the torque of a resistant force, due to the shape of the liquid, are considered. Assuming the liquid has a sufficiently high velocity, the Reynolds number does indeed have a small value. The regulating system of motion is derived in an appropriate formulation through Euler's equations of motion. The averaging method is used to approach a suitable form of the motion's governing system. In addition to using Taylor’s method to reach a solution for the averaged equations of motion of the RB, some initial conditions are considered to approach the required results. The asymptotic approach of the averaged system besides the numerical analysis enables us to obtain the appropriate results of the problem. To draw attention to the beneficial effects of the different values of the body’s parameter on the motion's behavior, these results are graphed through a computer program along with the associated phase plane curves. These diagrams illustrate the influence of several values respected to the GM, charge, body-constant torques, and resistive force torque. The stability of the RB's motion has also been discussed through the represented phase plane diagrams. These results are viewed as a generalization of prior ones, which have been reported for the scenario of an uncharged body or the absence case of the GM. The significance of the obtained results is due to its numerous real-world applications in life, such as for spaceships and wagons carrying liquid fuel.

Analysis of the Stress–Strain State of the Elastic Moment Medium When a Spherical Cavity Diffracts the Wave

Analysis of the Stress–Strain State of the Elastic Moment Medium When a Spherical Cavity Diffracts the Wave

The Influence of Cavity Size and Location Within Insulation Paper on the Partial Discharge Activities

This paper examines the influence of cavity size and location in the insulation paper on the Partial Discharge (PD) activities through Finite Element Method (FEM). The model consisted of a conductor wrapped with insulation paper. Two different locations of the spherical cavities were introduced in this study, namely Location 1 (L1) and Location 2 (L2), located at the center and left corner of the insulation paper. The model introduced two different sizes of cavities with diameters of 0.5 mm and 0.8 mm. An AC voltage source of 17 kV, 50 Hz, was applied at the conductor while the bottom of the insulation paper was grounded. The real and apparent PDs were obtained by integrating the current flowing through the cavity and ground electrode with the respective surface area. The simulation was carried out for 100 cycles. The resultant model was used to study the PD occurrence, magnitude, and Phase Resolved Partial Discharge (PRPD) within the insulation paper. It is found that the large cavity size produces a lower number of PD occurrences per cycle than the small cavity size. The large cavity size produces a higher charge magnitude as compared with the small cavity size. The PD occurrence per cycle and charge magnitude are higher for the cavity location at L1 compared to L2. The PRPD yields the same pattern for cavity location at L1 and L2, whereby the differences are only on the charge magnitude and PD occurrence per cycle.

Static and Seismic Response of Deep Spherical Cavities

Static and Seismic Response of Deep Spherical Cavities

Resonance nesting and mode degeneracy of bilayer spherical dielectric cavities within zero-index materials

Resonance nesting and mode degeneracy of bilayer spherical dielectric cavities within zero-index materials

Effects of a spherical slip cavity filled with micropolar fluid on a spherical viscous droplet

An analytical study for the quasisteady flow caused by a spherical viscous fluid droplet translating at a concentric position in a second immiscible micropolar fluid within a spherical cavity with a slip surface is presented. Attention is focused on the case when one of the two fluid phases has a microstructure nature (micropolar fluid). The droplet translates along a diameter connecting their centres under the conditions of low Reynolds numbers. To solve the Stokes equations for the velocity fields inside and outside the droplet, general solutions are obtained in terms of spherical coordinates based on the concentric position. For the case of the viscous droplet within a micropolar fluid, a boundary condition related to vorticity with microrotation is used. The wall correction factors acted on the viscous droplet for the different cases are represented through graphs for various values of relative viscosity, radii ratio of droplet and cavity, and the parameter that connects the vorticity with microrotation. The wall-corrected drag force is found to be a monotonically increasing function of the ratio of drop-to-cavity radii. The present work is important because of its applications in various natural, industrial, and biological processes, such as raindrop formation, the study of blood flow, liquid–liquid extraction, the prediction of atmospheric conditions, sedimentation phenomena, and the rheology of emulsions.

The Dynamics of Small Satellites with the Three-Axial Gravitational Damper

The questions of the dynamics of the angular motion of nanosatellites with gravitational dampers are considered. The damper is a solid body rotating in a spherical cavity with a viscous liquid filling and creating internal friction with the dissipation of the kinetic energy of the angular motion. Unlike classical models of similar viscous dampers using the M.A. Lavrentiev with spherical dynamic symmetry of the body-damper, in this work the body-damper has a central triaxial ellipsoid of inertia, which increases the efficiency of interaction with an external gravitational field. This makes it possible to use almost any autonomous nanosatellite assembly as such an internal body-damper, placing it in a sealed spherical shell inside a spherical cavity with a viscous liquid in the center of mass of the main body-satellite body. The presence of a three-axis inertia tensor of the damper body changes and complicates the mathematical model of the angular motion in comparison with the classical one, which can be considered as a certain generalization and development of research in this direction.

Compression and Ordering of Hollow Microgels in Monolayers Formed at Liquid-Liquid Interfaces.

Monolayers of polymer microgels with a spherical cavity adsorbed at the liquid-liquid interface were studied using mesoscopic computer simulations. One liquid, named water, was always considered as a good solvent, while the microgel solubility in the second liquid, named oil, was varied. The symmetric and asymmetric cases of vanishing and the strong differences in solubility between the network particles and the liquids were considered. The simulations provided us with an insight into the shape and volume changes of the microgels upon compression, making it possible to relate the response of the individual network with the collective order and structure of the monolayer. Similar to regular microgels, the compression of the monolayer of hollow particles led to a decrease in lateral sizes accompanied by shape transformation from a flattened to a nearly spherical shape. However, the presence of a cavity filled with solvent caused some unique differences in the behavior of the system. The adsorption pathway of hollow microgels at the liquid interface predefines: (a) the position of the particles with respect to the interface and (b) the structure of the monolayer. A striking discovery is that in the symmetric case of similar solubility of the microgel in both liquids, it is possible to produce a monolayer in which one part of the network faces the aqueous phase and the other part faces the oil phase. The polymer concentration profiles plotted along the normal to the interface reveal a redistribution of polymeric mass of the microgels relative to the interface, distinguishing between the microgels whose cavities are filled with water and oil, respectively. Moreover, the ratio between the microgels faced in water and oil does not change upon compression and predetermines the response and order of the monolayer.

The impurity effect on the capacitance of ionic liquid-based supercapacitors: A classical density functional theory study of ionic liquids inside the spherical cavity of the porous electrode

The effect of impurities on the capacitance curve has been investigated for ionic liquid-based supercapacitors. The coarse-grained model in the framework of classical density functional theory (CDFT) was used to predict the electric double layer (EDL) formed at the concave wall of the spherical cavity of a porous electrode. Our results demonstrate that the adsorption and desorption of impurities by the cavity have a significant impact on the shape of the capacitance curve. In some cases, a bell-camel shape transition in the capacitance curve occurs due to the adsorption of impurities. By increasing the impurity concentration and its attraction with the cavity, the position of the observed maximums in the camel shape of the capacitance curves shifts toward a higher electrode potential. In addition, we have shown that impurity adsorption affects the value of the zeta potential by reducing the total net ion charges stored inside the cavity. Increasing the electrode potential to a specific value causes the total desorption of impurities; hereinafter, we call that the potential of zero impurity adsorption, ΨZIA. The amount of this potential depends on the concentration of impurities, cavity size, impurity-cavity attraction, and the shape of ions in ionic liquids. As we expected, the impurity has no effect on the amount of capacitance for electrode potentials higher than ΨZIA. Finally, the differential capacitance curves for symmetric impure ionic liquid in spherical cavities have been compared to those for slit pores. Results show the same behavior for both of them, but the effect of impurity can be ignored at lower electrode potential in the case of spherical cavities due to the more confinement effect.

Loading-unloading of spherical and cylindrical cavities in cohesive-frictional materials with arbitrary radially symmetric boundary conditions

Many scenarios in geotechnical engineering involve cavity unloading from a loaded state under different boundary conditions, especially for thick-walled cylinder tests in laboratory conditions. A novel analytical cavity expansion-contraction solution is proposed for modeling thick-walled cylinder tests during a complete loading-unloading process under arbitrary symmetric boundary conditions. The proposed solution has potential implication in investigating ambiguous boundary effects for problems involving cavity expansion-contraction. The mechanical model considers two concentric layers of materials around the cavity, where the inner layer is considered as cohesive-frictional and the circumambient infinite layer is assumed as elastic to simulate the arbitrary radially symmetric boundary condition, including two extreme scenarios with constant-pressure and zero-displacement boundaries. The derived solution provides the evolutions of cavity pressure and distributions of stresses and displacements in both layers during the loading-unloading process, which is then rigorously validated against finite element results. The effects of boundary conditions and size of the cohesive-frictional layer have been comprehensively investigated by analyzing the cavity pressure and the developments of plastic zones during expansion and contraction. The developed solution has been proved to be applicable in geotechnical engineering, with comparisons between analytical results and experimental data for pressuremeter tests in calibration chambers and pile installation tests in a rigid container. The proposed solution might also be helpful in the analysis of autofrettaged pressure vessels.

LOCAL MODEL OF THE THERMOELASTIC STATE OF A POROUS MATERIAL

In the paper, a local stationary model of the thermoelastic state of a porous material is constructed. The model is based on uncoupled boundary value problems for stationary equations of heat conduction and thermoelasticity for a space with two spherical cavities. The temperature field is determined by the constant temperature on the surfaces of the cavities, which are considered free of forces. The problem was solved by the generalized Fourier method (GFM), for which the paper presents its further development for a certain class of thermoelasticity problems. For this purpose, systems of equally directed spherical coordinates were introduced, the origins of which are connected with the centers of the cavities. In the work, a new set of axisymmetric basic solutions of the Lamé equation for a sphere is constructed and addition theorems are proved for it and for solutions of the vector biharmonic equation in the given coordinate systems. The GFM formalism made it possible to reduce the boundary value problems to algebraic solvable systems with Fredholm operators in the space l2 under the condition that the spherical surfaces do not intersect. The reduction method was used for the numerical solution of the systems. Graphs of stresses on the surface of one of the cavities and stresses on the axis of symmetry of the problem between the cavities at different relative sizes of the cavities and at different temperatures of their heating were obtained. The obtained results agree with those known for one cavity. The convergence of the reduction method is verified numerically.

Slow hydrogel matrix degradation enhances salivary gland mimetic phenotype.

We recently developed a salivary gland tissue mimetic (SGm), comprised of salivary gland cells encapsulated in matrix metalloproteinase (MMP)-degradable poly(ethylene glycol) hydrogels within arrays of ∼320 µm diameter spherical cavities molded in PDMS. The SGm provides a functional and physiologically relevant platform well-suited to high-throughput drug screening for radioprotective compounds. However, the utility of the SGm would benefit from improved retention of acinar cell phenotype and function. We hypothesized that tuning biochemical cues presented within the PEG hydrogel matrix would improve maintenance of acinar cell phenotype and function by mimicking the natural extracellular matrix microenvironment of the intact gland. Hydrogels formed using slower-degrading MMP-sensitive peptide crosslinkers showed >2-fold increase in sphere number formed at 48 h, increased expression of acinar cell markers, and more robust response to calcium stimulation by the secretory agonist, carbachol, with reduced SGm tissue cluster disruption and outgrowth during prolonged culture. The incorporation of adhesive peptides containing RGD or IKVAV improved calcium flux response to secretory agonists at 14 days of culture. Tuning the hydrogel matrix improved cell aggregation, and promoted acinar cell phenotype, and stability of the SGm over 14 days of culture. Furthermore, combining this matrix with optimized media conditions synergistically prolonged the retention of the acinar cell phenotype in SGm. STATEMENT OF SIGNIFICANCE: Salivary gland (SG) dysfunction occurs due to off-target radiation due to head and neck cancer treatments. Progress in understanding gland dysfunction and developing therapeutic strategies for the SG are hampered by the lack of in vitro models, as salivary gland cells rapidly lose critical secretory function within 24 hours in vitro. Herein, we identify properties of poly(ethylene glycol) hydrogel matrices that enhance the secretory phenotype of SG tissue mimetics within the previously-described SG-microbubble tissue chip environment. Combining slow-degrading hydrogels with media conditions optimized for secretory marker expression further enhanced functional secretory response and secretory marker expression.

Surfaces with modified morphology and wettability arrangement: a potential medium for water harvesting in desertification areas

Abstract The cost of water transport for irrigating drought-endurable plants in desertification areas makes it important to develop other water sources. Research shows that freshwater produced by dewing could satisfy the water requirement during germination of desert plants, therefore, functional materials that promote dew formation provide solutions for reduction of plant irrigation costs in desertification regions. In this review, feasibility of utilizing trace irrigation for ensuring survival of desert plants has been demonstrated. The technologies of preparing water harvesting materials with modified microstructure and wettability arrangement have been introduced, it has been shown that surface embedded with a bump array which has counter wettability compared with its plane section is a common morphology adopted by current works. After comparing climates in desertification regions with those in dewing chambers, it has been found that currently, the expected values of dew productivities of most water harvesting materials in deserted areas will not be as efficient as they performed in experiments due to low relative humidity. However, hydrophobic surface with submicron scale hydrophilic spherical cavity array produced by nanosphere lithography has shown reliable prospects in reducing the energy barrier of heterogeneous nucleation and thus become a more potential medium in dew water production.

Elasto-thermodiffusive nonlocal responses for a spherical cavity due to memory effect

Elasto-thermodiffusive nonlocal responses for a spherical cavity due to memory effect

Stability of a two-electron system under pressure confinement: structural and quantum information theoretical analysis

The stability of a two-electron Zee system trapped inside an impenetrable spherical cavity is analyzed using an explicitly correlated multi-exponent Hylleraas-type basis set in the framework of the Ritz variational method. The wave function is considered to be consistent with Dirichlet’s boundary condition. Four different values are considered, where denotes the critical nuclear charge beyond which the system is embedded in a discrete positive energy continuum due to the impenetrable nature of the cavity. The energy contribution due to the total correlation (in the presence of both radial and angular correlation) effect, the radial correlation limit, and the angular correlation limit are also studied in detail. The thermodynamic pressure felt by the two-electron Zee system inside the cavity is estimated, and a formula replicating the behavior between the pressure and volume of the cavity is deduced by a fitting procedure. Different geometrical properties, e.g. radial moments (, , , , ; p = ), angular moments (, ), and related important physical quantities, are determined. The variation of Kirkwood and Buckingham polarizabilities w.r.t. the pressure felt by the two-electron Zee system is analyzed. A one-electron radial density is estimated for each pair of (), which has been employed to generate the electrostatic potential as well as different information theoretical measures like Shannon entropy, Fisher entropy, Rényi entropy, Tsallis entropy, and Onicescu informational energy. The chosen information theoretical measures have been found to be sensitive tools for describing changes in the electronic structure due to spatial confinement. An interesting interplay between the electronic and nuclear contribution to the classical electrostatic potential is observed, leading to a shift in the position of its characteristic minimum due to compression. Wherever possible, a comparison is made in order to ascertain the high accuracy of our numerical results. The procedure of analytic evaluation of the integrals needed to estimate the atomic properties under consideration is discussed in detail.