Spherical Container Research Articles

Stability of spherically confined free boundary drops with line tension

We study the geometry of a stable drop of incompressible liquid constrained to lie in a spherical container. The energy functional is comprised of the surface tension, the wetting energy and the line tension. It is shown that the only stable equilibrium drops having the topology of a disc are flat discs and spherical caps. Sharp conditions for the stability of equilibrium spherical caps and flat discs are given.

Magnetohydrodynamic creeping flow around a weakly permeable spherical particle in cell models

The present paper studies the impact of applied uniform transverse magnetic field on the flow of incompressible conducting fluid around a weakly permeable spherical particle bounded by a spherical container. Analytical solution of the problem is obtained using Happel and Kuwabara cell models. The concerned flow is parted in two regions, bounded fluid region and internal porous region, to be governed by Stokes and Darcy’s law respectively. At the interface between the fluid and the permeable region, the boundary conditions used are continuity of normal component of velocity, Saffman’s boundary condition and continuity of pressure. For the cell surface, Happel and Kuwabara models together with continuity in radial component of the velocity has been used. Expressions for drag force, hydrodynamic permeability and Kozeny constant acting on the spherical particle under magnetic effect are presented. Representation of hydrodynamic permeability for varying permeability parameters, particle volume fraction, slip parameter and Hartmann numbers are represented graphically. Also, the magnitude of Kozeny constant for weakly permeable and semipermeable sphere under a magnetic effect has been presented. In limiting cases many important results are obtained.

ОСАЖДЕНИЕ БИДИСПЕРСНОГО КЛАСТЕРА ТВЕРДЫХ СФЕРИЧЕСКИХ ЧАСТИЦ

A new method for the experimental study of gravitational sedimentation of a polydisperse cluster of solid spherical particles in a viscous fluid is presented. The method is based on the preliminary ultrasonic mixing of the particles in a spherical container and assumes the introduction of a spherical cluster of particles at a given concentration and zero initial velocity into a fluid. This method is used to determine sedimentation characteristics of a bidisperse cluster of particles (steel balls, 2 and 3 mm in diameter) in silicone oil. A qualitative pattern of the cluster evolution, a sedimentation rate, and a drag coefficient are obtained. A comparative analysis of sedimentation characteristics of monodisperse and bidisperse particle clusters is carried out in the range of Reynolds numbers Re = (0.30÷0.66)·10−3. It is shown that, in contrast to a monodisperse cluster of particles, the drag coefficient of the bidisperse cluster of particles does not correspond to a correlation CD = 24/Rec for the Stokes sedimentation.

Study of heat sink effects during melting of constrained phase change material inside a spherical enclosure

Abstract This paper presents an analytical investigation to study the heat sink effects during melting of phase change material (PCM) encapsulated in spherical container. The heat sink is treated as a negative uniform volumetric heat generation term in the energy equation. The performed exact solution can be used as a reference to validate the numerical simulations and other approximate methods related to thermal energy storage within PCM in spherical capsules. The mathematical model is based on pure conduction in the PCM, subjected to a convection heat transfer at the external surface of spherical shell. The complimentary error function and variables separation method have been used to resolve energy equation in both solid and liquid phases in transient regime. The heat transfer within the PCM was analytically modelled during melting process. The natural convection inside PCM liquid phase was considered via the liquid fraction dependency of the effective thermal conductivity. The results predicted by the current model have been compared with those previously published in the literature, and a good agreement is showed. Then, a parametric study for different Rayleigh number, Biot number, Stefan number and heat dissipation power is conducted. The results show that the complete melting of PCM will not be achieved if the heat sink power exceeds certain limit value, which is strongly depending on Rayleigh and Biot numbers.

Spring Model - Chromatin Modeling Tool Based on OpenMM.

Chromatin structure modeling is a rapidly developing field. Parallel to the enormous growth of available experimental data, there is a growing need of building and visualizing 3D structures of nuclei, chromosomes, chromatin domains, and single loops associated with particular gene loci. Here, we present a tool for chromatin domain modeling; it is available as a webservice and standalone python script. Our tool is based on molecular mechanics and utilizes the OpenMM engine for model generation. In this method the user provides contacts between chromatin regions and obtains a 3D structure that satisfies them. Additional parameters allow for the control of fibre stiffness, initial structure adjustments and simulation resolution, there are also options for structure refinement and modeling in a spherical container. The user may provide contacts in the form of bead indices, or insert interactions in genome coordinates sourced from BEDPE files. After the simulation is complete, the user is able to download the structure in the Protein Data Bank (PDB) format for further analysis. We dedicate this tool to all who are interested in chromatin structures. It is suitable for quick visualization of datasets, studying the impact of structural variants (SVs), inspecting the effects of adding and removing particular contacts, and measuring features such as maximum distances between sites (e.g.promoter-enhancer), or local chromatin density.

Melting and solidification of PCMs inside a spherical capsule: A critical review

Abstract To date, numerous phase change materials (PCM) have been developed for application in latent heat storage systems. There are many issues in the process from the development of PCM to using them in storage systems, which should be resolved. The problem of heat transfer in PCMs during the phase change process is the most important one. Latent heat storage containers usually have simple geometrical forms such as a sphere, cylinder, cylindrical annulus, rectangular enclosure, etc. A large number of papers were published on melting and solidification processes in PCMs. Therefore, there is a pressing necessity for generalizing the art of the state in this field and establish how accumulated knowledge meets practical requirements. The present review considers the current state in investigations of heat transfer in a spherical shell. Heat transfer in PCMs during constrained melting (solid PCM fixed inside the vessel), unconstrained (unfixed) melting and solidification, and phase change in finned shells are analyzed. It is shown that currently, there is no satisfactory description of the constrained melting process. For unconstrained melting and solidification, some correlations are suggested, describing these processes. The applicability range of the proposed correlations, as well as their accuracy were investigated and established. To intensify the process of phase change inside the spherical container, the use of orthogonal fins is appropriate option compared to the employ of circumferential fins.

Capillary wave turbulence experiments in microgravity

Using the FLUIDICS (Fluid Dynamics in Space) experiment in the International Space Station, turbulence of capillary waves at the air-water interface is experimentally investigated in weightlessness. Capillary waves are excited in a spherical container partially filled with water and undergoing sinusoidal or random oscillations. The fluctuations of the interface, recorded with two capacitive probes are analyzed by means of the frequency power spectrum of wave elevation. For high enough forcing amplitudes, we report power-law spectra with exponents close to the prediction of weak wave turbulence theory. However, in this experiment the free-surface steepness is not small compared to 1 and thus the investigated regimes correspond to strongly nonlinear wave turbulence.

New Simulator for Neuroendoscopy: A Realistic and Attainable Model

To present an attainable and realistic model for neuroendoscopic simulation which replicates exercises of tissue biopsy and coagulation and membrane fenestration. We presented a stepwise method to create a neuroendoscopic simulation model using bovine brain and membrane units made by a soda cup covered by an amniotic membrane inside an expanded polystyrene spherical container. We used face validation for preliminary evaluation. We also rated the students before and after training with the NEVAT global rating scale (GRS) and recorded the time required to complete all 3 procedures (third ventriculostomy, tissue biopsy, and coagulation). The total cost of the model was $5. The experts consider this new model as capable of reproducing real surgical situations with great similarity to the human brain. We tested the model in 20 trainees. The median GRS score before the training was 9 (range, 7-12). After repeated training and performance feedback, the final median GRS score was 41 (range, 37.5-45; P < 0.0001). The time needed to finish the exercises before training was 33 minutes (range, 30.5-42.5 minutes), and after using the model the final median time was 20 minutes (range, 17.5-22 minutes; P<0.0001). Simulators for neuroendoscopy described so far are reliable, but they entail a high cost. Models with live animals, although of lower cost, are questioned from an ethical point of view. In the current work, we describe a high fidelity ventricular neuroendoscopic simulator model that, because of its low cost, can be replicated in any training center that has a neuroendoscope.

Electro-optic sensor for static fields

A sensor has been developed for low frequency and DC electric fields E. The device is capable of measuring fields with varDelta mathrm{E}= 4 (1) V/cm resolution. It is based on a Y-cut Z-propagation lithium niobate electro-optic crystal. For a particular commercially available bare crystal, we achieved an in air time constant tau _mathrm{c}(mathrm air)= 6.4(1.8) h for the decay of the electro-optic signal. This enables field monitoring for several hours. As an application, we demonstrated that a constant electric field E^{mathrm{ext}} = 640 V/cm applied via external electrodes to a particular spherical glass container holding an Xe/He gas mixture decays inside this cell with a time constant tau _{E}^{mathrm{glass}} = 2.5(5) h. This is sufficient for the needs of experiments searching for a permanent electric dipole moment in ^{129}Xe. An integrated electric field sensor has been constructed which is coupled to a light source and light detectors via optical fibers. The sensor head does not contain any electrically conducting material.

Spontaneous Domain Formation in Spherically Confined Elastic Filaments.

Although the free energy of a genome packing into a virus is dominated by DNA-DNA interactions, ordering of the DNA inside the capsid is elasticity driven, suggesting general solutions with DNA organized into spool-like domains. Using analytical calculations and computer simulations of a long elastic filament confined to a spherical container, we show that the ground state is not a single spool as assumed hitherto, but an ordering mosaic of multiple homogeneously ordered domains. At low densities, we observe concentric spools, while at higher densities, other morphologies emerge, which resemble topological links. We discuss our results in the context of metallic wires, viral DNA, and flexible polymers.

Liquid–liquid core–shell configurable mesoscale spherical acoustic lens with subwavelength focusing

In this work, we present a lens based on a thin hollow ABS spherical container structure, which can be filled up with different compatible liquids. The acoustic jet can be dynamically shaped by either shifting the operating frequency or modifying the geometry of the lens. We show for the first time that a spherical Ethanol ABS core–shell acoustical lens immersed in water with low diameter-to-wavelength ratio equal to 6.67 and refraction index of 1.24 achieves a focusing spot narrower than 0.85λ. Experimental measurements validate simulation results and demonstrate the viability of these configurable spherical lenses in underwater acoustic focusing applications.

An image processing algorithm to estimate the melt fraction and energy storage of a PCM enclosed in a spherical capsule

The experimental investigation of the melting behavior of a phase change material (PCM) inside a spherical container is reported. PCM considered for the study is lauric acid whose melting point is about 43°C. Unconstrained melting experiments are carried out at two different temperatures, ie, at 60°C and 80°C. The initial temperature of the PCM is taken as 30°C. To carry out a detailed analysis of the heat transfer, the transient variations in the melt fraction and amount of energy stored are derived. In order to estimate the liquid/solid volumes, a novel image processing technique is developed. In this approach, a circle-fitting algorithm is employed to obtain the amount of PCM melted inside a spherical container. The total instantaneous amount of heat transport to the PCM is measured with an uncertainty of about 6.1%. The results obtained by the introduced circle-fitting algorithm have been compared qualitatively and quantitatively with the solid modeling method. The present technique could capture the asymmetric behavior of the solid PCM. The experimental findings show that the rate of melt fraction is high at the beginning of the experiment due to a larger area of contact between the spherical container and solid PCM. Further, parametric analysis has been performed and reported in terms of Fourier, Stefan, and Grashof numbers.

Shape and Size Control of Artificial Cells for Bottom-Up Biology.

Bottom-up biology is an expanding research field that aims to understand the mechanisms underlying biological processes via in vitro assembly of their essential components in synthetic cells. As encapsulation and controlled manipulation of these elements is a crucial step in the recreation of such cell-like objects, microfluidics is increasingly used for the production of minimal artificial containers such as single-emulsion droplets, double-emulsion droplets, and liposomes. Despite the importance of cell morphology on cellular dynamics, current synthetic-cell studies mainly use spherical containers, and methods to actively shape manipulate these have been lacking. In this paper, we describe a microfluidic platform to deform the shape of artificial cells into a variety of shapes (rods and discs) with adjustable cell-like dimensions below 5 μm, thereby mimicking realistic cell morphologies. To illustrate the potential of our method, we reconstitute three biologically relevant protein systems (FtsZ, microtubules, collagen) inside rod-shaped containers and study the arrangement of the protein networks inside these synthetic containers with physiologically relevant morphologies resembling those found in living cells.

A visualization study on the unconstrained melting of paraffin in spherical container

A visualization experiment is carried out to investigate the void-affected unconstrained melting process in a spherical container. Factors including the diameter of spherical container (20.05–70.30 mm), filling ratio of PCM (0.8–0.98), heating temperature (32–47 °C) and initial temperature (7–22 °C) are studied. Melting behaviors concerning the evolution of solid-liquid interface and the motion of solid PCM are revealed, from which a new unconstrained melting mode (i.e., floating melting which occurs before the close-contact melting) is observed due to the existence of void in solid PCM. In addition, the quantitative results of floating melting time, total melting time and liquid fraction are obtained. The results show that as the melting mode changes from floating melting to close-contact melting, the melting rate is slightly enhanced. With the increase of spherical container diameter, the floating melting time increases first and then decreases, while the total melting time has a continually increasing trend. The higher heating temperature and higher initial temperature will decrease the floating melting time and total melting time. As the filling ratio of PCM increases, the floating melting time and the total melting time increase at first and then decrease. Finally, the correlations of dimensionless total melting time and liquid fraction are proposed.

Extended uncertainty principle and thermodynamics

In this paper, we discuss the EUP and thermodynamics. Using three-dimensional extension of the EUP, we find the EUP-corrected Poisson bracket and use it to compute the number of microstates. We use it to discuss some physical models such as monatomic gas in a spherical container, monatomic gas in a cylindrical container, and interacting gas in a spherical container.

MOTION OF A POROUS SPHERICAL SHELL IN A SPHERICAL CONTAINER

In this paper slow motion of a porous spherical shell with radially varying permeability in a spherical container at the instant it passes through the center of the spherical container is discussed. The container is filled by a viscous incompressible fluid. Flow outside the porous spherical shell is governed by the Stokes equation and inside the spherical shell by the Brinkman equation. The boundary conditions used at the surface of the porous spherical shell are the continuity of velocity and stress and the no-slip condition is used on qn impermeable sphere. Exact solution of the problem is obtained and relevant quantities such as stream lines, velocity, pressure, wall correction factor, and drag on surface of the spherical shell are obtained. The influence of the permeability parameter on the flow has been discussed and exhibited graphically. We found that decrease in permeability of the porous shell caused increase in drag and wall correction factor. In the limit case obtained results reduce to the well known classical results.

Drift Behavior of a Spherical Container Containing Liquid

Drift Behavior of a Spherical Container Containing Liquid

Improved method for implementing contact angle condition in simulation of liquid sloshing under microgravity

SummaryThe finite element simulation of liquid sloshing under microgravity is focused on in this paper. For this class of flows, an important issue is to implement the contact angle boundary condition appropriately. A novel method of adding infinitely small free‐surface mesh just adjacent to the contact line is proposed here, which coincides with the physical definition of the contact angle. This free‐surface mesh has its orientation determined according to the contact angle, and the mean curvature at the contact line can be computed using this orientation. Hence, surface tension force can be computed and incorporated as an essential boundary condition into the pressure solve. This method is convenient to be applied in three‐dimensional simulations, and the use of relatively coarse meshes near the contact line is allowed. In order to validate the proposed method, several numerical simulations of flows in two‐dimensional circular and three‐dimensional cylindrical and spherical containers are presented, including calculation of equilibrium positions of the free surfaces, unsteady flows of liquid reorientation, and large‐amplitude nonlinear liquid sloshing under lateral excitation in microgravity. Parts of the numerical results are compared with the theoretical and published experimental results.

Quasi-static gas pressure generated by explosive charge blasting in a spherical explosion containment vessel

Quasi-static pressure is important for the design of explosion containment vessels. Experiments of the spherical vessel under blast loading, in which the quasi-static pressure was measured by the pressure sensors of two different installations, i.e. flush installation and guide-hole installation, were carried out. The data obtained by the pressure sensors are consistent with each other. Based on the formula form derived theoretically, the empirical formula was obtained by fitting the data. The main results are as follows:(1) the pressure in the vessel goes into quasi-static state after the blast wave reflects back and forth three times in the vessel; (2) the quasi-static pressure in the spherical vessel is proportional to the explosion equivalent-to-vessel volume ratio, and the empirical coefficient is 1.10 MPa·m3/kg TNT.

Pipeline pneumatic conveyor with using the container's kinetic energy

The implementation of the complex pipeline pneumatic conveyor becomes possible when employing the spherical containers (capsules) which enable the using of the downward rolling to decrease the energy consumption. On the vertical sections along the track it is viable to chute containers by gravity. The mathematical formulation for the spherical container's downward rolling and its moving down by gravity is given in the article.