Cylindrical Interfaces Research Articles

Effect of a uniform magnetic field on the nonlinear instability of double cylindrical interfaces concerning three magnetic liquids

The present manuscript relates to the movement of three immersed viscous magnetic liquids in porous media that are positioned between three concentric cylindrical interfaces. Every cylindrical layer has an axial extension that extends in both vertical directions to infinity. Moreover, the pressure gradients are the driving force behind the uniform motion of all fluids in a similar upward motion at varying velocities. Permanent magnetic fields are tangentially oriented exert stress on the system. The computations are rendered simpler by applying the viscous potential theory. The Maxwell equations are utilized for the magnetic field, while the Brinkman-Darcy equations define the fluid mobility. Moreover, the rise of the disturbance and the subsequent extraction of fuel from the tiny cracks of the reservoir stone can be managed through the implementation of engineering techniques such as electromagnetic field impacts and oil extraction engineering. Typically, the nonlinear strategy involves incorporating the applicable nonlinear boundary conditions and analyzing the linearized equations of motion. This research offers a framework for verifying theoretical models and simulations based on experimental observations. The inclusion of a homogeneous magnetic field introduces complexity to the system, rendering it a suitable candidate for validating and improving models in the field Magneto hydrodynamics. The originality of the problem lies in the dual nonlinear stability of cylindrical interfaces when subjected to uniform magnetic field. Accordingly, two nonlinear characteristic differential equations controlling the surface displacements are produced. The nonlinear stability prerequisite is met by applying the matrix concept and the multiple scale technique in conjunction with a theoretical analysis of stability. Additionally, the Routh-Hrutwitz criterion is encompassed to judge the stability cofiguration. A detailed examination of the associated nonlinear stability requirements is showed. Meanwhile, the estimated limited solutions of perturbed surfaces are achieved. For the cylindrical middle layer, it is found that the outer cylindrical interface has a more stabilizing effect than the inner one. The approximate solutions for displacements at the interface are calculated. The influence of Weber numeral of the problem on the stability profile is investigated.

Importance of the tail corrections on surface tension of curved liquid-vapor interfaces

We report molecular simulations of the liquid-vapor cylindrical interface of methane. We apply the truncated Lennard-Jones potential and specific long-range corrections for the surface tension developed especially for cylindrical interfaces. We investigate the impact of the cutoff on the radial density profile, the intrinsic and long-range correction parts to the surface tension, and Tolman length. We also study the curvature dependence of the surface tension as a function of the cutoff used. In this work we shed light that both density and Tolman length are cutoff-dependent whereas the total surface tension is slightly curvature and cutoff dependent.

Determination of the Thermoelastic States of Piecewise Inhomogeneous Thermosensitive Bodies with Cylindrical Interfaces

We suggest a method for the determination of the thermoelastic state caused by plane axisymmetric temperature fields and surface loads in layered isotropic bodies with cylindrical interfaces. The temperature and coordinate dependences of the moduli of elasticity, coefficients of linear temperature expansion, and Poisson ratios are taken into account. The method is based on the solution of the systems of integral-algebraic equations for radial displacements. In the case of a cylinder, these systems are obtained from the integral representation of the solution of the problem for the ordinary differential equation with generalized derivatives. In this case, we use the Green function of the elasticity problem for a homogeneous cylinder. In the cases of a layered space with cylindrical cavity, a continuous cylinder, and the continuous space, the corresponding systems and the remaining relations required for the determination of the thermoelastic state are obtained as a result of the limit transitions. The relations for the determination of thermal stresses in the corresponding single-layer bodies are presented. The numerical investigations are performed for a three-layer cylinder with functionally gradient layer.

Surface tension and long range corrections of cylindrical interfaces.

The calculation of the surface tension of curved interfaces has been deeply investigated from molecular simulation during this last past decade. Recently, the thermodynamic Test-Area (TA) approach has been extended to the calculation of surface tension of curved interfaces. In the case of the cylindrical vapour-liquid interfaces of water and Lennard-Jones fluids, it was shown that the surface tension was independent of the curvature of the interface. In addition, the surface tension of the cylindrical interface is higher than that of the planar interface. Molecular simulations of cylindrical interfaces have been so far performed (i) by using a shifted potential, (ii) by means of large cutoff without periodic boundary conditions, or (iii) by ignoring the long range corrections to the surface tension due to the difficulty to estimate them. Indeed, unlike the planar interfaces there are no available operational expressions to consider the tail corrections to the surface tension of cylindrical interfaces. We propose here to develop the long range corrections of the surface tension for cylindrical interfaces by using the non-exponential TA (TA2) method. We also extend the formulation of the Mecke-Winkelmann corrections initially developed for planar surfaces to cylindrical interfaces. We complete this study by the calculation of the surface tension of cylindrical surfaces of liquid tin and copper using the embedded atom model potentials.

Stability of constrained cylindrical interfaces and the torus lift of Plateau–Rayleigh

Surface tension acting at a cylindrical interface holds an underlying liquid in motionless equilibrium. This static base state is subject to dynamic capillary instability, including Plateau–Rayleigh breakup. If the interface is partially supported by a cylindrical cup-like solid, the extent of the wetting contact can significantly influence the dynamics and the stability of the configuration. The equation for the motion of small disturbances is formulated as an eigenvalue equation on linear operators. A solution is constructed on a constrained function space using a Rayleigh–Ritz procedure. The influence of the extent-of-constraint on the dispersion relation and on modal structures is reported. In the extreme, the support reduces to a wire, aligned axially, and just touching the interface. From prior work, this constraint is known to stabilize the Plateau–Rayleigh limit by some 13%. We report the wavenumber of maximum growth and estimate the time to breakup. The constraint is then bent in-plane to add a weak secondary curvature to the now nearly cylindrical base state. This is referred to as the torus lift of the cylinder. The static stability of these toroidal equilibria, calculated using a perturbation approach, shows that the position of constraint is crucial – constraint can stabilize (outside) or destabilize (inside). The combined influence of secondary curvature and wire constraint on the Plateau–Rayleigh limit is tracked. Finally, attention is restricted to constraints that yield a lens-like cylindrical meniscus. For these lenses, the torus lift is used as apparatus along with a symmetrization procedure to prove a large-amplitude static stability result. Our study is conveniently framed by a classic paper on rivulets by Davis (J. Fluid Mech., vol. 98, 1980, p. 225).

Simulation of leaky Rayleigh wave at air–solid cylindrical interfaces by finite element method

The finite element method is used to simulate the laser-excited leaky Rayleigh wave at air–solid cylindrical interfaces. A whole arithmetic of fluid–solid interaction is presented, which includes a coupling matrix that describing the process of the interaction between fluid and solid, the Arbitrary Lagrangian–Eulerian (ALE) formulation for treating the variation of fluid domain, which results from the Rayleigh wave propagating on the cylindrical interface, etc. Typical calculation is executed and the results show that the polarity of leaky Rayleigh waveform gradually changes as it propagates on the air–solid cylindrical interface.

Thermocapillary transport of energy during water evaporation

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

Holographic interferometric visualization of the Richtmyer-Meshkov instability induced by cylindrical shock waves

Results of quantitative holographic interferometric flow visualization of cylindrical interface instability induced by converging cylindrical shock waves are reported. Experiments were conducted in an annular vertical co-axial diaphragmless shock tube, in which cylindrical soap bubbles filled with He, Ne, Air, Ar, Kr, Xe and SF_6 were co-axially placed in its test section. Pressure histories at different radii during the shock wave implosion and reflection from the center were measured. Diagnostic method base on double exposure holographic interferometry was applied for the measurement of turbulent mixing zone at the interface. The observed cylindrical interfaces were found to have a higher growth rate of turbulent mixing zone than that of the plane shock / plane interface.

Stability of Interfaces with Self‐Gravity, Relative Flow, andBField

Observations with the Hubble Space Telescope (Hester et al.) of spectacular fingers or elephant trunks of gas protruding from a large star-forming cloud in the Eagle Nebula stimulate renewed interest in the stability of interfaces between different media in molecular clouds. Instability and nonlinear growth of crenelations of interfaces can lead to mass concentrations that in turn lead to star formation. In an earlier study of the stability of interfaces, we took into account the important physical effects—the different densities and temperatures of the media, the relative motion (Kelvin-Helmholtz instability), the gravitational acceleration perpendicular to the interface (Rayleigh-Taylor instability), and self-gravity. A new self-gravitational instability of an interface was found that was independent of the wavelength of the perturbation. At short wavelengths, the perturbations are essentially distortional, but compression becomes important as the Jeans length is approached from below. The e-folding time for the instability is comparable with the free-fall collapse time for the denser fluid. In the present work, we generalize our earlier theory in two ways: by including ordered magnetic fields parallel to the interface, and by examining the stability of long cylindrical interfaces. We show that dynamically important magnetic fields in the media can quench instabilities if the fields are oriented in different directions (that is, crossed); however, for astronomically plausible geometries in which the fields are closer to being parallel, but of different strengths in the two media, instabilities are free to grow in directions normal to the fields. A cylindrical interface between an interior medium of density ρ1 and an exterior medium of density ρ2 provides a model for the long filaments of dense gas observed in some molecular clouds. We show that such an interface with ρ1 > ρ2 is stable to kink modes but unstable to sausage modes owing to self-gravity for long axial wavelengths, λz > 3.8d, where d is the diameter of the cylinder. This instability will tend to form prolate ellipsoidal density concentrations aligned with the cylinder axis.

A NOTE ON WAVE MOTIONS WITH A CYLINDRICAL FLUID INTERFACE STABILIZED BY ROTATION

Abstract The Rayleigh's capillary instability of a cylindrical fluid interface can be suppressed by the centrifugal force due to coaxial rotation when the outer fluid is heavier than the inner one. Thus, wave motions on the rotationally stabilized cylindrical interfaces can occur in natural and technological processes, notwithstanding the lack of coherent treatment in the literature. This work provides a supplementary linear analysis of various wave motions in a three-dimensional framework for two-phase inviscid fluid systems with cylindrical interfaces stabilized by rotation. Many previous results found in the literature are recast in a general from. With gravity acting perpendicularly to the rotation axis, the interface disturbance is considered as an externally forced wave motion. The condition for the stability of the gravity-induced interface displacement in a two-phase rotating system is found to be exactly the same as that for the one-phase case such as an air column in a rotating liquid.

Ultrasonic Propagation at Cylindrical Metal-Ceramic Interfaces in Composites

AbstractThe nature of ultrasonic propagation at cylindrical interfaces is being explored as a potential method for inferring the modulus of the interface in metal matrix composites. In many metal matrix composite systems leaky interface waves have been found to propagate along the interface. The velocity of these waves depends sensitively upon the local moduli and provides a potential basis for measuring these quantities. The opportunity exists to exploit the leaky character of these waves for microscopic imaging at the interface.

A Method for Calculating the Absorbed Dose near Interface from 10 B(n,α) 7 Li Reaction

A simplified method is presented for calculating the absorbed dose delivered from the ${}^{10}{\rm B}(n,\alpha){}^{7}{\rm Li}$ reaction by thermal neutron in medium near the interface of a boron-containing region and a boron-free one. The method takes into account the contribution of the recoiled lithium particle to the absorbed dose and the variation of with charged particle energy. Using combined LET values derived from the of alpha particle and lithium recoil, so-called geometrical factors for calculating the absorbed dose for plane, spherical, and cylindrical interfaces are presented. The geometrical factor for the cylindrical interface is applied to estimate the absorbed dose in the cerebral vascular wall in the boron neutron-capture therapy of brain tumors in man.