Concentric Cylindrical Geometry Research Articles

Interface initiation and propagation in liquid demixing with electric fields

We investigate the dynamics of liquid-liquid phase separation confined in a charged concentric cylindrical geometry. Two main time scales characterize the non-equilibrium interface behavior: (1) the lag time t(L) for forming an interface, and (2) the relaxation time to equilibrium. We find that t(L) increases as parameters (temperature, bulk composition, and surface charge) approach the electrostatic spinodal line in the phase diagram. Close to this line, t(L) is proportional to a renormalized bulk concentration with an exponent of -1.16 ± 0.03. The relaxation of the interface to equilibrium can be divided into three phases: early, intermediate (power-law), and late (exponential). During power-law relaxation, the location of the rescaled interface is proportional to time with an exponent of -0.94 ± 0.04. Exponential relaxation occurs as a consequence of finite-size effects, and the associated time constant decreases with decreasing system size (with a power-law scaling), decreasing concentration, and increasing surface charge. The time constant also decreases with increasing (decreasing) temperature when the concentration is below (above) the critical concentration.

Investigation on magnetoacoustic signal generation with magnetic induction and its application to electrical conductivity reconstruction

A theoretical study on the magnetoacoustic signal generation with magnetic induction and its applications to electrical conductivity reconstruction is conducted. An object with a concentric cylindrical geometry is located in a static magnetic field and a pulsed magnetic field. Driven by Lorentz force generated by the static magnetic field, the magnetically induced eddy current produces acoustic vibration and the propagated sound wave is received by a transducer around the object to reconstruct the corresponding electrical conductivity distribution of the object. A theory on the magnetoacoustic waveform generation for a circular symmetric model is provided as a forward problem. The explicit formulae and quantitative algorithm for the electrical conductivity reconstruction are then presented as an inverse problem. Computer simulations were conducted to test the proposed theory and assess the performance of the inverse algorithms for a multi-layer cylindrical model. The present simulation results confirm the validity of the proposed theory and suggest the feasibility of reconstructing electrical conductivity distribution based on the proposed theory on the magnetoacoustic signal generation with magnetic induction.

Velocity slip in microscale cylindrical Couette flow: The Langmuir model

The velocity slip on the solid surfaces of microscale cylindrical Couette flow is investigated using the Langmuir adsorption model for the gas-surface molecular interaction. The accommodation coefficient in the Maxwell model, which is a free parameter based on the concept of diffusive reflection, is replaced by a physical parameter of heat adsorption in the Langmuir model. The phenomenon of velocity inversion is then clearly explained by introducing a velocity polar on the hodograph plane. It is also shown that the quantity used to determine the momentum slip in a concentric cylindrical geometry should be based upon the angular velocity, not the velocity itself. Finally, and despite their totally independent considerations of the gas-surface molecular interaction, the Maxwell and Langmuir slip models are shown to be in qualitative agreement with direct simulation Monte Carlo data in capturing the general features of the flow field.

A General Approach to Modeling Conduction and Concentration Dynamics in Excitable Cells of Concentric Cylindrical Geometry

This paper discusses mathematical approaches for modeling the propagation of the action potential and ion concentration dynamics in a general class of excitable cells and cell assemblies of concentric cylindrical geometry. Examples include myelinated and unmyelinated axons, single strands of interconnected cardiac cells and outer hair cells. A key feature in some of the cells is the presence of a small working volume such as the periaxonal space between the myelin sheath and the axon in the myelinated axon and the extracisternal space between the plasma membrane and the subsurface cisterna of the outer hair cell. Proper treatment of these cell types requires a modeling approach which can readily address these anatomical properties and the non-uniform biophysical properties of the concentric membranes and the ionic composition of the volumes between the membranes. An electrodiffusion approach is first developed in which the Nernst–Planck equation is used to characterize axial ion fluxes. It is then demonstrated that this “full” model can be stepwise reduced, eventually becoming equivalent to the standard cable equation formulation. This is done in a manner that permits direct comparisons between the full and simplified models by running simulations using a single parameter set. An intermediate approach where the contributions of the axial currents to ion concentration changes and the effect of varying ion concentrations on solution conductivities are ignored is derived and is found adequate in many cases. Two application examples are given: a “cardiac strand” model, for which the intermediate formulation is shown sufficient and a model of the myelinated axon, for which the full electrodiffusion formulation is clearly necessary. The latter finding is due to spatial inhomogeneities in the anatomy and distribution of ion channels and transporters in the myelinated axon and the restricted periaxonal space between the myelin sheath and the axon.

An experimental study of conduction heat transfer in rarefied polyatomic gases

Experimental data have been obtained for the conduction heat transfer through a rarefied polyatomic gas (benzene or n-hexane) in a concentric cylindrical geometry. The results are of direct relevance in evacuated solar collector technology. The data were fitted to within 7% over the whole transition region by a simple semi-empirical equation, previously used for monatomic gases. A Monte Carlo simulation of the system was undertaken to obtain heat conduction and temperature profiles over the transition region in benzene and n-hexane gases.

Short-pulse wave scattering from a cylindrical shell with slit-coupled coaxial interior

In a previous frequency domain study by the authors (see ibid., vol.39, p.1085-97, Aug. 1991), it was shown that the hybrid ray-mode system format introduced for scattering from cylindrical targets with aperture-coupled waveguide-like interiors continues to provide a cogent observable-based parameterization of the scattering in the time domain. Utilizing rigorous as well as phenomenological constructs, causal arrivals and physical turn-on times for well convergent resonant expansions are identified for the wavefront-dominated exterior as well as for the guided-mode-dominated interior wave processes. The validity of this parameterization of the scattered field is confirmed by interpretation of reference data generated via direct numerical Fourier inversion from the frequency domain to the time domain. Although applied so far only to concentric cylindrical geometry and single mode propagation in the interior, it is anticipated that the formalism can also accommodate nonconcentric and noncircular configurations and higher mode operating regimes.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Double injection in cylindrical germanium structures

Current-voltage characteristics and electric field distributions have been measured on large hollow-core coaxial germanium devices operating in the double-injection semiconductor regime. The I-V characteristics obey an I α V2 relationship and the magnitude of the current is predicted to within a factor of 2 by I = δqμpμnτ (p0−n0)V2, where the term δ is a constant scaling factor dependent upon the concentric cylindrical geometry. The shape of the electric field is obtained from potential probe measurements taken along the radius r of a p+ − π − n+ structure with the current density directed radially outward. In this case the field follows an E α [(r2/r)2 − 1]1/2 dependence over the central portion of the device and diffusion effects are present at the inner (r1) and outer (r2) injecting boundaries. A first-order correction for diffusion at the contacts is made by the application of an effective radii difference r2eff − r1eff = r2 − r1 − 2QLa, where La is the ambipolar diffusion length and Q is a constant with values ≈ 0.5. A small-signal equivalent circuit representation for double injection in the concentric cylindrical geometry is established from impedance measurements over the frequency range 103≲ω≲106. Field and charge carrier distributions for cylindrical double injection in the diffusion-dominated regime are also discussed.