Non-conducting Walls Research Articles

Anisotropic dynamics of dipolar liquids in narrow slit pores

We report molecular dynamics simulation results for Stockmayer fluids confined to narrow slitlike pores with structureless, nonconducting walls. The translational and rotational dynamics of the dipolar particles have been investigated by calculating autocorrelation functions, diffusion coefficients, and relaxation times for various pore widths (five or less particle diameters) and directions parallel and perpendicular to the walls. The dynamic properties of the confined systems are compared to bulk properties, where corresponding bulk and pore states at the same temperature and chemical potential are determined in parallel grand canonical Monte Carlo simulations. We find that the dynamic behavior inside the pore depends on the distance from the walls and can be strongly anisotropic even in globally isotropic systems. This concerns especially the particles in the surface layers close to the walls, where the single particle and collective dipolar relaxation resemble that of true two-dimensional dipolar fluids with different in-plane and out-of-plane relaxations. On the other hand, bulklike relaxation is observed in the pore center of sufficiently wide pores.

The derivation and validation of the practical operating equation for electromagnetic flowmeters: case of having an electrolytic conductor flowing through

In this paper, the practical operating equation for the electromagnetic flowmeter is derived for the case of having a circular pipe with an electrolytic conductor flowing through. It is assumed further that the magnetic field is uniform and the velocity profile is axisymmetric (assuming nonconducting walls). The derivation was done before by many authors to whom the author refer to in this paper, but the approach provided here is comprehensive and simple. To add to that, the solution for the electromagnetic flowmeter's operating equation illustrated in this paper is new and is provided using very simple mathematical concepts, eliminating the complexity of solutions provided by other authors in the past. In the end, the practical operating equation derived was validated using a new approach based on the finite element analysis and the moving stream method to estimate the error resulting from using this operating equation with the assumptions of having a uniform magnetic field and an axisymmetric velocity profile, which are difficult to achieve in practice. This error can be used in a dry calibration to estimate the error caused by variable flow characteristics.

Direct numerical simulation of MHD flow with electrically conducting wall

The 2D vortex problem and 3D turbulent channel flow are treated numerically to assess the effect of electrically conducting walls on turbulent MHD flow. As a first approximation, the twin vortex pair is considered as a model of a turbulent eddy near the wall. As the eddy approaches and collides with the wall, a high value electrical potential is induced inside the wall. The Lorentz force, associated with the potential distribution, reduces the velocity gradient in the near-wall region. When considering a fully developed turbulent channel flow, a high electrical conductivity wall was chosen to emphasize the effect of electromagnetic coupling between the wall and the flow. The analysis was performed using DNS. The results are compared with a non-MHD flow and MHD flow in the insulated channel. The mean velocity within the logarithmic region in the case of the electrically conducting wall is slightly higher than that in the non-conducting wall case. Thus, the drag is smaller compared to that in the non-conducting wall case due to a reduction of the Reynolds stress in the near wall region through the Lorentz force. This mechanism is explained via reduction of the production term in the Reynolds shear stress budget.

The thermal characteristics of a hot wire in a near-wall flow

A two-dimensional numerical study is carried out to obtain the correction curve for the near-wall measurements by an infinitely long hot wire having been calibrated under free stream condition for the two extreme cases of isothermal and adiabatic wall conditions. Unlike previous studies particularly in experiments where the correction curve is primarily based on only the distance ( h) between the wall and the wire expressed in wall units ( Y + ≡ hU τ ν ) , it is found that a second dimensionless parameter h 0 (≡ h/ D) accounting for the effect of the hot wire diameter ( D) is necessary to describe fully the overall near-wall correction curve. Our calculations also reveal a possible reason for the apparent discrepancy between the near-wall hot wire correction curves of Chew and Shi [Y.T. Chew, S.X. Shi, Wall proximity influence on hot-wire measurements, In: R.M.C. So, C.G. Speziale, B.E. Launder (Eds.), Near-Wall Turbulent Flows, Elsevier, Amsterdam, 1993, pp. 609–619] and Lange et al. [C.F. Lange, F. Durst, M. Breuer, Wall effects on heat losses from hot-wires. Int. J. Heat Fluid Flow 20 (1999) 34] next to a thermally non-conducting wall.

Stability of narrow-gap MHD Taylor-Couette flow with radial heating and constant heat flux at the outer cylinder

A linear stability analysis has been presented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field and constant heat flux at the outer cylinder. The narrow-gap equations with respect to axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls are considered. A parametric study covering on the basis of ?, the ratio of the angular velocity of the outer cylinder to that of inner cylinder, Q, the Hartmann number which represents the strength of the axial magnetic field, and N, the ratio of the Rayleigh number and Taylor number representing the supply of heat to the outer cylinder at constant rate is presented. The three cases of ? < 0 (counter rotating), ? > 0 (co-rotating) and ? = 0 (stationary outer cylinder) are considered wherein the magnetic Prandtl number is assumed to be small. Results show that the stability characteristics depend mainly on the conductivity on the cylinders and not on the heat supplied to the outer cylinder. As a departure from earlier results corresponding to isothermal as well as hydromagnetic flow, it is found that the critical wave number is strictly a monotonic decreasing function of Q for conducting walls. Also, the presence of constant heat flux leads to a fall in the critical wave number for counter rotating cylinders, which states that for large values of -?, there occur transition from axisymmetric to non-axisymmetric disturbance whether the flow is hydrodynamic or hydromagnetic and this transition from axisymmetric to non-axisymmetric disturbance occur earlier as the strength of the magnetic field increases.

On the electrostatics of pneumatic conveying of granular materials using electrical capacitance tomography

In this work the electrostatics of the pneumatic conveying of granular materials in a non-conducting (PVC) pipe is studied using Electrical Capacitance Tomography (ECT) system. The non-conducting wall in general attains static charges arising from particle-wall collisions in the initial periods of conveying process and then reaches equilibrium with the surroundings. The polarity of particles and conveying pipe inner wall agrees reasonably well with the contact potential difference measurements. The perturbations in the capacitance signal due to charge accumulation are larger with smaller air superficial velocity. The denser flow regimes give larger wall residual charge. Wall charging process shows similar trend described by surface potential taken from electrostatic voltmeter to that revealed by ECT measurements. Also the addition of small amount (0.5% by weight) of anti-static agent (Larostat-519) in the powder form decreases the electrostatic charge generation by altering the dynamics of particle–particle and the particle–wall collisions.

Optimization of insulating coating formation technology on the structural materials for heavy liquid metal coolants

Development of liquid metals as coolants for blankets and diverters of tokamaks can lead us to choose coolant with higher safety standards than lithium. Heavy liquid metal coolants ensure higher safety of energy installations. Heavy liquid metal coolants facilitate formation of oxygen based electroinsulating coatings and maintain their stability. Conclusions of the most effective methods of electroinsulating coating formation are based on results of direct measure of magnetohydrodynamic resistance of different heavy liquid metal coolants. It has been proven experimentally that value of magnetohydrodynamic resistance to heavy liquid metal flow in round steel ducts with electroinsulating coatings in a transverse magnetic field is between the theoretical values for electroconductive walls and fully nonconducting walls. Electroinsulating coatings created in heavy liquid metal coolants are able to decrease the value of magnetohydrodynamic resistance by more than 5–10 times (depending on the coolant).

Stability of aluminium reduction cells with mean flow

We report results of the linear stability analysis undertaken to investigate the effect of the mean flow of liquid metal on the stability of aluminum reduction cells. A simplified model of the cell is considered that consists of thin layers of aluminum and cryolite superimposed in an infinite horizontal channel with electrically non-conducting walls. A vertical uniform magnetic field and an electric current are applied in the opposite directions. In the basic steady state, a uniform flow of aluminum is assumed, while cryolite is at rest. The onset of the instability is caused by the action of two different mechanisms. The first is the Kelvin-Helmholtz instability of the mean flow. The second, essentially the MHD mechanism, is a consequence of destabilizing electromagnetic (Lorentz) forces produced by nonuniformities of the electric current due to interface deflections. We use the shallow water approximation and solve the problem for the cases of pure Kelvin-Helmholtz (zero magnetic field) and pure MHD (zero mean flow) instabilities and for the general case. We compute the stability chart and derive the parameters that determine the stability threshold. It is found that, while both playing a destabilizing role, the instability mechanisms do not affect each other. In particular, a uniform mean flow changes the direction of propagation of interfacial waves but leaves the MHD stability threshold unaltered. Figs 4, Refs 12.

Ferroelectric states of a dipolar fluid confined to a slit–pore

Monte-Carlo simulation results are reported for a strongly coupled dipolar soft-sphere (DSS) fluid confined by two planar, non-conducting walls with wall separation L z =7 σ ( σ being the diameter of the spheres). Simulations are performed in an isothermal–isobaric ensemble where the pressure parallel to the walls is fixed. Choosing appropriate values for temperature and dipole moment we demonstrate that the confined system, when compressed towards high parallel pressures, develops spontaneous polarization (i.e. ferroelectric behavior) similar to what is seen in bulk DSS fluids. In the pressure range investigated the ferroelectric states of the confined system are liquid-like in directions parallel to the walls, but stratified in z-direction. A further confinement-induced effect, which can be understood via energetic arguments, is that the global director d ̂ characterizing the ferroelectric order points in a direction parallel to the walls. Due to this restriction the isotropic-to-ferroelectric transition occurs at significantly lower pressures/densities than in the bulk where the direction of d ̂ is unrestricted.

Ferroelectric states of a dipolar fluid confined to a slit–pore

Monte-Carlo simulation results are reported for a strongly coupled dipolar soft-sphere (DSS) fluid confined by two planar, non-conducting walls with wall separation L z =7 σ ( σ being the diameter of the spheres). Simulations are performed in an isothermal–isobaric ensemble where the pressure parallel to the walls is fixed. Choosing appropriate values for temperature and dipole moment we demonstrate that the confined system, when compressed towards high parallel pressures, develops spontaneous polarization (i.e. ferroelectric behavior) similar to what is seen in bulk DSS fluids. In the pressure range investigated the ferroelectric states of the confined system are liquid-like in directions parallel to the walls, but stratified in z -direction. A further confinement-induced effect, which can be understood via energetic arguments, is that the global director d ̂ characterizing the ferroelectric order points in a direction parallel to the walls. Due to this restriction the isotropic-to-ferroelectric transition occurs at significantly lower pressures/densities than in the bulk where the direction of d ̂ is unrestricted.

Spontaneous orientational order in confined dipolar fluid films

We report Monte Carlo simulation results for a strongly coupled dipolar soft-sphere (DSS) fluid confined to a nanoscopic slit pore with structureless, nonconducting walls. The central topic of our investigation are the conditions under which the pore fluid can spontaneously order into a globally polarized (i.e., ferroelectric) state. Polarized states are observed in bulk DSS fluids at sufficiently low temperatures and high densities/pressures. The confined system is simulated in the (N,Lz,P∥,T) ensemble, where N is the particle number, Lz the wall separation, P∥ the pressure parallel to the walls, and T the temperature. Fixing T and P∥ such that the corresponding bulk system is ferroelectric, and considering confined films with various thicknesses proportional to Lz, we first demonstrate that the long-range orientational order persists down to Lz≈6σ. We then specialize to the case Lz=7σ, for which we investigate in detail the spatial and orientational structure as functions of P∥. It turns out that the transition from the globally isotropic to the globally polarized phase occurs at significantly lower pressures/densities than in the bulk, indicating that spatial confinement can support the onset of ferroelectric order. We explain this phenomenon within the framework of a simple mean-field theory based on the assumption that confinement effectively restricts orientational fluctuations, as suggested by the Monte Carlo results.

Magnetohydrodynamic turbulent flow in a channel at low magnetic Reynolds number

Effects of the Lorentz force on near-wall turbulence structures are investigated using the direct numerical simulation technique with the assumption of no induced magnetic field at low magnetic Reynolds number. A uniform magnetic field is applied in the streamwise (x), wall-normal (y) or spanwise (z) direction to turbulent flow in an infinitely long channel with non-conducting walls. The Lorentz force induced from the magnetic field suppresses the dynamically significant coherent structures near the wall. The skin friction decreases with increasing streamwise and spanwise magnetic fields, whereas it increases owing to the Hartmann effect when the strength of the wall-normal magnetic field exceeds a certain value. All the turbulence intensities and the Reynolds shear stress decrease with the wall-normal and spanwise magnetic fields, but the streamwise velocity fluctuations increase with the streamwise magnetic field although all other turbulence intensities decrease. It is also shown that the wall-normal magnetic field is much more effective than the streamwise and spanwise magnetic fields in reducing turbulent fluctuations and suppressing the near-wall streamwise vorticity, even though the wall-normal magnetic field interacts directly with the mean flow and results in drag increase at strong magnetic fields. In the channel with a strong streamwise magnetic field, two-dimensional streamwise velocity fluctuations u(y, z) exist, even after other components of the velocity fluctuations nearly vanish. In the cases of strong wall-normal and spanwise magnetic fields, all turbulence intensities, the Reynolds shear stress and vorticity fluctuations decrease rapidly and become zero. The turbulence structures are markedly elongated in the direction of the applied magnetic field when it is strong enough. It is shown that this elongation of the structures is associated with a rapid decrease of the Joule dissipation in time.

Magnetohydrodynamic flow in a rectangular duct with suction and injection

The effects of suction or injection on an incompressible laminar flow in a rectangular duct with nonconducting walls in the presence of an imposed transverse magnetic field are examined. Analytical solutions are obtained for the velocity and magnetic field, which are useful for obtaining the current density and electric field strength.

Electrophoretic Motion of a Spherical Particle with a Thick Double Layer in Bounded Flows

The electrophoretic mobility of a spherical colloidal particle with low zeta potential near a solid charged boundary is calculated numerically for arbitrary values of the double layer thickness by a generalization of Teubner's method to the case of bounded flow. Three examples are considered: a sphere near a nonconducting planar wall with electric field parallel to the wall, near a perfectly conducting planar wall with electric field perpendicular to the wall, and on the axis of a cylindrical pore with electric field parallel to the axis. The results are compared with recent analytical calculations using the method of reflections. For the case of a charged sphere near a neutral surface, the reflection results are quite good, provided there is no double layer overlap, in which case there can be extra effects for constant potential particles that are entirely missed by the analytical expressions. For a neutral sphere near a charged surface, the reflection results are less successful. The main reason is that the particle feels the profile of the electroosmotic flow, an effect ignored by construction in the method of reflections. The general case is a combination of these, so that the reflections are more reliable when the electrophoretic motion dominates the electroosmotic flow. The effect on particle mobility of particle-wall interactions follows the trend expected on geometric grounds in that sphere–plane interactions are stronger than sphere–sphere interactions and the effect on a sphere in a cylindrical pore is stronger still. In the latter case, particle mobility can fall by more than 50% for thick double layers and a sphere half the diameter of the pore. The agreement between numerical results and analytical results follows the same trend, being worst for the sphere in a pore. Nevertheless, the reflections can be reliable for some geometries if there is no double layer overlap. This is demonstrated for a specific example where reflection results have previously been compared with experiments on protein mobility through a membrane (J. Enniset al.,1996,J. Membrane Sci.119, 47).

Stability of hydromagnetic dissipative Couette flow with non-axisymmetric disturbance

A linear stability analysis has been implemented for hydromagnetic dissipative Couette flow, a viscous electrically conducting fluid between rotating concentric cylinders in the presence of a uniform axial magnetic field. The small-gap equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. Both types of boundary conditions, conducting and non-conducting walls, are considered. A parametric study covering wide ranges of μ, the ratio of angular velocity of the outer cylinder to that of inner cylinder, and Q, the Hartmann number which represents the strength of axial magnetic field, is conducted. Results show that the stability characteristics depend on the conductivity of the cylinders. For the case of non-conducting walls, it is found that the critical disturbance is a non-axisymmetric mode as the value of μ is sufficiently negative and the domain of Q where non-axisymmetric instability modes prevail is limited. Similar results are obtained for conducting walls at low Hartmann number. In addition, the transition of the onset of instability from non-axisymmetric modes to axisymmetric modes for the case μ=−1 with increasing strength of magnetic field are discussed in detail. For high values of the Hartmann number, the critical disturbance is always the axisymmetric stationary mode for non-conducting walls but not for conducting walls. For −1[les ]μ<1, it is demonstrated that non-axisymmetric instability modes prevail in a wide range of Q for conducting walls and axisymmetric oscillatory modes may, in fact, become more critical than both of the non-axisymmetric and axisymmetric stationary modes at higher values of the Hartmann number.

Kinetic modeling of the charging of nonconducting walls in a low pressure radio frequency inductively coupled plasma

This article investigates the overall charging of a nonconducting, plane wall (for instance a wafer) in a low pressure inductively coupled plasma. The problem is addressed using a two-dimensional kinetic model for a low pressure inductive discharge. Comparisons to experimental results show good agreement with the charging profiles predicted by the model. It is pointed out that the surface charge profile on a nonconducting wall is determined by the plasma homogeneity and the high energy part of the electron distribution function. An interpretation of the radial profiles of the sheath potential drop and of the surface charge potential in terms of the differential temperature of the electron distribution function in different energy ranges is presented.

Boundary Effects on the Bipolar Behavior of a Spherical Particle in an Electrolytic Cell

A combined analytic and numerical study is presented for the bipolar behavior of a spherical particle in the proximity of a large plane wall. The electric field is exerted in two fundamental cases: normal to a perfectly conducting plane and parallel to a perfectly nonconducting wall. Linearly polarized electrode kinetics is assumed for the electrochemical reaction occurring at the particle surface. The governing equations for the electric potential field applicable to the systems are solved using bispherical coordinates. The current‐density distribution and the current‐enhancement factor of the particle are determined for various cases. It is found that the current‐enhancement factor of the particle can be increased or decreased by the presence of the plane wall, depending on the relative conductivity of the particle with respect to the surrounding electrolytic solution (κ*) and the relative resistance of the reaction arising at the particle surface with respect to the conduction inside the particle (γ). The interaction effects between the wall and the particle can be significant when the gap thickness gets close to zero. For the special case of κ* − γ = 1, the current‐density distribution and the current‐enhancement factor of the spherical particle are not affected by the presence of the wall.

Velocity gradient at the wall of a packed bed reactor with single phase liquid flow: measurements and modelling

The average velocity gradient was measured by means of microelectrodes embedded in a non-conducting wall of a packed bed reactor with single phase liquid flow. We showed that these experimental results could be correctly predicted by the hydrodynamic model developed by Vortmeyer and Schuster for the evaluation of steady flow profiles in circular packed beds.

On the radial distribution and nonambipolarity of charged particle fluxes in a nonmagnetized planar inductively coupled plasma

The radial distribution of electron and ion fluxes to conducting and nonconducting walls in a planar inductively coupled plasma has been studied experimentally and theoretically. Measurements of electron and ion currents have been performed using electrostatic probe arrays. Radially resolved measurements of ion impact energies have been performed using an ion energy analyzer array. For conducting walls it is shown by calculations and measurements that electron and ion currents are not in balance locally but that diffusion is nonambipolar. The ion impact energies measured on a conducting surface show a significant radial variation in accord with our theoretical model. For nonconducting surfaces the ambipolar fluxes of electrons and ions result in the formation of a surface charge potential profile across the surface. Voltages of the order of several volts between the center and the periphery of the surface are measured.

Electrophoresis of a colloidal sphere in a circular cylindrical pore

AbstractThe electrophoretic motion of a dielectric sphere along the centerline of a long circular cylindrical pore is studied theoretically. The imposed electric field is constant and parallel to the nonconducting pore wall, and the particle and wall surfaces are assumed uniformly charged. Electrical double layers adjacent to solid surfaces are assumed to be thinner than particle radius and gap width between surfaces. The presence of the pore wall affects particle velocity: 1. an electroosmotic flow of the suspending fluid exists due to interaction between the electric field and the charged wall; 2. the local electric field on the particle surface is enhanced by the insulated wall, speeding up the particle; and 3. the wall increases viscous retardation of the moving particle. To solve electrostatic and hydrodynamic governing equations, general solutions are constructed from fundamental solutions in both cylindrical and spherical coordinate systems. Boundary conditions are enforced at the pore wall by Fourier transforms and then on the particle surface by a collocation technique. Typical electric‐field‐line, equipotential‐line and streamline patterns for the fluid phase are exhibited, and corrections to the Smoluchowski equation for particle electrophoretic velocity are presented for various relative separation distances between the particle and wall. The presence of the pore wall always reduces the electrophoretic velocity; however, the net wall effect is quite weak, even for very small gap width between the particle and wall.