Tube Radius Research Articles

ОСОБЛИВОСТІ ЗМІНИ ТЕПЛОФІЗИЧНИХ ВЛАСТИВОСТЕЙ НАДКРИТИЧНОЇ ВОДИ ПІД ЧАС ТЕЧІЇ В КРУГЛИХ ТРУБАХ, ЩО ОБІГРІВАЮТЬСЯ

Для процесу течії надкритичної води в каналі, що обігрівається, проведено дослідження особливостей просторового розподілу фізичних властивостей води, зумовлених їх істотною температурною залежністю, характерною для надкритичних середовищ у ділянці псевдофазового переходу. На основі комп'ютерного моделювання розв'язано задачу тепломасоперенесення у вертикальній круглій трубі під час висхідного руху в ній води надкритичних параметрів. Показано, що характер розподілу властивостей теплоносія у поздовжньому перетині труби певною мірою визначається рухом в ньому фронту псевдофазового переходу. Проаналізовано вплив величини густини теплового потоку, що підводиться до стінки труби, на положення границь початку і кінця зони псевдофазового переходу і на пов'язані з цим особливості просторової зміни фізичних властивостей теплоносія. Наведено результати СFD моделювання з розподілу уздовж довжини труби, що обігрівається, таких властивостей надкритичної води, як густина, динамічна в'язкість, коефіцієнт теплопровідності і питома теплоємність. Виконано зіставлення особливостей розподілу зазначених властивостей, розрахованих за температурою на стінці труби і на її осі. Досліджено характер зміни питомої теплоємності по радіусу труби і проаналізовано вплив рівня теплового потоку, що підводиться, на положення максимуму теплоємності в різних поперечних перетинах каналу.

Onset of transition in the flow of polymer solutions through microtubes

Experiments are performed to characterize the onset of laminar–turbulent transition in the flow of high-molecular-weight polymer solutions in rigid microtubes of diameters in the range $390~\unicode[STIX]{x03BC}\text{m}{-}470~\unicode[STIX]{x03BC}\text{m}$ using the micro-PIV technique. By considering flow in tubes of such small diameters, the present study probes higher values of elasticity numbers ($E\equiv \unicode[STIX]{x1D706}\unicode[STIX]{x1D708}/R^{2}$) compared to existing studies, where $\unicode[STIX]{x1D706}$ is the longest relaxation time of the polymer solution, $R$ is the tube radius and $\unicode[STIX]{x1D708}$ is the kinematic viscosity of the polymer solution. For the Newtonian case, our experiments indicate that the natural transition (without the aid of any forcing mechanism) occurs at Reynolds number ($Re$) $2000\pm 100$. As the concentration of polymer is increased, initially there is a delay in the onset of the transition and the transition Reynolds number increases to $2500$. Further increase in concentration of the polymer results in a decrease in the Reynolds number for transition. At sufficiently high concentrations, the added polymer tends to destabilize the flow and the transition is observed to happen at $Re$ as low as $800$. It is also observed that the addition of polymers, regardless of their concentration, reduces the magnitude of the velocity fluctuations after transition. Dye-stream visualization is further used to corroborate the onset of transition in the flow of polymer solutions. The present work thus shows that addition of polymer, at sufficiently high concentrations, destabilizes the flow when compared to that of a Newtonian fluid, thereby providing additional evidence for ‘early transition’ or ‘elasto-inertial turbulence’ in the flow of polymer solutions. The data for the transition Reynolds number $Re_{t}$ from our experiments (for tubes of different diameters, and for two different polymers at varying concentrations) collapse well according to the scaling relation $Re_{t}\propto 1/\sqrt{E(1-\unicode[STIX]{x1D6FD})}$, where $\unicode[STIX]{x1D6FD}$ is the ratio of solvent viscosity to the viscosity of the polymer solution.

The electron properties of infinite length single-walled silicon nanotubes are studied by density functional theory

In this article, we aim to use LGTO-PBC-DFT calculation method with PBEPBE/6–31G(d) basis sets and PBC model to optimize geometric structure, obtain electron characteristics and band gaps of (n, m) chiral (6 ≤ n ≤ 16, 2 ≤ m ≤ 8); (n, 0) zigzag (3 ≤ n ≤ 15) and (n, n) armchair (2 ≤ n ≤ 8) pure infinite length single-walled Silicon nanotubes. We have obtained that the HOCO-LUCO gaps decrease with the radii of the SWSiNTs increase by using the PBEPBE functional and 6–31G(d) basis set. most of the infinite length SWSiNTs which we studied are narrow band gaps semiconductors. perhaps the surface structure is the most important factor affecting the band gap of the nanotubes. There have been a research on the infinite silicon nanotubes and with the increase of the tube radius, an indirectdirect band gap transition has been revealed. For all the armchair SWSiNTs, the infinite zigzag SiNTs (n,0), (3 ≤ n ≤ 9) and the infinite chiral SWSiNTs (6, 2), (9, 3), (10, 5), (12, 6) are semiconductors with indirect band gaps. While for the infinite zigzag SiNTs (n, 0) 15 ≥ n ≥ 10, and the infinite chiral SWSiNT (12, 4) are semiconductors with direct gaps at Ｘ point, the direct gaps open at Ｘ point. It is possible that direct band gap will become potential building blocks for electronic and optoelectronic devices.

Numerical study of the influence of dielectric tube on propagation of atmospheric pressure plasma jet based on coplanar dielectric barrier discharge

A 2D fluid model was employed to simulate the influence of dielectric on the propagation of atmospheric pressure helium plasma jet based on coplanar dielectric barrier discharge (DBD). The spatio-temporal distributions of electron density, ionization rate, electrical field, spatial charge and the spatial structure were obtained for different dielectric tubes that limit the helium flow. The results show that the change of the relative permittivity of the dielectric tube where the plasma jet travels inside has no influence on the formation of DBD itself, but has great impact on the jet propagation. The velocity of the plasma jet changes drastically when the jet passes from a tube of higher permittivity to one of lower permittivity, resulting in an increase in jet length, ionization rate and electric field, as well as a change in the distribution of space charges and discharge states. The radius of the dielectric tube has a great influence on the ring-shaped or solid bullet structure. These results can well explain the behavior of the plasma jet from the dielectric tube into the ambient air and the hollow bullet in experiments.

Nonlinear electrophoresis of a tightly fitting sphere in a cylindrical tube

We investigate electrophoresis of a tightly fitting sphere of radius $R-h_{0}$ on the axis of a circular tube of radius $R$, using lubrication theory and ideas due to Schnitzer & Yariv (Phys. Fluids, vol. 26, 2014, 122002). The electrical charge clouds on both the cylindrical wall and the surface of the sphere are assumed thin compared to the gap between the sphere and cylinder, so that charge clouds do not overlap and ion exclusion effects are minimal. Nevertheless, non-uniform pumping of counter-ions within the charge clouds leads to a change in the ionic concentration outside the charge clouds in the narrow gap between sphere and cylinder. The electro-osmotic slip velocities at the two surfaces are modified, leading to a decrease in the electrophoretic velocity of the sphere at low Péclet numbers and an increase in the velocity at high Péclet numbers. When the field strength $E_{0}$ is low, it is known that the electrophoretic velocity $U_{0}$ is proportional to $E_{0}(\unicode[STIX]{x1D701}_{s}-\unicode[STIX]{x1D701}_{c})$ which is zero when the zeta potential $\unicode[STIX]{x1D701}_{s}$ on the sphere surface is equal to the zeta potential $\unicode[STIX]{x1D701}_{c}$ on the cylinder. The perturbation to the above low field strength electrophoretic velocity (at high Péclet number) is predicted to be proportional to $E_{0}^{3}(\unicode[STIX]{x1D701}_{s}+\unicode[STIX]{x1D701}_{c})^{2}(\unicode[STIX]{x1D70E}_{s}+\unicode[STIX]{x1D70E}_{c})$, where $\unicode[STIX]{x1D70E}_{s}$ and $\unicode[STIX]{x1D70E}_{c}$ are the surface charge densities on the sphere and cylinder. The choice of materials with similar or identical zeta potentials (and surface charge densities) for the cylinder and sphere should therefore facilitate the observation of velocities nonlinear in the field strength $E_{0}$, since the reference linear electrophoretic velocity will be small.

Solar jet on 2014 April 16 modeled by Kelvin–Helmholtz instability

We study here the arising of Kelvin–Helmholtz Instability (KHI) in one fast jet of 2014 April 16 observed by the Atmospheric Imaging Assembly (AIA) on board Solar Dynamics Observatory (SDO) in different UV and EUV wavelengths. The evolution of jet indicates the blob like structure at its boundary which could be one of the observable features of the KHI development. We model the jet as a moving cylindrical magnetic flux tube of radius a embedded in a magnetic field Bi and surrounded by rest magnetized plasma with magnetic field Be. We explore the propagation of the kink MHD mode along the jet that can become unstable against the KHI if its speed exceeds a critical value. Concerning magnetic fields topology we consider three different configurations, notably of (i) spatially homogeneous magnetic fields (untwisted magnetic flux tube), (ii) internal (label ‘i’) twisted magnetic field and external homogeneous one (label ‘e’) (single-twisted flux tube), and (iii) both internal and external twisted magnetic fields (double-twisted magnetic flux tube). Electron number densities in the two media ni and ne are assumed to be homogeneous. The density contrast is defined in two ways: first as ne/ni and second as ne/(ni+ne). Computations show that the KHI can occur at accessible flow velocities in all the cases of untwisted and single-twisted flux tubes. It turns out, however, that in the case of a double-twisted flux tube the KHI can merge at an accessible jet speed only when the density contrast is calculated from the ratio ne/(ni+ne). Evaluated KHI developing times and kink mode wave phase velocities at wavelength of 4 Mm lie in the ranges of 1–6.2 min and 202–271 km s−1, respectively—all being reasonable for the modeled jet.

Numerical investigation on paraffin/expanded graphite composite phase change material based latent thermal energy storage system with double spiral coil tube

Latent thermal energy storage (LTES) by using phase change material (PCM) is a promising technology which can solve the temporal and geographical mismatch problems between energy supply and demand in utilization of solar thermal energy and industrial waste heat. However, until now, it is still challenging to provide LTES systems with high energy storage efficiency because of the low thermal conductivity of the PCM and suboptimum structure of heat exchanger. In this work, a novel LTES system with paraffin/expanded graphite (EG) composite PCM and double spiral coil tube as heat-exchange tube was constructed. The radius of the double spiral coil-shaped tube was determined by means of the quasi steady state method. And the effects of heat transfer fluid (HTF) inlet position and the ratio of the heat-exchange area between the inner and outer coil tube on the latent heat storage performance of this system were investigated. Compared with single coil tube, LTES system with double spiral coil tube could reduce the time to finish latent heat storage.

Enhancement of the water flow velocity through carbon nanotubes resulting from the radius dependence of the friction due to electron excitations.

Secchi etal. [Nature (London) 537, 210 (2016)10.1038/nature19315] observed a large enhancement of the permeability and slip length in carbon nanotubes when the tube radius is of the order of 15 nm, but not in boron nitride nanotubes. It will be pointed out that none of the parameters that appear in the usual molecular dynamics treatments of water flow in carbon nanotubes have a length scale comparable to 15 nm, which could account for the observed flow velocity enhancement. It will be demonstrated here, however, that if the friction force between the water and the tube walls in carbon nanotubes is dominated by friction due to electron excitations in the tube walls, the enhanced flow can be accounted for by a reduction in the contribution to the friction due to electron excitations in the wall, resulting from the dependence of the electron energy band gap on the tube radius.

Azimuthal Fermionic Current in the Cosmic String Spacetime Induced by a Magnetic Tube

In this paper, we calculate the vacuum expectation value of the azimuthal fermionic current, associated with a massive fermionic quantum field in the spacetime of an idealized cosmic string, considering the presence of a magnetic tube of radius a, coaxial to the string. In this analysis three distinct configurations of magnetic field are considered: (i) a magnetic field concentrated on a surface of the tube; (ii) a magnetic field presenting a 1 / r radial dependence; and (iii) an homogeneous magnetic field. In order to develop this analysis , we construct the complete set of normalized solution of the Dirac equation in the region outside the tube. By using the mode-sum formula, we show that the azimuthal induced current is formed by two contributions: the first being the current induced by a line of magnetic flux running along the string, and the second, named core-induced current, is induced by the non-vanishing extension of the magnetic tube. The first contribution depends only on the fractional part of the ration of the magnetic flux inside the tube by the quantum one; as to the second contribution, it depends on the total magnetic flux. We specifically analyze the core-induced current in several limits of the parameters and distance to the tube.

Ignition properties of helium discharges in dielectric tubes with radius from 50 µm to 3 mm

A numerical study on the ignition properties of helium discharge confined in a dielectric tube is conducted with a fluid model. As the tube radius R increasing from 50 µm to 3 mm, the ignition voltage firstly reduces, then increases after R exceeding 1 mm. An ion sheath is formed between the discharge channel and the tube wall. The width of sheath decide whether a ring‐shape or a solid‐shape discharge morphology can be formed. Moreover, the dynamic contraction of the discharge channel is observed. Under conditions of low applied voltage and low seed electron density, the cross‐section of the discharge front is adjusted to contract to enhance the self‐built electric field, and therefore to sustain the propagation.

Crossover of the Power-Law Exponent for Carbon Nanotube Conductivity as a Function of Salinity

On the basis of the Poisson-Boltzmann equation in cylindrical coordinates, we calculate the conductivity of a single charged nanotube filled with electrolyte. The conductivity as a function of the salt concentration follows a power-law, the exponent of which has been controversially discussed in the literature. We use the co-ion-exclusion approximation and obtain the crossover between different asymptotic power-law behaviors analytically. Numerically solving the full Poisson-Boltzmann equation, we also calculate the complete diagram of exponents as a function of the salt concentration and the pH for tubes with different radii and p Ka values. We apply our theory to recent experimental results on carbon nanotubes using the p Ka as a fit parameter. In good agreement with the experimental data, the theory shows power-law behavior with the exponents 1/3 at high pH and 1/2 at low pH, with a crossover depending on salt concentration, tube radius and p Ka.

The electron properties of infinite length single-walled silicon nanotubes are studied by density functional theory

In this article, we aim to use LGTO-PBC-DFT calculation method with PBEPBE/6–31G(d) basis sets and PBC model to optimize geometric structure, obtain electron characteristics and band gaps of (n, m) chiral (6 ≤ n ≤ 16, 2 ≤ m ≤ 8); (n, 0) zigzag (3 ≤ n ≤ 15) and (n, n) armchair (2 ≤ n ≤ 8) pure infinite length single-walled Silicon nanotubes.We have obtained that the HOCO-LUCO gaps decrease with the radii of the SWSiNTs increase by using the PBEPBE functional and 6–31G(d) basis set. Most of the infinite length SWSiNTs which we studied are narrow band gaps semiconductors. Perhaps the surface structure is the most important factor affecting the band gap of the nanotubes. There have been a research on the infinite silicon nanotubes and with the increase of the tube radius, an indirectdirect band gap transition has been revealed.For all the armchair SWSiNTs, the infinite zigzag SiNTs (n,0), (3 ≤ n ≤ 9) and the infinite chiral SWSiNTs (6, 2), (9, 3), (10, 5), (12, 6) are semiconductors with indirect band gaps. While for the infinite zigzag SiNTs (n, 0) 15 ≥ n ≥ 10, and the infinite chiral SWSiNT (12, 4) are semiconductors with direct gaps at Ｘ point, the direct gaps open at Ｘ point. It is possible that direct band gap will become potential building blocks for electronic and optoelectronic devices.

Technical note: Influence of surface roughness and local turbulence on coated-wall flow tube experiments for gas uptake and kinetic studies

Abstract. Coated-wall flow tube reactors are frequently used to investigate gas uptake and heterogeneous or multiphase reaction kinetics under laminar flow conditions. Coating surface roughness may potentially distort the laminar flow pattern, induce turbulence and introduce uncertainties in the calculated uptake coefficient based on molecular diffusion assumptions (e.g., Brown/Cooney–Kim–Davis (CKD)/Knopf–Pöschl–Shiraiwa (KPS) methods), which has not been fully resolved in earlier studies. Here, we investigate the influence of surface roughness and local turbulence on coated-wall flow tube experiments for gas uptake and kinetic studies. According to laminar boundary theory and considering the specific flow conditions in a coated-wall flow tube, we derive and propose a critical height δc to evaluate turbulence effects in the design and analysis of coated-wall flow tube experiments. If a geometric coating thickness δg is larger than δc, the roughness elements of the coating may cause local turbulence and result in overestimation of the real uptake coefficient (γ). We further develop modified CKD/KPS methods (i.e., CKD-LT/KPS-LT) to account for roughness-induced local turbulence effects. By combination of the original methods and their modified versions, the maximum error range of γCKD (derived with the CKD method) or γKPS (derived with the KPS method) can be quantified and finally γ can be constrained. When turbulence is generated, γCKD or γKPS can bear large difference compared to γ. Their difference becomes smaller for gas reactants with lower uptake (i.e., smaller γ) and/or for a smaller ratio of the geometric coating thickness to the flow tube radius (δg ∕ R0). On the other hand, the critical height δc can also be adjusted by optimizing flow tube configurations and operating conditions (i.e., tube diameter, length, and flow velocity), to ensure not only unaffected laminar flow patterns but also other specific requirements for an individual flow tube experiment. We use coating thickness values from previous coated-wall flow tube studies to assess potential roughness effects using the δc criterion. In most studies, the coating thickness was sufficiently small to avoid complications, but some may have been influenced by surface roughness and local turbulence effects.

A theoretical model of the inversion tube over a conical die

As an important impact energy absorber and a way to produce double-wall tubes, the inversion of the metal tube over a conical die is investigated in this study. Adopting the deformation profile inspired by FEM simulations, a theoretical model is proposed assuming the energy is dissipated by bending and compression in the meridional direction, and expansion in the circumferential direction. FEM simulations with a large range of geometrical parameters are used to validate the theoretical model, and results show that both the compressional force and the final circular radius of tube predicted by the theoretical model are quite accurate. Then, the energy dissipations along the axis of the tube by various mechanisms are analyzed in detail, and it is identified that the tube deformation in the thickness direction is the major reason of the current model’s deviation. Besides, the influence of the die radius, the friction between die and tube, as well as the dynamic effect are discussed.

Surface-wave-sustained plasma torch for water treatment

In this study the effects of water treatment by surface-wave-sustained plasma torch at 2.45 GHz are studied. Changes in two directions are obtained: (i) changes of the plasma characteristics during the interaction with the water; (ii) water physical and chemical characteristics modification as a result of the plasma treatment. In addition, deactivation of Gram positive and Gram negative bacteria in suspension are registered. A number of charged and excited particles from the plasma interact with the water. As a result the water chemical and physical characteristics such as the water conductivity, pH, H2O2 concentration are modified. It is observed that the effect depends on the treatment time, wave power, and volume of the treated liquid. At specific discharge conditions determined by the wave power, gas flow, discharge tube radius, thickness and permittivity, the surface-wave-sustained discharge (SWD) operating at atmospheric pressure in argon is strongly non-equilibrium with electron temperature Te much higher than the temperature of the heavy particles (gas temperature Tg). It has been observed that SWD argon plasma with Tg close to the room temperature is able to produce H2O2 in the water with high efficiency at short exposure times (less than 60 sec). The H2O2 decomposition is strongly dependant on the temperature thus the low operating gas temperature is crucial for the H2O2 production efficiency. After scaling up the device, the observed effects can be applied for the waste water treatment in different facilities. The innovation will be useful especially for the treatment of waters and materials for medical application.

The effect of electrostatic and gravity force on offset wire inside tube

In a straw-tube detector, a wire that is offset with respect to the tube axis experiences a Coulomb force when high voltage is applied between the anode wire and the tube. This force results in a shifting of the wire and straw, in addition to the gravitational sag, and is a function of the tube and wire radius, initial offset, high voltage, tension and length. The presence of such effects is well known, but the precise magnitude of the shift for the anode wires under conditions of detector operation have not been previously documented with measurable confidence. In this work, we provide the first systematic measurements for the wire shift in straw-tube detectors due to gravity and the electrostatic force using an x-ray scanner developed for the Mu2e experiment. The data are compared to the solutions of the differential equations governing the system, and we find a good match between the two. The solutions can predict the final wire and straw positions from the initial positions measured without the high voltage, and the final wire and straw positions can then be used as an input to the track reconstruction software to improve the track position resolution.

Steady Displacement of Long Gas Bubbles in Channels and Tubes Filled by a Bingham Fluid.

Bingham fluids behave like solids below a von Mises stress threshold, the yield stress, while above it they behave like Newtonian fluids. They are characterized by a dimensionless parameter, Bingham number (Bn), which is the ratio of the yield stress to a characteristic viscous stress. In this study, the non-inertial steady motion of a finite size gas bubble in both a plane 2D channel and an axi-symmetric tube filled by a Bingham fluid has been studied numerically. The Bingham number, Bn, is in the range 0 ≤ Bn ≤ 3, where Bn=0 is the Newtonian case, while the Capillary number which is the ratio of a characteristic viscous force to the surface tension has values Ca=0.05, 0.10, and 0.25. The volume of all axi-symmetric and 2D bubbles has been chosen to be identical for all parameter choices and large enough for the bubbles to be long compared to the channel/tube width/diameter. The Bingham fluid constitutive equation is approximated by a regularized equation. During the motion, the bubble interface is separated from the wall by a static liquid film. The film thickness scaled by the tube radius (axi-symmetric)/half of the channel height (2D) is the dimensionless film thickness, h. The results show that increasing Bn initially leads to an increase in h, however, the profile h versus Bn can be monotonic or non-monotonic depending on Ca values and 2D/axi-symmetric configurations. The yield stress also alters the shape of the front and rear of the bubble and suppresses the capillary waves at the rear of the bubble. The yield stress increases the magnitude of the wall shear stress and its gradient and therefore increases the potential for epithelial cell injuries in applications to lung airway mucus plugs. The topology of the yield surfaces as well the flow pattern in the bubble frame of reference varies significantly by Ca and Bn.

Estimation of Maximum Pressure Stress Intensity in a Welding Tee

The required thickness of welding tees is neither specified in ASME (2012, “Factory-Made Wrought Buttwelding Fittings,” American Society of Mechanical Engineers, New York, Standard No. B16.9-2012) nor is a clear calculation method provided in codes such as ASME (2016, “Process Piping,” American Society of Mechanical Engineers, New York, Standard No. B31.3-2016). This can lead to uncertainty regarding the pressure capacity of a tee fitting, particularly one that has suffered from erosion or corrosion. Code methods including area replacement (ASME, 2016, “Process Piping,” American Society of Mechanical Engineers, New York, Standard No. B31.3-2016) or pressure-area (ASME, 2015, “Boiler and Pressure Vessel Code Section VIII Division 2,” American Society of Mechanical Engineers, New York, Standard No. BPVC-VIII-2-2015; BSI, 2014, “Unfired Pressure Vessels Part 3: Design,” BSI, London, UK, Standard No. BS EN 13445-3) do not directly account for the effect which the curvature of the crotch region may have on the stress state in the tee. The approach adopted in this work is to liken the geometry of the tee crotch to the intrados of a torus or pipe bend. The shell theory applicable to the torus is adapted for the tee in order to derive a relationship for circumferential membrane stress. An equivalent tube radius is assigned by determining the local radius of shell curvature in the plane passing through the crotch center of the curvature. The actual stresses in the tee crotch are significantly reduced by the adjoining straight portions. This effect is difficult to quantify theoretically and has thus been investigated by means of finite element analysis (FEA)-based assessments. An empirical relationship was then established providing a conservative correlation between the theoretical stresses and the program calculated local stress intensities.

Entanglement transitions in one-dimensional confined fluid flows

The strength of entanglement present in a tubular structure consisting of short filaments is assessed using a periodic boundary condition model by employing the magnitude of the eigenvalues of the periodic linking matrix associated to the filamental structure. The effects of tube radius and of the alignment of the filaments on the strength of entanglement are shown to suggest that strongly aligned flow systems exhibit a stronger entanglement than those consisting of randomly aligned filaments of the same density. Our results could be used to quantify the entanglement of vortex filaments and understand the effects of vortex filament alignment in fluid flows.

Kelvin–Helmholtz Instability in a Cool Solar Jet in the Framework of Hall Magnetohydrodynamics: A Case Study

We investigate the conditions under which the magnetohydrodynamic (MHD) modes in a cylindrical magnetic flux tube moving along its axis become unstable against the Kelvin--Helmholtz (KH) instability. We \textbf{use} the dispersion relations of MHD modes \textbf{obtained} from the linearized Hall MHD equations for cool (zero beta) plasma \textbf{by assuming} real wave numbers and complex angular wave frequencies\textbf{/complex wave phase velocities}. The dispersion equations are solved numerically at fixed input parameters and varying values of the ratio $l_\mathrm{Hall}/a$, where $l_\mathrm{Hall} = c/\omega_\mathrm{pi}$ ($c$ being the speed of light, and $\omega_\mathrm{pi}$ the ion plasma frequency) and $a$ is the flux tube radius. It is shown that the stability of the MHD modes depends upon four parameters: the density contrast between the flux tube and its environment, the ratio of external and internal magnetic fields, the ratio $l_\mathrm{Hall}/a$, and the value of the Alfv\'en Mach number \textbf{defined as the ratio of the tube axial velocity to Alfv\'en speed inside the flux tube}. It is found that at high density contrasts, for small values of $l_\mathrm{Hall}/a$, the kink ($m = 1$) mode can become unstable against KH instability at some critical Alfv\'en Mach number (or equivalently at critical flow speed), but a threshold $l_\mathrm{Hall}/a$ can suppress the onset of the KH instability. At small density contrasts, however, the magnitude of $l_\mathrm{Hall}/a$ does not affect noticeably the condition for instability occurrence---even though it can reduce the critical Alfv\'en Mach number. It is established that the sausage mode ($m = 0$) is not subject to the KH instability.