Paramagnetic Fluid Research Articles

Magnetothermal Rayleigh-Benard Convection of Paramagnetic Oxygen Gas in a Rotating Shallow Vertical Cylindrical Container

We carried out complete transient three-dimensional numerical computations to clarify the heat transfer rate characteristics of magnetothermal Rayleigh-Benard convection of paramagnetic oxygen gas in a rotating shallow vertical cylindrical container. When the container without rotation was fixed at the location where (gradB2)Z became minimum on the center line, the average Nusselt number of magnetothermal Rayleigh-Benard convection increased in comparison with that of Rayleigh-Benard convection. When the container with rotation was fixed at the same location, the average Nusselt number of rotating magnetothermal Rayleigh-Benard convection increased in comparison with that of magnetothermal Rayleigh-Benard convection for the specific rotational Reynolds number. Key Words: Rayleigh-Benard convection, Magnetothermal convection, Oxygen gas, Paramagnetic fluid, Rotating cylindrical container

Mixed convection by buoyancy and magnetothermal forces

The magnetic force in the paramagnetic fluid depends on the local gradient of magnetic flux density and the temperature-dependent magnetic susceptibility. In the presence of the gravity, the buoyant force due to the temperature difference additionally overlaps, and the resultant flow becomes a mixed convection. In this study, the effect of the temperature-dependent magnetic force (magnetothermal force) on the natural convection was numerically investigated. The magnetic field formed by the permanent-magnet array was employed and effective one was discussed in terms of the heat transfer. A three-dimensional Rayleigh-Benard convection simulation was conducted with the magnet array below the bottom hot wall. It was found that the magnetothermal force enhances the convection not only where the magnet locates but also away from the magnet due to the force profile.

Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid

The finite temperature version of the Vashishta-Singwi (VS) dielectric scheme for the paramagnetic warm dense uniform electron fluid is revisited correcting for an earlier thermodynamic derivative error. The VS scheme handles quantum mechanical effects at the level of the random phase approximation and treats correlations via the density expansion of a generalized Singwi-Tosi-Land-Sjölander (STLS) closure that inserts a parameter determined by enforcing the compressibility sum rule. Systematic comparison with quasiexact results, based on quantum Monte Carlo simulations, reveals a structural superiority of the VS scheme towards strong coupling and a thermodynamic superiority of the STLS scheme courtesy of a favorable cancellation of errors. Guidelines are provided for the construction of dielectric schemes that are expected to be more accurate but computationally costly. Published by the American Physical Society 2024

Stochastic simulation of magnetically controlled convection in porous media with random porosity via Karhunen-Loève expansion and intrusive polynomial chaos expansion

Understanding and quantifying uncertainty factors are crucial for accurately predicting thermomagnetic convection phenomena. This study presented a mathematical model and algorithm framework for uncertainty analysis of thermomagnetic convection in porous media with random porosity. The proposed method combined Karhunen-Loève expansion and intrusive polynomial chaos expansion to represent the input random parameters and output response, respectively. The Galerkin projection method was employed to decouple the stochastic governing equations of thermomagnetic convection into deterministic governing equations that can be efficiently solved using the finite volume method. By solving the polynomial chaos expansion of the output response and employing the stochastic projection method to solve the associated decoupled governing equations, the temporal evolution and statistical characteristics of the output response were obtained. The study revealed that porosity uncertainty in the porous medium affects the thermomagnetic convection of paramagnetic fluid, exhibiting significant chaos effects. Monte Carlo simulations were performed to validate the accuracy of the proposed approach and demonstrate its computational efficiency compared to traditional Monte Carlo methods. This research provides valuable insights into the uncertainty analysis of thermomagnetic convection and offers a promising methodology for analyzing heat transfer in various porous media applications.

Measuring magnetic force field distributions in microfluidic devices: Experimental and numerical approaches.

Precisely and accurately determining the magnetic force and its spatial distribution in microfluidic devices is challenging. Typically, magnetic microfluidic devices are designed in a way to both maximize the force within the separation region and to minimize the necessity for knowing such details-such as designing magnetic geometries that create regions of nearly constant magnetic force or that dictate the behavior of the magnetic force to be highly predictable in a specified region. In this work, we present a method to determine the spatial distribution of the magnetic force field in a magnetic microfluidic device by particle tracking magnetophoresis. Polystyrene microparticles were suspended in a paramagnetic fluid, gadolinium, and this suspension was exposed to various magnetic field geometries. Polystyrene particle motion was tracked using a microscope and images processed using Fiji (ImageJ). From a sample with a large spatial distribution of particle tracks, the magnetic force field distribution was calculated. The force field distribution was fitted to nonlinear spatial distribution models. These experimental models are compared to and supported by 3D simulations of the magnetic force field in COMSOL.

Wigner crystallization in quasi-one-dimensional quantum wire

We study the ground-state properties of quasi-one-dimensional paramagnetic electron fluid using variational quantum Monte Carlo method. The electrons are transversally confined using the harmonically regularized Coulomb potential with long range order. In this work we have investigated the crossover from liquid to crystalline phase in the finite width paramagnetic quantum wire. The calculated pair correlation function shows the oscillations of period 2r_text {s} a_0, where a_0 is the Bohr’s radius and r_text {s} is Wigner Seitz radius or electron-density parameter which corresponds to a k=4k_text {F} peak with k_text {F} being Fermi wave vector in the static structure factor at finite electron density. It is a signature of the onset of Wigner crystallization. It is found that the cross-over from liquid to a quasi-Wigner phase is due to enhancement of the electron correlation effects as r_text {s} increases or as the wire width b decreases.

Thermomagnetic convection induced in a temperature stratified state by a Halbach magnetic field

Convection induced by the permanent magnets of the linear Halbach array is numerically investigated and validated experimentally. The working fluid is a paramagnetic fluid that is weakly attracted to the magnet with temperature dependency. The fluid is filled in a rectangular enclosure and heated from the top and cooled from the bottom. The external magnetic field is applied from the top wall. Two-dimensional computations show that the Halbach magnet array can induce a strong thermomagnetic force widely in the fluid layer compared with the conventional alternate magnetic pole array. The upward flow is induced below the edges of the center magnet and then separated left and right along the top heated wall. The local Nusselt number shows a higher value and wider area than those by the conventional pole array. An experiment using the Halbach array kit is conducted and the obtained local Nusselt number profile agrees well with the computational data both qualitatively and quantitatively.

Wire-width and electron-density dependence of the crossover in the peak of the static structure factor from 2kF → 4kF in one-dimensional paramagnetic electron gases

We use the variational quantum Monte Carlo (VMC) method to study the wire-width $(b)$ and electron-density $({r}_{\text{s}})$ dependences of the ground-state properties of quasi-one-dimensional paramagnetic electron fluids. The onset of a quasi-Wigner crystal phase is known to depend on electron density and the crossover occurs in the low density regime. We study the effect of wire width on the crossover of the dominant peak in the static structure factor from $k=2{k}_{\text{F}}$ to $k=4{k}_{\text{F}}$. It is found that, for a fixed electron density, in the charge structure factor the crossover from the dominant peak occurring at $2{k}_{\text{F}}$ to $4{k}_{\text{F}}$ occurs as the wire width decreases. Our study suggests that the crossover is due to the interplay of both ${r}_{\text{s}}$ and $b<{r}_{\text{s}}$. The finite wire-width correlation effect is reflected in the peak height of the charge and spin structure factors. We fit the dominant peaks of the charge and spin structure factors assuming fit functions based on our finite wire-width theory and clues from bosonization, resulting in a good fit of the VMC data. The pronounced peaks in the charge and spin structure factors at $4{k}_{\text{F}}$ and $2{k}_{\text{F}}$, respectively, indicate the complete decoupling of the charge and spin degrees of freedom. Furthermore, the wire-width dependence of the electron correlation energy and the Tomonaga-Luttinger parameter ${K}_{\ensuremath{\rho}}$ is found to be significant.

Significantly Improved Separation Efficiency of Refractory Weakly Magnetic Minerals by Pulsating High-Gradient Magnetic Separation Coupling with Magnetic Fluid

High-gradient magnetic separation (HGMS) is indispensably applied in the rougher separation stage of refractory weakly magnetic minerals. The most difficult problem while processing refractory weakly magnetic minerals is the low selectivity of HGMS caused by the competing capture of magnetic valuable and gangue minerals. In this study, a paramagnetic fluid is introduced into HGMS and an innovative method, termed high-gradient magnetic separation coupling with magnetic fluid (HGMSCMF), with a significantly high selectivity is proposed. A new competing force (magnetic repulsive force) generated by the magnetic fluid will enlarge the force difference of valuable and gangue minerals and improve selectivity. The relative magnetic force acting on the magnetic valuable and gangue minerals can be adjusted by varying the fluid volume susceptibility, with the optimal fluid susceptibility approaching that of gangue minerals. HGMSCMF experiments on an ilmenite ore using paramagnetic MnCl2 solutions showed that the selectivity was remarkably improved by increasing MnCl2 concentrations (fluid susceptibility). The TiO2 grade and mass of magnetic products could be simultaneously improved by increasing the applied induction in HGMSCMF, whereas in conventional HGMS, the TiO2 grade and recovery decreased and increased, respectively. HGMSCMF is applicable to various matrices (or separators), and a significantly improved TiO2 grade (close to that of industrial concentrates) could be obtained with only one-stage HGMSCMF. The recycling of magnetic fluid and cost economy of HGMSCMF are also discussed and analyzed. HGMSCMF presents several advantages over conventional HGMS and has great application prospects for realizing the clean and efficient utilization of refractory weakly magnetic minerals or materials.

Low-density phase diagram of the three-dimensional electron gas

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter $r_\text{s} = 86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid. However there is a possible magnetic phase transition from an antiferromagnetic crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$.

MAGNETOTHERMAL CONVECTION ON THE THERMALLY STRATIFIED FLUID LAYER BY PERMANENT MAGNETS

Magnetothermal convection can be induced in paramagnetic fluid by temperature differences and the magnetic field. In this study, convection was studied both experimentally and numerically for the thermally stratified fluid layer attained by heating the top wall and cooling the bottom wall. When a single block magnet was placed above the top hot wall, convection was confirmed near the magnet edges. In the case of multiple magnets with alternating magnetic poles, convection was observed near the magnet junction(s) since the local magnetic force became stronger than that at the magnet edges. This effect depended on the number of magnets. A pair of block magnets with one junction induced a pair of vortex flows, in which the the local Nusselt number reached its maximum. In the case of three magnets, the two maxima of the local Nusselt number near the magnet junctions became smaller than that obtained in the two-magnet case. This was due to the weakened magnetothermal force that occurred by shifting the low-temperature region outward below the magnet junctions.

An Analysis of a Laminar-Turbulent Transition and Thermal Plumes Behavior in a Paramagnetic Fluid Subjected to an External Magnetic Field

Transition to turbulence and changes in the fluid flow structure are subjects of continuous analysis and research, especially for unique fields of research such as the thermo-magnetic convection of weakly magnetic fluids. Therefore, an experimental and numerical research of the influence of an external magnetic field on a natural convection’s fluid flow was conducted in the presented research. The experimental part was performed for an enclosure with a 0.5 aspect ratio, which was filled with a paramagnetic fluid and placed in a superconducting magnet in a position granting the enhancement of the flow. The process was recorded as temperature signals from the thermocouples placed in the analyzed fluid. The numerical research enabled an investigation based not only on temperature, but velocities as well. Experimental and numerical data were analyzed with the application of extended fast Fourier transform and wavelet analysis. The obtained results allowed the determination of changes in the nature of the flow and visualization of the influence of an imposed strong magnetic field on a magnetic fluid. It is proved that an applied magnetic field actuates the flow in Rayleigh-Benard convection and causes the change from laminar to turbulent flow for fairly low magnetic field inductions (2T and 3T for ΔT = 5 and 11 °C respectively). Fast Fourier transform allowed the definition of characteristic frequencies for oscillatory states in the flow, as well as an observation that the high values of magnetic field elongate the inertial range of the flow on the power spectrum density. Temperature maps obtained during numerical simulations granted visualizations of thermal plume formation and behavior with increasing magnetic field.

Non-uniform magnetic field impact on thermomagnetic convection of paramagnetic air in a permanent magnet-inserted horizontal annulus

Heat transfer enhancement using an external magnetic field with a high level of energy economy is a promising subject. The permanent magnets with no additional electrical power consumption are adopted to produce the applied magnetic fields. The effects of the magnet assembly and magnet strength on the thermomagnetic convection of paramagnetic fluid in a horizontal annulus are studied numerically by a finite volume method. The variations of the flow pattern, thermal structure and convective heat transfer characteristics are investigated to clarify the heat transfer rate characteristics of thermomagnetic convection of paramagnetic air induced by both magnetic and gravitational buoyant forces for cases of moderate- and large-gap annuli. The results showed that the thermomagnetic convection is significantly affected by the gap width of the annulus and the magnetic field gradient induced by the permanent magnet. The average heat transfer increases more than 150% when one magnet is placed. It can be attributed to the more efficient disturbance in the boundary layer and improves heat transfer greatly. A stronger magnetic field induced better mixing in the flow which increase the Nusselt number. In addition, reducing the gap width of the annulus can effectively enhance heat transfer.

Asymmetrical Thermal Boundary Condition Influence on the Flow Structure and Heat Transfer Performance of Paramagnetic Fluid-Forced Convection in the Strong Magnetic Field

Continuous interest in space journeys opens the research fields, which might be useful in non-terrestrial conditions. Due to the lack of the gravitational force, there will be a need to force the flow for mixing or heat transfer. Strong magnetic field offers the conditions, which can help to obtain the flow. In light of this origin, presented paper discusses the dually modified Graetz-Brinkman problem. The modifications were related to the presence of the magnetic field influencing the flow and asymmetrical thermal boundary condition. Dimensionless numerical analysis was performed, and two dimensionless numbers (magnetic Grashof number and magnetic Richardson number) were defined for paramagnetic fluid flow. The results revealed the heat transfer enhancement due to the strong magnetic field influence accompanied by possible but not essential flow structure modifications. On the other hand, the flow structure changes can be utilized to prevent the solid particles’ sedimentation. The explanation of the heat transfer enhancement including energy budget and vorticity distribution was presented.

Interfacial vs Bulk Phenomena Effects on the Surface Tensions of Aqueous Magnetic Surfactants in Uniform Magnetic Fields.

The literature clearly reports that magnetic surfactant systems respond to magnetic fields. This manuscript investigates if the responses are because the magnetic fields directly alter the interfacial properties or if the surface-active properties are independent of the paramagnetic fluid responses. It uses uniform and gradient magnetic fields to determine the magnetically induced changes to the surface tensions independent of bulk paramagnetic fluid effects for ionic magnetic surfactants. The magnetically induced decrease in surface tensions is small compared to the bulk paramagnetic fluid effects. The reported decrease in surface tensions is significantly smaller than those previously found in the literature, which reported a combined interfacial and bulk paramagnetic effect. The magnetically induced surface tension changes are a function of the degree of association, α, of the magnetic moiety with the surfactant's amphiphilic structure. Therefore, the proposed answer to the question is that as α approaches zero, the magnetic properties of the magnetic surfactant system approaches the behavior of an ordinary paramagnetic fluid. For magnetic surfactants with α approaching one, there is a measurable interfacial response. For example in this study, a magnetic surfactant with α = 0.92 had a 2.5 times greater magnetically induced change in surface tension compared to a magnetic surfactant with α = undetectable, even thought they had similar magnetic moments.

Three-dimensional printing of diamagnetic microparticles in paramagnetic and diamagnetic media

We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

Resonant enhancement of thermomagnetic convection of paramagnetic fluid in an enclosure due to time-periodic magnetizing force

A numerical study is performed to demonstrate the thermomagnetic convection of air in a side-wall heated enclosure under constant gravity and time-periodic magnetizing force formed by current with sinusoidal waveform. Two cases have been considered: electric coil is located at the right side of the enclosure in case 1, and in case 2 the electric coil is below the enclosure. The spectral element method is applied to obtain the numerical solutions from the time-dependent Navier-Stokes equations including the magnetizing force term. The computed results show the existence of resonance, which is characterized by the maximum fluctuation of heat transfer in the interior. And the resonance phenomenon becomes more distinctive as Ra increases. Details of fluid flow and heat transfer under resonance is scrutinized by examining the evolution of oscillating components. The results indicate that case 1 exhibits advantages in using resonance to enhance the heat transfer rate, where a smaller magnetic strength is employed to simultaneously obtain larger fluctuations of fluid flow and heat transfer.

Rayleigh-Bénard Convection of Paramagnetic Liquid under a Magnetic Field from Permanent Magnets

The convection control is important in terms of the heat transfer enhancement and improvement of the applied devices and resultant products. In this study, the convection control by a magnetic field from block permanent magnets is numerically investigated on the Rayleigh-Bénard convection of paramagnetic fluid. To enhance the magnetic force from the available permanent magnets, pairs of alternating-pole magnets are employed and aligned near the bottom heated wall. The lattice Boltzmann method is employed for the computation of the heat and fluid flow with the consideration of buoyancy and magnetothermal force on the working fluid. It is found that, since the magnetic force at the junction of pair magnets becomes strong remarkably and in the same direction as the gravity, descending convection flow is locally enhanced and the pair of symmetrical roll cells near the magnet junction becomes longitudinal. The local heat transfer corresponds to the affected roll cell pattern; locally enhanced at the magnet junctions and low heat transfer area is shifted aside the magnet outer edge. The averaged Nusselt number on the hot wall also increases proportionally to the magnetic induction but it is saturated at high magnetic induction. This suggests the roll cell pattern is no more largely affected at extremely-high magnetic induction.

Natural convection of paramagnetic fluid along a vertical heated wall under a magnetic field from a single permanent magnet

The natural convection of a paramagnetic fluid is numerically investigated in the presence of a magnetic field from a block permanent magnet. One vertical wall of a cavity is partially heated at a constant heat flux to consider a single vertical heated wall. The permanent block magnet is placed behind the heated wall, of which the magnetic field is numerically obtained. Since the magnetic force is remarkable at edges of the block magnet, the magnetothermal force is also pronounced if the temperature difference exists by wall heating. The overlapping magnetothermal force works to repel the fluid. This results in the heat transfer enhancement near the upper magnet edge, and suppression near the lower magnet edge. The suppressing effect becomes remarkable rather than the enhancing one in cases of large magnetic induction, high wall heat flux, and high magnet elevation to the heated wall.

Inversion of flow and heat transfer of the paramagnetic fluid in a differentially heated cube

The present study addresses the detailed numerical analysis of the flow and heat transfer of a paramagnetic fluid inside a differentially heated cubical box and subjected to a strong non-uniform magnetic field. Two different heating scenarios are considered regarding an initial thermal stratification: unstable (heated from the bottom) and stable (heated from the top), both subjected to the same magnetic field. For a fixed value of the thermal Rayleigh number (Ra=1.4×105) integral heat transfer is measured over a range of imposed magnetic fields, 0 ≤ |b0|max ≤ 10 T. To obtain detailed insights into local wall-heat transfer and its dependency on the flow patterns generated, numerical simulations of the experimental setup are performed. A relatively good agreement between experiments and numerical simulations is obtained in predicting the integral heat transfer (with an averaged ΔNu¯<7% over the entire range of working parameters for both heating configurations). It is demonstrated that a strong convective motion can be generated under the influence of the magnetization force even for the heated-from-above situation that initially was in the pure conduction state. This magnetically assisted (heated from the bottom) and magnetically inverted (heated from the top) Rayleigh-Bénard convection produced up to 5 and 15 times more efficient heat transfer compared to the initial neutral situation, respectively.