Simulating magnetic nanoparticle behavior in low-field MRI under transverse rotating fields and imposed fluid flow

In the presence of alternating-sinusoidal or rotating magnetic fields, magnetic nanoparticles will act to realign their magnetic moment with the applied magnetic field. The realignment is characterized by the nanoparticle's time constant, τ. As the magnetic field frequency is increased, the nanoparticle's magnetic moment lags the applied magnetic field at a constant angle for a given frequency, Ω, in rad s⁻¹. Associated with this misalignment is a power dissipation that increases the bulk magnetic fluid's temperature which has been utilized as a method of magnetic nanoparticle hyperthermia, particularly suited for cancer in low-perfusion tissue (e.g., breast) where temperature increases of between 4 and 7 °C above the ambient in vivo temperature cause tumor hyperthermia. This work examines the rise in the magnetic fluid's temperature in the MRI environment which is characterized by a large DC field, B₀. Theoretical analysis and simulation is used to predict the effect of both alternating-sinusoidal and rotating magnetic fields transverse to B₀. Results are presented for the expected temperature increase in small tumors ( radius) over an appropriate range of magnetic fluid concentrations (0.002-0.01 solid volume fraction) and nanoparticle radii (1-10 nm). The results indicate that significant heating can take place, even in low-field MRI systems where magnetic fluid saturation is not significant, with careful the goal of this work is to examine, by means of analysis and simulation, the concept of interactive fluid magnetization using the dynamic behavior of superparamagnetic iron oxide nanoparticle suspensions in the MRI environment. In addition to the usual magnetic fields associated with MRI, a rotating magnetic field is applied transverse to the main B₀ field of the MRI. Additional or modified magnetic fields have been previously proposed for hyperthermia and targeted drug delivery within MRI. Analytical predictions and numerical simulations of the transverse rotating magnetic field in the presence of B₀ are investigated to demonstrate the effect of Ω, the rotating field frequency, and the magnetic field amplitude on the fluid suspension magnetization. The transverse magnetization due to the rotating transverse field shows strong dependence on the characteristic time constant of the fluid suspension, τ. The analysis shows that as the rotating field frequency increases so that Ωτ approaches unity, the transverse fluid magnetization vector is significantly non-aligned with the applied rotating field and the magnetization's magnitude is a strong function of the field frequency. In this frequency range, the fluid's transverse magnetization is controlled by the applied field which is determined by the operator. The phenomenon, which is due to the physical rotation of the magnetic nanoparticles in the suspension, is demonstrated analytically when the nanoparticles are present in high concentrations (1-3% solid volume fractions) more typical of hyperthermia rather than in clinical imaging applications, and in low MRI field strengths (such as open MRI systems), where the magnetic nanoparticles are not magnetically saturated. The effect of imposed Poiseuille flow in a planar channel geometry and changing nanoparticle concentration is examined. The work represents the first known attempt to analyze the dynamic behavior of magnetic nanoparticles in the MRI environment including the effects of the magnetic nanoparticle spin-velocity. It is shown that the magnitude of the transverse magnetization is a strong function of the rotating transverse field frequency. Interactive fluid magnetization effects are predicted due to non-uniform fluid magnetization in planar Poiseuille flow with high nanoparticle concentrations.     

A one-dimensional fluid simulation of a magnetized DC discharge including the non-uniform effects of the magnetic field

A one-dimensional simulation of a magnetized DC discharge is conducted based on the fluid equations that consider the non-uniform effects of the magnetic field. We apply a dielectric relaxation scheme (DRS) as an efficient numerical algorithm that was recently developed for simulation of low-temperature process plasmas. The simulation results, such as the spatial profiles of ion densities, electron densities, electron fluxes, and electric fields, are compared with the simulation results for which the non-uniform effects of the magnetic field are neglected.     

Simulation of induction at low magnetic Prandtl number

We consider the induction of a magnetic field in flows of an electrically conducting fluid at low magnetic Prandtl number and large kinetic Reynolds number. Using the separation between the magnetic and kinetic diffusive length scales, we propose a new numerical approach. The coupled magnetic and fluid equations are solved using a mixed scheme, where the magnetic field fluctuations are fully resolved and the velocity fluctuations at small scale are modeled using a large eddy simulation (LES) scheme. We study the response of a forced Taylor-Green flow to an externally applied field: topology of the mean induction and time fluctuations at fixed locations. The results are in remarkable agreement with existing experimental data; a global 1/f behavior at long times is also evidenced.     

Simulation of the External Magnetic Field Effect on Fusion Plasma

Issues of numerical simulation of an experiment on compression and heating of a target in a magnetic field are discussed. It is found that the applied magnetic field predominantly increases the plasma lifetime and plasma jet characteristics (velocity, Mach number, density, etc.). An analysis of the effects of the application of an external magnetic field on the behavior of plasma-driven guns (plasma jets) and laser-driven systems (laser beams) is carried out. Thermodynamic questions in simulation of experiments on magnetic inertial synthesis are touched upon.     

Numerical study of magnetic nanoparticles concentration in biofluid (blood) under influence of high gradient magnetic field

Ferrofluids are widely used in pharmaceutical industries as magnetic separation tools, anti-cancer drug carriers and micro-valve applications. The purpose of the current study is to investigate the effect of a magnetic field on the volume concentration of magnetic nanoparticles of a non-Newtonian biofluid (blood) as a drug carrier. The effect of particles on the flow field is considered. The governing non-linear differential equations, concentration and Naviar-stokes are coupled with the magnetic field. To solve these equations, a finite volume based code is developed and utilized. The results show accumulation of magnetic nanoparticles near the magnetic source until it looks like a solid object. The accumulation of nanoparticles is due to the magnetic force that overcomes the fluid drag force. As the magnetic strength and size of the magnetic particles increase, the accumulation of nanoparticles increases, as well. The magnetic susceptibility of particles also affects the flow field and the contour of the concentration considerably.     

Thermomagnetic natural convection of thermo-sensitive magnetic fluids in cubic cavity with heat generating object inside

Experiment and numerical study were conducted to investigate the heat transfer characteristics of a thermo-sensitive magnetic fluid (TSMF) filled in a cubic container with a heat generating square cylinder stick inside and under a uniform magnetic field. The experimental results show that, regardless of the heat generating object sizes, the heat transfer characteristic of the TSMF is enhanced when the magnetic field is applied to the TSMF. However, the heat transfer of the TSMF becomes poor as the size of the inside heat generating object increases because the space where the fluids go through becomes narrower and the flow is obstructed when the heat generating object size becomes bigger. Numerical simulation based on the Lattice Boltzmann method confirmed the experimental findings, and disclosed more flow details of the natural convection of the TSMF inside cavity.     

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为了提高等离子体废物处理效率,根据磁流体动力学理论,利用计算流体力学软件FLUENT,采用磁矢量势的方法对直流双阳极非转移型电弧等离子体炬进行了二维轴对称数值模拟。计算中采用了SIMPLE算法。数值模拟得到了等离子体的温度、速度等分布。结果表明,等离子体的温度随着轴向距离的增加而减小,随弧电流增加而增加;其速度随着轴向距离的增加而先增大后减小,随弧电流增加而增加;等离子体炬出口处的温度和速度随着径向距离的增加而减小。这些结果与实验结果基本相符。     

Characteristics of Dust Plasma Sheath in an Oblique Magnetic Field

The characteristics of dust plasma sheath in an oblique magnetic field are investigated with a fluid model. Hot electrons, cold ions, neutral particles, and dust grains are taken into account in this system. We perform a numerical simulation of the sheath. The results reveal that the magnetic field has significant effects on the sheath structure, and it also makes the suspension position of dust shift away from the wall.     

CFD simulation of the magnetophoretic separation in a microchannel

The CFD simulation of the separation of labeled biospecies from a native fluid flowing through a planar microchannel, mediated by a magnetic field is presented in this study. The fluid flow, coupled with Eulerian advection-convection concentration equation, is utilized to model the transport of the magnetic biospecies. A moderate-gradient magnetic field caused accumulation of the magnetic labeled species in the vicinity of the higher magnetic field region. The re-distribution of the magnetically labeled species in the region close to the highest magnetic field zone presents a scheme for the focusing or collection of these species from the heterogeneous samples under the simulation conditions. The magnetic-fluidic interactions and interplay between the magnetophoretic mass transfer and molecular diffusion for different throughputs are analyzed. The study found out that the axial magnetic forces, created from a dipole-like magnetic field, is playing a major role in the vortex formation, and this complements the downward vertical force in confining the particles to a small region near the point with the highest magnetic strength. Also, the study predicts that the generated viscous shear stress levels in the interior region of the channel provide a safe transport mechanism for the biological cells in the solution.     

Numerical analysis of the averaged flow field in a turbulent lattice Boltzmann simulation

A direct numerical simulation of a turbulent flow field with a lattice BGK method is presented. A spatial coarse graining of the numerical results is compared with the expected LBGK dynamics for a flow field on a reduced lattice size. This comparison permits to exhibit subgrid properties of the fluid which are not resolved on the coarse lattice. As expected from existing subgrid models, an effective viscosity can be measured that increases when the lattice is coarse grained. Turbulence models based on an effective viscosity are particularly interesting in a lattice Boltzmann simulation, due to the linearity of the propagation operator.     

磁流体粘度的实验研究

采用毛细法粘度计测量了水基Fe磁流体的粘度,分析了磁性粒子份额、表面活性剂含量以及外加磁场强度和方向对粘度的影响。实验结果表明,磁流体粘度随着磁性粒子和表面活性剂浓度的增加而增加;随着外加磁场强度的增大而增大,对于相同的磁流体,在外加磁场方向垂直于流动方向时的粘度大于外加磁场方向平行于流动方向时的粘度;表面活性剂含量的增大将减弱外加磁场对磁流体粘度的影响。     

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将等离子体作为磁流体,考虑其流体属性和电磁属性,介绍了利用FLUENT软件包并将其进行二次开发,解算电磁场方程、质量连续性方程、动量守恒方程、以及能量守恒方程的数值模拟方法,得到了以磁矢势为表达形式的电磁场分布、温度分布和速度分布.数值模拟了粉末球化所用的感应耦合等离子体炬电磁场分布、温度分布、速度分布.分析了温度分布、速度分布产生的物理原因,为感应耦合等离子体炬球化粉末颗粒提供理论性指导.     

Transport barrier inside the reversal surface in the chaotic regime of the reversed-field pinch

Magnetic field lines and the corresponding particle orbits are computed for a typical chaotic magnetic field provided by a magnetohydrodynamics numerical simulation of the reversed-field pinch. The m = 1 modes are phase locked and produce a toroidally localized bulging of the plasma which increases particle transport. The m = 0 and m = 1 modes produce magnetic chaos implying poor confinement. However, they also allow for the formation of magnetic islands which induce transport barriers inside the reversal surface.     

非均匀磁场中磁流体热磁对流的实验研究

建立了测量非均匀磁场条件下圆柱腔体内磁流体热磁对流特性的实验系统,实验结果显示,磁流体热磁对流特性受磁场强度、温差以及磁场梯度方向与温度梯度方向之间关系的控制,当磁场梯度方向与温度梯度方向一致时,外加磁场强化了磁流体的热磁对流过程,且随着磁场强度和温差的增大,热磁对流强度加强。当磁场梯度方向、温度梯度方向以及重力方向三者相同时,磁流体的热磁对流强度最剧烈。     

润湿性及磁场对液态金属自由表面膜流流动状态的影响

通过数值模拟及实验研究了润湿性及磁场对液态金属膜流流动状态的影响。首先,通过数值模拟研究了润湿性对膜流流动状态的影响。结果表明,当润湿性不好时,液态金属膜流容易发展为溪状流而不能完全覆盖底壁,入口膜厚较薄时更易发展为溪状流;在入口膜厚及其它情况相同时,密度越小越易发展为溪状流。其次,研究了磁场对膜流流动状态的影响。结果表明,槽道与流体润湿性不好时,有磁场情况下液态金属膜流覆盖底壁的区域较无磁场时增加,强磁场对膜流的湍流有抑制作用。最后,液态金属膜流实验结果表明,润湿性不好时,镓铟锡合金膜流容易收缩发展为溪状流,这与数值模拟的结果是一致的。上述研究结果对磁约束聚变堆液态第一壁的设计具有指导意义。     

Direct numerical simulation of the turbulent MHD channel flow at low magnetic Reynolds number for electric correlation characteristics

Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.     

Computer simulation of spectrometer magnets for some experimental installations

The significance of numerical simulation in the research of magnetic systems is determined by not only known advantages of the computing experiment, but also by the fact that the measurement of a magnetic field is a labour-consuming and expensive problem. Mathematical simulation allows one to investigate those parts of the magnet’s design where the measurements of the magnetic field are extremely complicated or even impossible. This work is aimed to generalize experience of the mathematical simulation of magnetic systems of various-type physical and electromechanical installations and to work out some recommendations of the optimal use of some software products for the numerical modeling of magnetostatic problems. This work also presents some results of a numerical analysis of the magnetic systems of the JINR’s physical installation MARUSYA with the purpose of studying an opportunity of designing magnetic systems with predetermined characteristics of the magnetic field. The article is published in the original.     

Experimental study and CFD simulation of rotational eccentric cylinder in a magnetorheological fluid

In this study, a magnetorheological (MR) fluid is prepared using carbonyl iron filings and low viscosity lubricating oil. The effects of magnetic field and weight percentage of particles on the viscosity of the MR fluid have been measured using a rotational viscometer. The yield stress under an applied magnetic field was also obtained experimentally. In the absence of an applied magnetic field, the MR fluid behaves as a Newtonian fluid. When the magnetic field is applied, the MR fluid behaves like Bingham plastics with a magnetic field dependent yield stress. Afterward, the results compared with those of CFD simulation of two eccentric cylinders in the MR fluid. Results show that the influences of MR effects, caused by the applied magnetic field, on the model characteristics are significant and not negligible. The viscosity is enhanced by increasing of the magnetic field, eccentricity ratio and weight percentage of suspensions. The MR effects and increasing of weight percentage and eccentricity ratio also provide an enhancement in the yield stresses and required total torque for rotation of inner cylinder. Also the simulation results indicate a good representation of the experiment by the model.     

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通过数值模拟及实验研究了润湿性及磁场对液态金属膜流流动状态的影响.首先,通过数值模拟研究了润湿性对膜流流动状态的影响.结果表明,当润湿性不好时,液态金属膜流容易发展为溪状流而不能完全覆盖底壁,入口膜厚较薄时更易发展为溪状流;在入口膜厚及其它情况相同时,密度越小越易发展为溪状流.其次,研究了磁场对膜流流动状态的影响.结果表明,槽道与流体润湿性不好时,有磁场情况下液态金属膜流覆盖底壁的区域较无磁场时增加,强磁场对膜流的湍流有抑制作用.最后,液态金属膜流实验结果表明,润湿性不好时,镓铟锡合金膜流容易收缩发展为溪状流,这与数值模拟的结果是一致的.上述研究结果对磁约束聚变堆液态第一壁的设计具有指导意义.     

两个非磁性颗粒在磁流体中的沉降现象研究

在磁场作用下,在磁流体里添加非磁性颗粒(non-magnetic particles,NPs),可以使得NPs形成不同的结构,操控NPs的运动从而影响磁流体的特性,这种应用逐渐受到了研究者的关注.为了更好地操控磁流体里NPs的运动,本文采用一种多物理模型研究在外加磁场作用下,磁流体中两个NPs沉降的运动过程.其中,用格子玻尔兹曼方法模拟磁流体的运动,外加磁场对磁流体的影响用一种自修正方法求解泊松方程,这个自修正方法可以使欧姆定律满足守恒定律.NPs之间的偶极干扰力采用偶极力模型,同时采用一种相对过渡平滑的共轭边界条件处理NPs与磁流体交界面的流固干扰以避免磁场密度过渡的突变.本文主要探究两个NPs在磁流体中的沉降,揭示磁场作用下NPs的相互干扰原理;同时,对控制NPs运动时的参数进行调节,得到NPs不同的运动轨迹,达到操控颗粒运动的目的.本研究可对NPs在磁流体中的应用提供定量的分析结果,对NPs在工业上的应用提供有力的理论支撑.