Thermal ratchet effects in ferrofluids

Temperature effects on drift of suspended single-domain particles induced by the Magnus force

We study the temperature dependence of the drift velocity of single-domain ferromagnetic particles induced by the Magnus force in a dilute suspension. A set of stochastic equations describing the translational and rotational dynamics of particles is derived, and the particle drift velocity that depends on components of the average particle magnetization is introduced. The Fokker-Planck equation for the probability density of magnetization orientations is solved analytically in the limit of strong thermal fluctuations for both the planar rotor and general models. Using these solutions, we calculate the drift velocity and show that the out-of-plane fluctuations of magnetization, which are not accounted for in the planar rotor model, play an important role. In the general case of arbitrary fluctuations, we investigate the temperature dependence of the drift velocity by numerically simulating a set of effective stochastic differential equations for the magnetization dynamics.

Smart Fluid Systems: The Advent of Autonomous Liquid Robotics

Organic, inorganic or hybrid devices in the liquid state, kept in a fixed volume by surface tension or by a confining membrane that protects them from a harsh environment, could be used as biologically inspired autonomous robotic systems with unique capabilities. They could change shape according to a specific exogenous command or by means of a fully integrated adaptive system, and provide an innovative solution for many future applications, such as space exploration in extreme or otherwise challenging environments, post-disaster search and rescue in ground applications, compliant wearable devices, and even in the medical field for in vivo applications. This perspective provides an initial assessment of existing capabilities that could be leveraged to pursue the topic of "Smart Fluid Systems" or "Liquid Engineered Systems".

Low drive field amplitude for improved image resolution in magnetic particle imaging

PURPOSE

Magnetic particle imaging (MPI) is a new imaging technology that directly detects superparamagnetic iron oxide nanoparticles. The technique has potential medical applications in angiography, cell tracking, and cancer detection. In this paper, the authors explore how nanoparticle relaxation affects image resolution. Historically, researchers have analyzed nanoparticle behavior by studying the time constant of the nanoparticle physical rotation. In contrast, in this paper, the authors focus instead on how the time constant of nanoparticle rotation affects the final image resolution, and this reveals nonobvious conclusions for tailoring MPI imaging parameters for optimal spatial resolution.

METHODS

The authors first extend x-space systems theory to include nanoparticle relaxation. The authors then measure the spatial resolution and relative signal levels in an MPI relaxometer and a 3D MPI imager at multiple drive field amplitudes and frequencies. Finally, these image measurements are used to estimate relaxation times and nanoparticle phase lags.

RESULTS

The authors demonstrate that spatial resolution, as measured by full-width at half-maximum, improves at lower drive field amplitudes. The authors further determine that relaxation in MPI can be approximated as a frequency-independent phase lag. These results enable the authors to accurately predict MPI resolution and sensitivity across a wide range of drive field amplitudes and frequencies.

CONCLUSIONS

To balance resolution, signal-to-noise ratio, specific absorption rate, and magnetostimulation requirements, the drive field can be a low amplitude and high frequency. Continued research into how the MPI drive field affects relaxation and its adverse effects will be crucial for developing new nanoparticles tailored to the unique physics of MPI. Moreover, this theory informs researchers how to design scanning sequences to minimize relaxation-induced blurring for better spatial resolution or to exploit relaxation-induced blurring for MPI with molecular contrast.

Rotational properties of ferromagnetic nanoparticles driven by a precessing magnetic field in a viscous fluid

We study the deterministic and stochastic rotational dynamics of ferromagnetic nanoparticles in a precessing magnetic field. Our approach is based on the system of effective Langevin equations and on the corresponding Fokker-Planck equation. Two key characteristics of the rotational dynamics, namely the average angular frequency of precession of nanoparticles and their average magnetization, are of interest. Using the Langevin and Fokker-Planck equations, we calculate both analytically and numerically these characteristics in the deterministic and stochastic cases, determine their dependence on the model parameters, and analyze in detail the role of thermal fluctuations.

Rotational ratchets with dipolar interactions

We report results from a computer simulation study on the rotational ratchet effect in systems of magnetic particles interacting via dipolar interactions. The ratchet effect consists of directed rotations of the particles in an oscillating magnetic field, which lacks a net rotating component. Our investigations are based on Brownian dynamics simulations of such many-particle systems. We investigate the influence of both the random and deterministic contributions to the equations of motion on the ratchet effect. As a main result, we show that dipolar interactions can have an enhancing as well as a dampening effect on the ratchet behavior depending on the dipolar coupling strength of the system under consideration. The enhancement is shown to be caused by an increase in the effective field on a particle generated by neighboring magnetic particles, while the dampening is due to restricted rotational motion in the effective field. Moreover, we find a nontrivial influence of the short-range, repulsive interaction between the particles.

Relaxation in x-space magnetic particle imaging

Magnetic particle imaging (MPI) is a new imaging modality that noninvasively images the spatial distribution of superparamagnetic iron oxide nanoparticles (SPIOs). MPI has demonstrated high contrast and zero attenuation with depth, and MPI promises superior safety compared to current angiography methods, X-ray, computed tomography, and magnetic resonance imaging angiography. Nanoparticle relaxation can delay the SPIO magnetization, and in this work we investigate the open problem of the role relaxation plays in MPI scanning and its effect on the image. We begin by amending the x-space theory of MPI to include nanoparticle relaxation effects. We then validate the amended theory with experiments from a Berkeley x-space relaxometer and a Berkeley x-space projection MPI scanner. Our theory and experimental data indicate that relaxation reduces SNR and asymmetrically blurs the image in the scanning direction. While relaxation effects can have deleterious effects on the MPI scan, we show theoretically and experimentally that x-space reconstruction remains robust in the presence of relaxation. Furthermore, the role of relaxation in x-space theory provides guidance as we develop methods to minimize relaxation-induced blurring. This will be an important future area of research for the MPI community.

Experimental investigation of a Brownian ratchet effect in ferrofluids

We test experimentally a Brownian ratchet system suggested by Engel [Phys. Rev. Lett. 91, 060602 (2003)]. This ratchet system is based on a magnetic fluid that contains nanometer sized magnetic particles in a thermal bath of carrier fluid. An external static magnetic field and, perpendicular to it, an oscillatory magnetic field act on the ferrofluid particles; the total magnetic field contains no rotating component. The directed effective rotation of the particles due to the ratchet effect induces a macroscopic torque density of the fluid. The torque on a spherical ferrofluid sample is measured in dependence on the field parameters. A quantitative comparison with predictions from a microscopic and a phenomenological model are given. Both models describe certain aspects of the measurements correctly, but qualitative discrepancies between both models and experiment are found, particularly in the high-frequency range.

Vortex and translational currents due to broken time-space symmetries

We consider the classical dynamics of a particle in a (d=2,3)-dimensional space-periodic potential under the influence of time-periodic external fields with zero mean. We perform a general time-space symmetry analysis and identify conditions, when the particle will generate a nonzero averaged translational and vortex currents. We perform computational studies of the equations of motion and of corresponding Fokker-Planck equations, which confirm the symmetry predictions. We address the experimentally important issue of current control. Cold atoms in optical potentials and magnetic traps are among possible candidates to observe these findings experimentally.

Brownian gyrator: a minimal heat engine on the nanoscale

A Brownian particle moving in the vicinity of a generic potential minimum under the influence of dissipation and thermal noise from two different heat baths is shown to act as a minimal heat engine, generating a systematic torque onto the physical object at the origin of the potential and an opposite torque onto the medium generating the dissipation.

Role of interactions in ferrofluid thermal ratchets

Orientational fluctuations of colloidal particles with magnetic moments may be rectified with the help of external magnetic fields with suitably chosen time dependence. As a result a noise-driven rotation of particles occurs giving rise to a macroscopic torque per volume of the carrier liquid. We investigate the influence of mutual interactions between the particles on this ratchet effect by studying a model system with mean-field interactions. The stochastic dynamics may be described by a nonlinear Fokker-Planck equation for the collective orientation of the particles which we solve approximately by using the effective field method. We determine an interval for the ratio between coupling strength and noise intensity for which a self-sustained rectification of fluctuations becomes possible. The ratchet effect then operates under conditions for which it was impossible in the absence of interactions.

Thermal Ratchet Effect in a Rotating Ferrofluid

Rotational Brownian motion of a colloidal magnetic particle in a ferrofluid under the influence of an external magnetic field may give rise to a noise induced rotation of the particle due to the rectification of thermal fluctuations. Via viscous coupling the associated angular momentum is transferred to the carrier liquid and can be measured as a macroscopic torque. In the present contribution we study the case of a rotating ferrofluid and elucidate the interplay between the ratchet effect and the non-zero vorticity of the flow.