Directed transport of suspended ferromagnetic nanoparticles under both gradient and uniform magnetic fields

Denisov, S. I.; Lyutyy, T. V.; Pavlyuk, M. O.

doi:10.1088/1361-6463/ab97da

Cited by 7 publications

(13 citation statements)

References 30 publications

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“…are the dimensionless characteristic frequencies arising from the uniform and gradient magnetic fields. We note that equations ( 8) and ( 9) generalize the corresponding equations derived in [31] for a time-independent gradient magnetic field. Equations ( 8) and ( 9), together with the initial conditions ϕ(0) = ϕ 0 ∈ [0, π] and r x (0) = r x0 ∈ (−∞, ∞), describe the coupled dynamics of the variables ϕ and r x .…”

Section: Model and Basic Equationsmentioning

confidence: 64%

“…By comparing (58) and (52), it is seen that |v 2 | |v 1 |. Surprisingly, according to (58), the maximum of the dimensional drift velocity, |V 2 | = 4M ga 2 /9πη (V 2 = Ωav 2 ), which is achieved in the harmonically oscillating gradient magnetic field, is close to the maximum velocity |V | = 2M ga 2 /9η in the case of the time-independent gradient magnetic field [31].…”

Section: Drift Velocity Far From the Originmentioning

confidence: 87%

“…These results, obtained in the second-order approximation in ν g and ν g |r x0 |, at ϕ 0 = 0, π are confirmed by the exact solutions (16). Note that, according to (31), the amplitude of the magnetization angle oscillations grows much more rapidly with increasing |r x0 | than the amplitude of the coordinate oscillations. For nanoparticles that are very far away from the origin, i.e., when ν g |r x0 | 1, formula (28) asymptotically reduces to the 2π-periodic step function…”

Section: Approximate Solutionsmentioning

confidence: 93%

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Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

Denisov,

Lyutyy,

Liutyi

2021

Preprint

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We study the nonlinear dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by a harmonically oscillating gradient magnetic field in the absence and presence of a static uniform magnetic field. Under some physically reasonable assumptions, we derive a coupled set of stiff ordinary differential equations for the magnetization angle and particle coordinate describing the rotational and translational motions of nanoparticles. Analytical solutions of these equations are determined for nanoparticles near and far from the coordinate origin, and their correctness is confirmed numerically. We show that if a uniform magnetic field is absent, the magnetization angle and particle coordinate of each nanoparticle are periodic functions of time. In contrast, the presence of a uniform magnetic field makes these functions aperiodic. In this case, we perform a detailed analysis of the nanoparticle dynamics and predict the appearance of the drift motion (directed transport) of nanoparticles. We calculate both analytically and numerically the drift velocity, study its dependence on time and model parameters, analyze the physical origin of the drift phenomenon and discuss its potential biomedical applications.

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Section: Model and Basic Equationsmentioning

confidence: 64%

Section: Drift Velocity Far From the Originmentioning

confidence: 87%

Section: Approximate Solutionsmentioning

confidence: 93%

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Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

Denisov,

Lyutyy,

Liutyi

2021

Preprint

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“…The joint action of the uniform and gradient magnetic fields induces both the rotational and translational motions. It has been shown [15] that nanoparticles subjected to timeindependent uniform and gradient magnetic fields can, depending on the initial particle positions, perform four regimes of their translational motion. But if nanoparticles are under the action of the uniform and timedependent gradient magnetic fields, then their dynamics becomes much more complex [16].…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Nanoparticle Dynamics in a Viscous Liquid: Deterministic Approach

Denisov

M.²,

Lyutyy³

et al. 2021

J. Nano- Electron. Phys.

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We study the deterministic dynamics of single-domain ferromagnetic nanoparticles in a viscous liquid induced by the joint action of the gradient and uniform magnetic fields. It is assumed that the gradient field depends on time harmonically and the uniform field has two components, perpendicular and parallel to the gradient one. We also assume that the anisotropy magnetic field is so strong that the nanoparticle magnetization lies along the anisotropy axis, i.e., the magnetization vector is 'frozen' into the particle body. With these assumptions and neglecting inertial effects we derive the torque and force balance equations that describe the rotational and translational motions of particles. We reduce these equations to a set of two coupled equations for the magnetization angle and particle coordinate, solve them numerically in a wide range of the system parameters and analyze the role of the parallel component of the uniform magnetic field. It is shown, in particular, that nanoparticles perform only periodic rotational and translational motions if the perpendicular component of the uniform magnetic field is absent. In contrast, the nanoparticle dynamics in the presence of this component becomes non-periodic, resulting in the drift motion (directed transport) of nanoparticles. By analyzing the short and long-time dependencies of the magnetization angle and particle coordinate we show that the increase in the parallel component of the uniform magnetic field decreases both the particle displacement for a fixed time and its average drift velocity on each period of the gradient magnetic field.

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“…Since the direction of motion and average velocity of nanoparticles can easily be controlled by external magnetic fields, the Magnus mechanism of directed transport could be used in drug delivery and separation applications. The model of "frozen" magnetization also allowed us to determine the transport properties of suspended nanoparticles subjected to a time-independent gradient magnetic field [13], which is often used in separation processes [14]. In the given work, we study analytically the coupled translational and rotational dynamics of such nanoparticles in a time-varying gradient magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Suspended Nanoparticles in a Time-varyingGradient Magnetic Field: Analytical Results

Denisov

Lyutyy²,

Liutyi³

2020

J. Nano- Electron. Phys.

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We study theoretically the deterministic dynamics of single-domain ferromagnetic nanoparticles in dilute ferrofluids, which is induced by a time-varying gradient magnetic field. Using the force and torque balance equations, we derive a set of the first-order differential equations describing the translational and rotational motions of such particles characterized by small Reynolds numbers. Since the gradient magnetic field generates both the translations and rotations of particles, these motions are coupled. Based on the derived set of equations, we demonstrate this fact explicitly by expressing the particle position through the particle orientation angle, and vice versa. The obtained expressions are used to show that the solution of the basic set of equations is periodic in time and to determine the intervals, where the particle coordinate and orientation angle oscillate. In addition, this set of equations is solved approximately for the case of small characteristic frequency of the particle oscillations. With this condition, we find that all particles perform small translational oscillations near their initial positions. In contrast, the orientation angle oscillates near the initial angle only if particles are located in the vicinity of zero point of the gradient magnetic field. The possible applications of the obtained results in biomedicine and separation processes are also discussed.

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Directed transport of suspended ferromagnetic nanoparticles under both gradient and uniform magnetic fields

Cited by 7 publications

References 30 publications

Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

Drift of suspended single-domain nanoparticles in a harmonically oscillating gradient magnetic field

Numerical Analysis of the Nanoparticle Dynamics in a Viscous Liquid: Deterministic Approach

Dynamics of Suspended Nanoparticles in a Time-varyingGradient Magnetic Field: Analytical Results

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