Anisotropy of magnetoviscous effect in structure-forming ferrofluids

Simulating the flow of interacting ferrofluids with multiparticle collision dynamics

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

Multiparticle Collision Dynamics for Ferrofluids

Detailed studies of the intriguing field-dependent dynamics and transport properties of confined flowing ferrofluids require efficient mesoscopic simulation methods that account for fluctuating ferrohydrodynamics. Here, we propose such a new mesoscopic model for the dynamics and flow of ferrofluids, where we couple the multi-particle collision dynamics method as a solver for the fluctuating hydrodynamics equations to the stochastic magnetization dynamics of suspended magnetic nanoparticles. This hybrid model is validated by reproducing the magnetoviscous effect in Poiseuille flow, obtaining the rotational viscosity in quantitative agreement with theoretical predictions. We also illustrate the new method for the benchmark problem of flow around a square cylinder. Interestingly, we observe that the length of the recirculation region is increased whereas the drag coefficient is decreased in ferrofluids when an external magnetic field is applied, compared with the field-free case at the same effective Reynolds number. The presence of thermal fluctuations and the flexibility of this particle-based mesoscopic method provides a promising tool to investigate a broad range of flow phenomena of magnetic fluids and could also serve as an efficient way to simulate solvent effects when colloidal particles are immersed in ferrofluids.

On the yielding of a point-defect-rich model crystal under shear: insights from molecular dynamics simulations

In real crystals and at finite temperatures point defects are inevitable. Under shear their dynamics severely influence the mechanical properties of these crystals, giving rise to non-linear effects, such as ductility. In an effort to elucidate the complex behavior of crystals under plastic deformation it is crucial to explore and to understand the interplay between the timescale related to the equilibrium point-defect diffusion and the shear-induced timescale. Based on extensive non-equilibrium molecular dynamics simulations we present a detailed investigation on the yielding behavior of cluster crystals, an archetypical model for a defect-rich crystal: in such a system clusters of overlapping particles occupy the lattice sites of a regular (FCC) structure. In equilibrium particles diffuse via site-to-site hopping while maintaining the crystalline structure intact. We investigate these cluster crystals at a fixed density and at different temperatures where the system remains in the FCC structure: temperature allows us to vary the diffusion timescale appropriately. We then expose the crystal to shear, thereby choosing shear rates which cover timescales that are both higher and lower than the equilibrium diffusion timescales. We investigate the macroscopic and microscopic response of our cluster crystal to shear and find that the yielding scenario of such a system does not rely on the diffusion of the particles - it is rather related to the plastic deformation of the underlying crystalline structure. The local bond order parameters and the measurement of local angles between neighboring clusters confirm the cooperative movement of the clusters close to the yield point. Performing complementary, related simulations for an FCC crystal formed by harshly repulsive particles reveals similarities in the yielding behavior between both systems. Still we find that the diffusion of particles does influence characteristic features in the cluster crystal, such as a less prominent increase of order parameters close to the yield point. Our simulations provide for the first time an insight into the role of the diffusion of defects in the yielding behavior of a defect-rich crystal under shear. These observations will thus be helpful in the development of theories for the plastic deformation of defect-rich crystals.

Structure and rheology of soft hybrid systems of magnetic nanoparticles in liquid-crystalline matrices: results from particle-resolved computer simulations

Hybrid mixtures composed of magnetic nanoparticles (MNP) in liquid crystalline (LC) matrices are a fascinating class of soft materials with intriguing physical properties and a wide range of potential applications, e.g., as stimuli-responsive and adaptive materials. Already in the absence of an external stimulus, these systems can display various types of orientationally disordered and ordered phases, which are enriched by self-assembled structures formed by the MNPs. In the presence of external fields, one typically observes highly nonlinear macroscopic behavior. However, an understanding of the structure and dynamics of such systems on the particle level has, so far, remained elusive. In the present paper we review recent computer simulation studies targeting the structure, equilibrium dynamics and rheology of LC-MNP systems, in which the particle sizes of the two components are comparable. As a numerically tractable model system we consider mixtures of soft spherical or elongated particles with a permanent magnetic dipole moment and ellipsoidal non-magnetic particles interacting via a Gay-Berne potential. We address, first, equilibrium aspects such as structural organization and self-assembly (cluster formation) of the MNPs in dependence of the orientational state of the matrix, the role of the size ratio, the impact of an external magnetic field, and the translational and orientational diffusion of the two components. Second, we discuss the non-equilibrium dynamics of LC-MNP mixtures under planar shear flow, considering both, spherical and non-spherical MNPs. Our results contribute to a detailed understanding of these intriguing hybrid materials, and they may serve as a guide for future experiments.

Chain Formation and Phase Separation in Ferrofluids: The Influence on Viscous Properties

Ferrofluids have attracted considerable interest from researchers and engineers due to their rich set of unique physical properties that are valuable for many industrial and biomedical applications. Many phenomena and features of ferrofluids' behavior are determined by internal structural transformations in the ensembles of particles, which occur due to the magnetic interaction between the particles. An applied magnetic field induces formations, such as linear chains and bulk columns, that become elongated along the field. In turn, these structures dramatically change the rheological and other physical properties of these fluids. A deep and clear understanding of the main features and laws of the transformations is necessary for the understanding and explanation of the macroscopic properties and behavior of ferrofluids. In this paper, we present an overview of experimental and theoretical works on the internal transformations in these systems, as well as on the effect of the internal structures on the rheological effects in the fluids.

Steady-state rheology and structure of soft hybrid mixtures of liquid crystals and magnetic nanoparticles

Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, λ, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered values of λ. At low and intermediate values of λ, a crossover from Newtonian to non-Newtonian behavior is observed as the rate of applied shear is increased. In contrast, for large values of λ, such a crossover is not observed within the range of shear rates considered. Also, the extent of the non-Newtonian regime increases as λ is increased. These features can be understood via the shear-induced changes of the microstructure. In particular, the LCs display a shear-induced isotropic-to-nematic transition at large shear rates with a shear-rate dependent degree of nematic ordering. The DSS show a shear-induced nematic ordering only for large values of λ, where the particles self-assemble into chains. Moreover, at large λ and low shear rates, our simulations indicate that the DSS form ferromagnetic domains.

Energy dissipation of rigid dipoles in a viscous fluid under the action of a time-periodic field: The influence of thermal bath and dipole interaction

Ferrofluid heating by an external alternating field is studied based on the rigid dipole model, where the magnetization of each particle in a fluid is supposed to be firmly fixed in the crystal lattice. Equations of motion, employing Newton's second law for rotational motion, the condition of rigid body rotation, and the assumption that the friction torque is proportional to angular velocity are used. This oversimplification permits us to expand the model easily: to take into account the thermal noise and interparticle interaction that allows us to estimate from unified positions the role of thermal activation and dipole interaction in the heating process. Our studies are conducted in three stages. The exact expressions for the average power loss of a single particle are obtained within the dynamical approximation. Then, in the stochastic case, the power loss of a single particle is estimated analytically using the Fokker-Planck equation and numerically using the effective Langevin equation. Finally, the power loss for the particle ensemble is obtained using the molecular dynamics method. Here, the local dipole fields are calculated approximately based on the Barnes-Hut algorithm. The revealed trends in the behavior of both a single particle and the particle ensemble suggest the way of choosing the conditions for obtaining the maximum heating efficiency. The competitiveness character of the interparticle interaction and thermal noise is investigated in detail. Two situations, when the thermal noise rectifies the power loss reduction caused by the interaction, are described. The first of them is related to the complete destruction of dense clusters at high noise intensity. The second one originates from the rare switching of the particles in clusters due to thermal activation, when the noise intensity is relatively weak. In this way, the constructive role of noise appears in the system.