Magnetoviscous and viscoelastic phenomena in ferrofluids are intimately related to their internal... more Magnetoviscous and viscoelastic phenomena in ferrofluids are intimately related to their internal structures. The available kinetic models describing the rheological behaviour rely on strong assumptions and simplifications of these structures. Using equilibrium and nonequilibrium computer simulations, here we discuss the validity of the crucial assumption of rigid, chain-like aggregates underlying the chain model. The simulation results support the existence of chain-like aggregates in strongly interacting ferrofluids, at least for sufficiently strong magnetic fields. In addition, shear-induced degradation of the clusters is observed, which apparently is related to strong shear thinning behaviour. For weakly interacting ferrofluids, only slightly anisotropic spatial structures are observed. In this regime, the simulation results of the magnetoviscous effect are in good agreement with the predictions of a dynamical mean-field theory. Further, we explore some first steps towards a unified kinetic model that is applicable in both, the weakly and strongly interacting regimes.
Bulletin of the American Physical Society, Feb 28, 2012
assembled at liquid interfaces thanks to particle localization and mobility at the interface in c... more assembled at liquid interfaces thanks to particle localization and mobility at the interface in combination with tailoring of specific interactions. Many recent advances have been made in the understanding of the adsorption and assembly at liquid interfaces of small hydrophobic nanoparticles, stabilized by short-chain rigid dispersants, but the corresponding studies on coreshell nanoparticles sterically stabilized by extended hydrophilic polymer brushes are presently missing. Such particles offer significant advantages in terms of fabrication of functional, responsive and bio-compatible materials. We present here a combination of experimental and numerical data together with an intuitive and simple model aimed at elucidating the mechanisms governing the adsorption of iron oxide nanparticles (5-10nm) stabilized by low molecular weight poly(ethylene glycol) (1.5-10 kDa). We show that the adsorption dynamics and the structure of the final assembly depend on the free energy of the particles at the interface and discuss the thermodynamics of the adsorpt
The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane ... more The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane Couette flow are studied. Analytical expressions for the off-equilibrium magnetization and the shear viscosity are obtained within the so-called effective field approximation. We also investigate the predictions of a different approximation based on the linearized moment expansion. Direct numerical simulation of the kinetic model are performed in order to test the range of validity of these approximations.
The anisotropy of the magnetoviscous effect in ferrofluids subjected to weak planar Couette flow ... more The anisotropy of the magnetoviscous effect in ferrofluids subjected to weak planar Couette flow is investigated by extensive molecular simulations. The field and concentration dependence of the viscosity coefficients are found to depend on the relative orientation of the magnetic field with respect to the flow geometry. Comparison with dynamical mean-field models shows satisfactory agreement for moderate interaction strengths. In the semidilute regime it is found that the anisotropy contains valuable information on particle interaction.
Page 1. Magnetoviscous model fluids This article has been downloaded from IOPscience. Please scro... more Page 1. Magnetoviscous model fluids This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2003 J. Phys.: Condens. Matter 15 S1403 (http://iopscience.iop.org/0953-8984/15/15/307) ...
Extensive molecular simulations on a model ferrofluid are performed in order to study magnetovisc... more Extensive molecular simulations on a model ferrofluid are performed in order to study magnetoviscous and viscoelastic phenomena in semidilute ferrofluids. Simulation results of the nonequilibrium magnetization, shear viscosity, and normal stress differences are presented. Rotational and configurational contributions to the shear viscosity are analyzed and their influence on the magnetoviscous effect is discussed. The simplified model of noninteracting magnetic dipoles describes the nonequilibrium magnetization and the rotational viscosity, but does not account for configurational viscosity contributions and normal stress differences. Improved mean-field models that overcome these limitations show good agreement with the simulation results for weak dipolar interactions where the models should apply. Comparisons to simulation results for various interaction strengths allow us to determine the range of validity of the mean-field models.
Detailed studies of the intriguing field-dependent dynamics and transport properties of confined ... more 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.
The effect of coupling between the dipole moment and the orientation is explored based on a relax... more The effect of coupling between the dipole moment and the orientation is explored based on a relaxation equation for the second rank alignment tensor characterizing the molecular order in liquid crystals and a corresponding equation for the electric polarization. The orientational dynamics leads to a time dependence of the electric polarization. We propose a possibility to measure these effects via the resulting magnetic fields of the magnitude |B| approximately equal to 10(-9)T . Furthermore, the presence of the electric polarization modifies the orientational dynamics as demonstrated in solution phase diagrams.
Journal of Non-newtonian Fluid Mechanics, Mar 1, 2006
A two-alignment tensor model for the dynamics of side chain liquid-crystalline polymers is applie... more A two-alignment tensor model for the dynamics of side chain liquid-crystalline polymers is applied to the case of planar shear flow. The predictions of the model are worked out for the case of stationary and oscillatory shear flow. In stationary shear, a flow induced isotropic-to-nematic phase transition is observed as well as a stress plateau for intermediate shear rates. In
The dynamical behavior of molecular alignment strongly affects physical properties of nematic liq... more The dynamical behavior of molecular alignment strongly affects physical properties of nematic liquid crystals. A theoretical description can be made by a nonlinear relaxation equation of the order parameter and leads to the prediction that rather complex even chaotic orientational behavior occur. Here the influence of fluctuating shear rates on the orientational dynamics especially on chaotic solutions is discussed. With the help of phase portraits and time evolution diagrams, we investigated the influence of different fluctuation strengths on the flow aligned, isotropic, and periodic solutions. To explore the effect of fluctuations on the chaotic behavior, we calculated the largest Lyapunov exponent for different fluctuation strengths. We found in all cases that small fluctuations of the shear rate do not affect the basic features of the dynamics of tumbling nematics. Furthermore, we present an amended potential modeling the isotropic to nematic transition and discuss the equivalence and difference to the commonly used Landau-de Gennes potential. In contrast to the Landau-de Gennes potential, our potential has the advantage to restrict the order parameter to physically admissible values. In the case of extensional flow, we show that the amended potential leads for increasing extensional rate to a better agreement with experimental results.
Ferrofluid flow is fascinating since their fluid properties can conveniently be manipulated by ex... more Ferrofluid flow is fascinating since their 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 multi-particle collision dynamics method for modelling hydrodynamics with Brownian Dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics and resulting stresses. Since both, multi-particle 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 the new scheme to simulate ferrofluid shear flow over rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in gradient direction.
Mathematical Models and Methods in Applied Sciences
The magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel ... more The magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel relaxation as well as Brownian diffusion of the whole particle. We here present semi-analytical and numerical solutions of the kinetic equation, describing the combined rotation of particle orientation and magnetization. The solutions are based on an expansion of the joint probability density into a complete set of bipolar harmonics, leading to a coupled set of ordinary differential equations for the expansion coefficients. Extending previous works, we discuss the spectrum of relaxation times as well as convergence and limits of applicability of the method. Furthermore, we also provide the numerical scheme in electronic form, so that readers can readily implement and use the model.
Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in ... more Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in their local dynamical properties. Using detailed molecular simulations, we find that for su ciently low temperatures and su ciently high shear rates supercooled liquids also show transient, inhomogeneous flow patterns (shear banding) in start-up of steady shear flow, similar to what has already been observed for many other soft glassy systems. We verify that the onset of transient shear banding coincides quite well with the appearance of a stress overshoot for temperatures in the supercooled regime. We find that the slower bands adapt less well to the imposed deformation and therefore accumulate higher shear stresses compared to the fast bands at comparable local shear rates. Our results also indicate that the shear rates of the fast and slow bands are adjusted such that the local dissipation rate is approximately the same in both bands.
The derivation of time evolution equations for slow collective variables starting from a microsco... more The derivation of time evolution equations for slow collective variables starting from a microscopic model system is demonstrated for the tutorial example of the classical, two-dimensional XY model. Projection operator techniques are used within a nonequilibrium thermodynamics framework together with molecular simulations in order to establish the building blocks of the hydrodynamics equations: Poisson brackets that determine the deterministic drift, the driving forces from the macroscopic free energy and the friction matrix. The approach is rather general and can be applied for deriving the equations of slow variables for a broad variety of systems.
Magnetoviscous and viscoelastic phenomena in ferrofluids are intimately related to their internal... more Magnetoviscous and viscoelastic phenomena in ferrofluids are intimately related to their internal structures. The available kinetic models describing the rheological behaviour rely on strong assumptions and simplifications of these structures. Using equilibrium and nonequilibrium computer simulations, here we discuss the validity of the crucial assumption of rigid, chain-like aggregates underlying the chain model. The simulation results support the existence of chain-like aggregates in strongly interacting ferrofluids, at least for sufficiently strong magnetic fields. In addition, shear-induced degradation of the clusters is observed, which apparently is related to strong shear thinning behaviour. For weakly interacting ferrofluids, only slightly anisotropic spatial structures are observed. In this regime, the simulation results of the magnetoviscous effect are in good agreement with the predictions of a dynamical mean-field theory. Further, we explore some first steps towards a unified kinetic model that is applicable in both, the weakly and strongly interacting regimes.
Bulletin of the American Physical Society, Feb 28, 2012
assembled at liquid interfaces thanks to particle localization and mobility at the interface in c... more assembled at liquid interfaces thanks to particle localization and mobility at the interface in combination with tailoring of specific interactions. Many recent advances have been made in the understanding of the adsorption and assembly at liquid interfaces of small hydrophobic nanoparticles, stabilized by short-chain rigid dispersants, but the corresponding studies on coreshell nanoparticles sterically stabilized by extended hydrophilic polymer brushes are presently missing. Such particles offer significant advantages in terms of fabrication of functional, responsive and bio-compatible materials. We present here a combination of experimental and numerical data together with an intuitive and simple model aimed at elucidating the mechanisms governing the adsorption of iron oxide nanparticles (5-10nm) stabilized by low molecular weight poly(ethylene glycol) (1.5-10 kDa). We show that the adsorption dynamics and the structure of the final assembly depend on the free energy of the particles at the interface and discuss the thermodynamics of the adsorpt
The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane ... more The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane Couette flow are studied. Analytical expressions for the off-equilibrium magnetization and the shear viscosity are obtained within the so-called effective field approximation. We also investigate the predictions of a different approximation based on the linearized moment expansion. Direct numerical simulation of the kinetic model are performed in order to test the range of validity of these approximations.
The anisotropy of the magnetoviscous effect in ferrofluids subjected to weak planar Couette flow ... more The anisotropy of the magnetoviscous effect in ferrofluids subjected to weak planar Couette flow is investigated by extensive molecular simulations. The field and concentration dependence of the viscosity coefficients are found to depend on the relative orientation of the magnetic field with respect to the flow geometry. Comparison with dynamical mean-field models shows satisfactory agreement for moderate interaction strengths. In the semidilute regime it is found that the anisotropy contains valuable information on particle interaction.
Page 1. Magnetoviscous model fluids This article has been downloaded from IOPscience. Please scro... more Page 1. Magnetoviscous model fluids This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2003 J. Phys.: Condens. Matter 15 S1403 (http://iopscience.iop.org/0953-8984/15/15/307) ...
Extensive molecular simulations on a model ferrofluid are performed in order to study magnetovisc... more Extensive molecular simulations on a model ferrofluid are performed in order to study magnetoviscous and viscoelastic phenomena in semidilute ferrofluids. Simulation results of the nonequilibrium magnetization, shear viscosity, and normal stress differences are presented. Rotational and configurational contributions to the shear viscosity are analyzed and their influence on the magnetoviscous effect is discussed. The simplified model of noninteracting magnetic dipoles describes the nonequilibrium magnetization and the rotational viscosity, but does not account for configurational viscosity contributions and normal stress differences. Improved mean-field models that overcome these limitations show good agreement with the simulation results for weak dipolar interactions where the models should apply. Comparisons to simulation results for various interaction strengths allow us to determine the range of validity of the mean-field models.
Detailed studies of the intriguing field-dependent dynamics and transport properties of confined ... more 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.
The effect of coupling between the dipole moment and the orientation is explored based on a relax... more The effect of coupling between the dipole moment and the orientation is explored based on a relaxation equation for the second rank alignment tensor characterizing the molecular order in liquid crystals and a corresponding equation for the electric polarization. The orientational dynamics leads to a time dependence of the electric polarization. We propose a possibility to measure these effects via the resulting magnetic fields of the magnitude |B| approximately equal to 10(-9)T . Furthermore, the presence of the electric polarization modifies the orientational dynamics as demonstrated in solution phase diagrams.
Journal of Non-newtonian Fluid Mechanics, Mar 1, 2006
A two-alignment tensor model for the dynamics of side chain liquid-crystalline polymers is applie... more A two-alignment tensor model for the dynamics of side chain liquid-crystalline polymers is applied to the case of planar shear flow. The predictions of the model are worked out for the case of stationary and oscillatory shear flow. In stationary shear, a flow induced isotropic-to-nematic phase transition is observed as well as a stress plateau for intermediate shear rates. In
The dynamical behavior of molecular alignment strongly affects physical properties of nematic liq... more The dynamical behavior of molecular alignment strongly affects physical properties of nematic liquid crystals. A theoretical description can be made by a nonlinear relaxation equation of the order parameter and leads to the prediction that rather complex even chaotic orientational behavior occur. Here the influence of fluctuating shear rates on the orientational dynamics especially on chaotic solutions is discussed. With the help of phase portraits and time evolution diagrams, we investigated the influence of different fluctuation strengths on the flow aligned, isotropic, and periodic solutions. To explore the effect of fluctuations on the chaotic behavior, we calculated the largest Lyapunov exponent for different fluctuation strengths. We found in all cases that small fluctuations of the shear rate do not affect the basic features of the dynamics of tumbling nematics. Furthermore, we present an amended potential modeling the isotropic to nematic transition and discuss the equivalence and difference to the commonly used Landau-de Gennes potential. In contrast to the Landau-de Gennes potential, our potential has the advantage to restrict the order parameter to physically admissible values. In the case of extensional flow, we show that the amended potential leads for increasing extensional rate to a better agreement with experimental results.
Ferrofluid flow is fascinating since their fluid properties can conveniently be manipulated by ex... more Ferrofluid flow is fascinating since their 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 multi-particle collision dynamics method for modelling hydrodynamics with Brownian Dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics and resulting stresses. Since both, multi-particle 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 the new scheme to simulate ferrofluid shear flow over rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in gradient direction.
Mathematical Models and Methods in Applied Sciences
The magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel ... more The magnetization dynamics of suspended superparamagnetic particles is governed by internal Néel relaxation as well as Brownian diffusion of the whole particle. We here present semi-analytical and numerical solutions of the kinetic equation, describing the combined rotation of particle orientation and magnetization. The solutions are based on an expansion of the joint probability density into a complete set of bipolar harmonics, leading to a coupled set of ordinary differential equations for the expansion coefficients. Extending previous works, we discuss the spectrum of relaxation times as well as convergence and limits of applicability of the method. Furthermore, we also provide the numerical scheme in electronic form, so that readers can readily implement and use the model.
Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in ... more Supercooled liquids and other soft glassy systems show characteristic spatial inhomogeneities in their local dynamical properties. Using detailed molecular simulations, we find that for su ciently low temperatures and su ciently high shear rates supercooled liquids also show transient, inhomogeneous flow patterns (shear banding) in start-up of steady shear flow, similar to what has already been observed for many other soft glassy systems. We verify that the onset of transient shear banding coincides quite well with the appearance of a stress overshoot for temperatures in the supercooled regime. We find that the slower bands adapt less well to the imposed deformation and therefore accumulate higher shear stresses compared to the fast bands at comparable local shear rates. Our results also indicate that the shear rates of the fast and slow bands are adjusted such that the local dissipation rate is approximately the same in both bands.
The derivation of time evolution equations for slow collective variables starting from a microsco... more The derivation of time evolution equations for slow collective variables starting from a microscopic model system is demonstrated for the tutorial example of the classical, two-dimensional XY model. Projection operator techniques are used within a nonequilibrium thermodynamics framework together with molecular simulations in order to establish the building blocks of the hydrodynamics equations: Poisson brackets that determine the deterministic drift, the driving forces from the macroscopic free energy and the friction matrix. The approach is rather general and can be applied for deriving the equations of slow variables for a broad variety of systems.
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