scholarly journals Dynamical Effective Field Model for Interacting Ferrofluids: II. The proper relaxation time and effects of dynamic correlations

2021 ◽  
Author(s):  
Angbo Fang
Keyword(s):  
Relaxation Time ◽  
Brownian Dynamics ◽  
Field Model ◽  
Volume Fraction ◽  
Effective Field ◽  
Rotational Relaxation ◽  
Dynamic Factor ◽  
Nonadiabatic Effects ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

Abstract The recently proposed dynamical effective field model (DEFM) is quantitatively accurate for ferrofluid dynamics. It is derived in paper I within the framework of dynamical density functional theory (DDFT) along with a phenomenological description of nonadiabatic effects. However, it remains to clarify how the characteristic rotational relaxation time of a dressed particle, denoted by τr, is quantitatively related to that of a bare particle, denoted by τr0. By building macro-micro connections via two different routes, I reveal that under some gentle assumptions τr can be identified with the mean time characterizing long-time rotational self-diffusion. I further introduce two simple but useful integrated correlation factors, describing the effects of quasi-static (adiabatic) and dynamic (nonadiabatic) inter-particle correlations, respectively. In terms of both the dynamic magnetic susceptibility is expressed in an illuminating and elegant form. Remarkably, it shows that the macro-micro connection is established via two successive steps: a dynamical coarse-graining with nonadiabatic effects accounted for by the dynamic factor, followed by equilibrium ensemble averaging captured by the static factor. By analyzing data from Brownian dynamics simulations on monodisperse interacting ferrofluids, I find τr/τr0 is, somehow unexpectedly, insensitive to changes of particle volume fraction. A physical picture is proposed to explain it. Furthermore, an empirical formula is proposed to characterize the dependence of τr/τr0 on dipole-dipole interaction strength. The DEFM supplemented with this formula leads to parameter-free predictions in good agreement with results from Brownian dynamics simulations. The theoretical developments presented in this paper may have important consequences to studies of ferrofluid dynamics in particular and other systems modelled by DDFTs in general.

Multi-Block Copolymers in Selective Solvent: A Brownian Dynamics Simulation

2004 ◽  
Vol 856 ◽  
Author(s):  
Yongsheng Liu ◽  
Huifen Nie ◽  
Rama Bansil ◽  
Zhenli Zhang ◽  
Sharon Glotzer
Keyword(s):  
Brownian Dynamics ◽  
Volume Fraction ◽  
Dynamics Simulation ◽  
Multiblock Copolymers ◽  
Brownian Dynamics Simulation ◽  
Selective Solvent ◽  
Bcc Lattice ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations ◽  
Poor Solvent

ABSTRACTWe performed Brownian Dynamics simulations of multiblock copolymers of A and B polymers in a solvent selective for the A block at a volume fraction of 20%. Tri-, penta- and heptabocks were simulated. Fourier transformation reveals micellar clusters arranged in a BCC lattice, in agreement with scattering experiments. The clusters were analyzed using a percolation approach and we observed larger clusters when the outermost block was in the poor solvent condition. The ratio of number of loops to bridges decreases as the number of blocks in the copolymer increases, as does the polydispersity. Increased penalty of looping as the number of blocks increases leads to a larger number of smaller clusters with more bridges.

scholarly journals Structure formation in suspensions under uniform electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Georgios G. Vogiatzis ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
External Field ◽  
Structure Formation ◽  
Brownian Dynamics ◽  
Volume Fraction ◽  
Structural Evolution ◽  
Thermal Fluctuations ◽  
Branch Points ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe structure formation of particles with induced dipoles dispersed in a viscous fluid, under a spatially and temporarily uniform external electric or magnetic field, is investigated by means of Brownian Dynamics simulations. Dipole–dipole interactions forces, excluded volume forces and thermal fluctuations are accounted for. The resulting structures are characterized in terms of average orientation of their inter-particle vectors (second Legendre polynomial), network structure, size of particle clusters, anisotropy of the gyration tensor of every cluster and existence of (cluster) percolation. The magnitude of the strength of the external field and the volume fraction of particles are varied and the structural evolution of the system is followed in time. The results show that the characteristic timescale calculated from the interaction of only two dipoles is also valid for the collective dynamics of many-particle simulations. In addition, the magnitude of the strength of the external field in the range of values we investigate influences only the magnitude of the deviations around the average behavior. The main characteristics (number density of branch-points and thickness of branches) of the structure are mainly affected by the volume fraction. The possibility of 3D printing these systems is explored. While the paper provides the details about the case of an electric field, all results presented here can be translated directly into the case of a magnetic field and paramagnetic particles.

scholarly journals Structure evolution of suspensions under time-dependent electric or magnetic field

2021 ◽  
Author(s):  
Konstantinos Manikas ◽  
Markus Hütter ◽  
Patrick D. Anderson
Keyword(s):  
Magnetic Field ◽  
Field Strength ◽  
Brownian Dynamics ◽  
Thermal Fluctuations ◽  
Time Dependent ◽  
Structure Evolution ◽  
Strength Increase ◽  
Large Rotation ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

AbstractThe effect of time-dependent external fields on the structures formed by particles with induced dipoles dispersed in a viscous fluid is investigated by means of Brownian Dynamics simulations. The physical effects accounted for are thermal fluctuations, dipole-dipole and excluded volume interactions. The emerging structures are characterised in terms of particle clusters (orientation, size, anisotropy and percolation) and network structure. The strength of the external field is increased in one direction and then kept constant for a certain amount of time, with the structure formation being influenced by the slope of the field-strength increase. This effect can be partially rationalized by inhomogeneous time re-scaling with respect to the field strength, however, the presence of thermal fluctuations makes the scaling at low field strength inappropriate. After the re-scaling, one can observe that the lower the slope of the field increase, the more network-like and the thicker the structure is. In the second part of the study the field is also rotated instantaneously by a certain angle, and the effect of this transition on the structure is studied. For small rotation angles ($$\theta \le 20^{{\circ }}$$ θ ≤ 20 ∘ ) the clusters rotate but stay largely intact, while for large rotation angles ($$\theta \ge 80^{{\circ }}$$ θ ≥ 80 ∘ ) the structure disintegrates and then reforms, due to the nature of the interactions (parallel dipoles with perpendicular inter-particle vector repel each other). For intermediate angles ($$20<\theta <80^{{\circ }}$$ 20 < θ < 80 ∘ ), it seems that, during rotation, the structure is altered towards a more network-like state, as a result of cluster fusion (larger clusters). The details provided in this paper concern an electric field, however, all results can be projected into the case of a magnetic field and paramagnetic particles.

scholarly journals Influence of size polydispersity on magnetic field tunable structures in magnetic nanofluids containing superparamagnetic nanoparticles.

2021 ◽  
Author(s):  
Dillip Kumar Mohapatra ◽  
Philip James Camp ◽  
John Philip
Keyword(s):  
Magnetic Field ◽  
Particle Size ◽  
Light Scattering ◽  
Optical Microscopy ◽  
Brownian Dynamics ◽  
Phase Contrast ◽  
Superparamagnetic Nanoparticles ◽  
Magnetic Nanofluids ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

We probe the influence of particle size polydispersity on field-induced structures and structural transitions in magnetic fluids (ferrofluids) using phase contrast optical microscopy, light scattering and Brownian dynamics simulations. Three...

scholarly journals Hard discs under steady shear: comparison of Brownian dynamics simulations and mode coupling theory

2009 ◽  
Vol 367 (1909) ◽  
pp. 5033-5050 ◽  
Author(s):  
Oliver Henrich ◽  
Fabian Weysser ◽  
Michael E. Cates ◽  
Matthias Fuchs
Keyword(s):  
Brownian Dynamics ◽  
Mode Coupling ◽  
Transition Density ◽  
Two Dimensions ◽  
Coupling Theory ◽  
Mode Coupling Theory ◽  
Stationary Structure ◽  
Homogeneous Shear Flow ◽  
Dynamics Simulations ◽  
Brownian Dynamics Simulations

Brownian dynamics simulations of bidisperse hard discs moving in two dimensions in a given steady and homogeneous shear flow are presented close to and above the glass transition density. The stationary structure functions and stresses of shear-melted glass are compared quantitatively to parameter-free numerical calculations of monodisperse hard discs using mode coupling theory within the integration through transients framework. Theory qualitatively explains the properties of the yielding glass but quantitatively overestimates the shear-driven stresses and structural anisotropies.

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