Kinetics of internal structures growth in magnetic suspensions

Abstract

a b s t r a c tThe kinetics of aggregation of non Brownian magnetizable particles in the presence of a magnetic field is studied both theoretically and by means of computer simulations. A theoretical approach is based on a system of Smoluchowski equations for the distribution function of the number of particles in linear chain-like aggregates. Results obtained in the two dimensional (2D) and three dimensional (3D) models are analyzed in relation with the size of the cell, containing the particles, and the particle volume fraction ϕ. The theoretical model reproduces the change of the aggregation kinetics with the size of the cell and with the particle volume fraction as long as the lateral aggregation of chains is negligible.The simulations show that lateral aggregation takes place when, roughly, ϕ 2D > 5% and ϕ 3D > 1.5%.Dependence of the average size of the chains with time can be described by a power law; the corresponding exponent decreases with the particle volume fraction in relation with the lateral aggregation.In the 3D simulations, dense labyrinthine-like structures, aligned along the applied field, are observed when the particle concentration is high enough (ϕ 3D > 5%).

Shear Elasticity of Magnetic Gels with Internal Structures

“…The determination of the function presents a separate problem. Theoretical study of evolution over time of this function in the magnetic suspensions with a permanent viscosity of the currier liquid has been done in [ 63 ]. This model is based on the analysis of a system of the Smoluchowski equations, which describes the kinetic of the aggregation of the chains with a various number of particles.…”

Two-stage kinetics of field-induced aggregation of medium-sized magnetic nanoparticles

“…At longer times, lateral aggregation dominates over tip-to-tip aggregation and the chains can merge and form either a fibrous structure "frozen" in non-equilibrium state likely by inter-particle friction 22 or column structures confined by the walls orthogonal to the applied field 29 , or unconfined ellipsoidal drop-like aggregates under pulsed magnetic field 30,31 . Theoretical studies are mainly based on Langevin dynamics simulations 19,32,33 or solution of Smoluchowsky kinetic equation 23,24,27,28,[33][34][35] . A simplified theoretical approach, so-called hierarchical model, has been developed by See and Doi 36 considering only coalescence of the chains of equal sizes and showing a satisfactory agreement with experiments on 2a , even though it predicts monodisperse particle chains instead of experimentally observed polydisperse distribution.…”

Analysis of Styrene-Butadiene Based Thermoplastic Magnetorheological Elastomers with Surface-Treated Iron Particles

“…Based on the results of the m netic saturation, the carbonyl iron particles with surface-treatment of SiO2 (CC gra were used for this investigation. According to G. Bossis et al [22] and Hass [23], the time required to induce alignm of particles along an external field is proportional to the viscosity of the melted mat Moreover, alignment of CIP in the MRE has been proven to positively influence the M effect [22,23]. As shown in Table 3, the viscosity of 30 vol.-% STL is much higher than vol.-% STT, meaning that full alignment of particles is faster in the former composite.…”