Abstract
The 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.
Highlights
When dielectric or conductive particles are exposed to an external electric or magnetic field, dipoles are induced to the particles due to the difference in the dielectric permittivity or magnetic susceptibility between them, and the medium (Jones 1995)
The reason for neglecting the latter is that otherwise the computational cost would be prohibitive, in particular, since the main goal of this paper is to conduct an extensive study of the effect of dipole–dipole interactions and thermal fluctuations on the structure evolution and to resolve the physical behavior of the system
We use a Brownian Dynamics scheme and the deterministic part for the equilibration loop consists of the repulsive part of a Lennard-Jones potential (Jones and Chapman 1924; Smit 1992) with σ = 2Rp/rc, and ε = 1
Summary
When dielectric or conductive particles are exposed to an external electric or magnetic field, dipoles are induced to the particles due to the difference in the dielectric permittivity or magnetic susceptibility between them, and the medium (Jones 1995). The effect of the Mason number (Melle et al 2000), which is the ratio of viscous to magnetic forces, has been studied for the investigation of mixing on micrometer scales (Gao et al 2012; Melle et al 2003; Calhoun et al 2006) with a rotating field The behavior of such systems under the influence of an oscillating magnetic field has been investigated extensively over the past decade (Sánchez and Rinaldi 2010; Liu et al 2019; Soto-Aquino and Rinaldi 2015; Ido et al 2016; Jonasson et al 2019; Ruta et al 2015). The structures created in a spatially uniform external field have been studied at large timescales both athermally (no Brownian motion) (Martin et al 1998), and thermally (including Brownian motion) (Martin 2001)
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