Motion of paramagnetic particles in a viscous fluid under a uniform magnetic field: benchmark solutions

Abstract

Numerical simulations of the two-dimensional motion of multiple paramagnetic particles suspended in a viscous fluid subjected to a uniform magnetic field are presented. Both the magnetic field and flow field can be described efficiently with simple series in local coordinates attached to each particle. The coefficients of the series can be obtained with fast convergence when only a few leading coefficients are treated implicitly. Numerical results for the flow field are validated by comparing the data with those given by an asymptotic solution for a pair of particles separated by a small distance. The numerical results of the magnetic field are validated by comparison with the solutions in bipolar coordinates. Simulations of the motion of multiple particles reveal interesting phenomena and shed light on the fundamental mechanism of particles clustering into a straight chain. The data presented in this paper can be used as a benchmark solution for verifying codes for simulating the motion of paramagnetic particles in a magnetic field.

An immersed‐boundary finite‐volume method for direct simulation of flows with suspended paramagnetic particles

“…To validate the numerical method proposed in the present study, we perform numerical simulations on the two-dimensional particle motion and fluid flow for the case of two and three paramagnetic particles suspended in a square cavity filled with a nonmagnetic viscous fluid subjected to an external uniform magnetic field and then compare their results qualitatively with the finite-element solution of Kang et al [2] and quantitatively with the semi-analytical solutions of Suh and Kang [9]. Here, all the particles are of two-dimensional circular cylinder with the same radius, a = 1.…”

“…The proposed numerical method is validated by applying it to the two-dimensional motion of two and three particles suspended in a nonmagnetic viscous fluid inside a square cavity subjected to an external uniform magnetic field and then comparing the results with the semi-analytical benchmark solutions of Suh and Kang [9] and the finite-element solution of Kang et al [2]. In the present study, therefore, we will focus ourselves mainly on the validation of the proposed method rather than on the detailed explanation of interesting physical phenomena or fundamental mechanism because most of them were already fully discussed in Kang et al [2] and Suh and Kang [9].…”

“…In the present study, therefore, we will focus ourselves mainly on the validation of the proposed method rather than on the detailed explanation of interesting physical phenomena or fundamental mechanism because most of them were already fully discussed in Kang et al [2] and Suh and Kang [9]. Note that the proposed method can be extended to more general cases without difficulty: three-dimensional particulate flows, flows with a great number of particles, or flows under an arbitrary external magnetic field.…”

Magnetic interaction of Janus magnetic particles suspended in a viscous fluid

“…Even though modeling and simulation are employed to investigate the self-assembly and the dynamics of Janus particles [26][27][28][29][30][31], further studies are still required to understand the magnetic interaction lying behind the formation of various self-assembly structures and the fluid flow induced by the actuated particles. Direct numerical simulation schemes [32][33][34][35][36][37], which have been developed to solve particulate flows with isotropic magnetic particles, are promising options in tackling particulate flows with Janus magnetic particles if they are enhanced to take into account the magnetic anisotropy of the particles.…”

A Review on Mixing in Microfluidics

“…It was found that such a time-varying magnetic field enhances mixing, and switching the spinning direction further improves the mixing rate. It is well known that when a magnetic field is applied to a fluid containing scattered paramagnetic particles, they tend to align in a chain configuration (see e.g., [58][59][60]). Obviously the linear structure of particles should be more effective than the isolated ones in fluid stirring for mixing.…”