Journal of Nanomaterials

Volume 2019, Article ID 6312606, 17 pages

https://doi.org/10.1155/2019/6312606

## Numerical Simulation and Experimental Analysis of Microstructure of Magnetorheological Fluid

School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, China

Correspondence should be addressed to Yiping Luo; moc.anis@777pyl

Received 5 July 2019; Revised 13 September 2019; Accepted 16 October 2019; Published 14 November 2019

Academic Editor: Francesco Marotti de Sciarra

Copyright © 2019 Dongsheng Ji et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Magnetorheological fluid is a new type of smart material that is sensitive to magnetic fields and has controllable performance. It is widely regarded for its unique magnetorheological effect and good rheological properties. For materials, the microstructure determines its macroscopic properties. In order to better study its macroscopic properties, it is necessary to have a more comprehensive understanding and deep understanding of its microstructure. In this paper, the magnetization process of magnetorheological fluid is analyzed from a microscopic point of view. Based on Newton’s second law, the dynamic model of particle motion is established. The magnetic force, repulsive force, and viscous resistance of magnetic particles are analyzed. The finite difference numerical calculation method is used. The velocity-Verlet algorithm simulates the static microstructure chaining process of the magnetorheological fluid and the dynamic chaining process under shear force under different influencing factors. At the same time, a static observation device and a shear observation device were developed to observe the microstructure chaining morphology of magnetorheological fluid under different influencing factors, and to study the dynamic chaining law of magnetorheological fluid under the action of a shear force. Therefore, a reasonable contrast index is established, and the numerical simulation results are compared with the experimental observation results.

#### 1. Introduction

With the rapid development of modern science and technology, people pay more and more attention to smart materials. The special properties of magnetorheological fluid (MRF) attract the attention of many countries and many scholars. MRF is a stable suspension [1, 2], which is controlled by a magnetic field. It has a reversible reaction of milliseconds. This is also the fundamental reason why MRF produces MRF magnetorheological effect by forming a chain structure of magnetic particles under the action of a magnetic field. Therefore, only by studying the chaining process of magnetic particles under a magnetic field can we study the magnetorheological effect in essence.

Nowadays, many scientists have done a series of research on the chaining process of MRF particles. Shulman et al. [3] found that under the action of an external magnetic field, particles form elliptical polymers along the direction of the magnetic field and are arranged in chains from the microscopic structure of MRF. They approximated the equilibrium of the external and magnetic moments acting on the polymer by using knowledge of statistical physics, then obtained the shear stress of MRF. Lemaire et al. [4] also calculated from their own calculations the shear yield stress of MRF without demagnetization. Tang and Conrad [5] used the Maxwell stress tensor to mathematically simplify the flux linkage to a uniform plate and estimate the shear yield stress of the MRF. Rosenweig [6] also used the Maxwell stress tensor and proposed an average field continuous model based on the method of asymmetric stress analysis. It should be considered that under the action of a magnetic field, the particle chain may not be completely linear along the direction of the magnetic field. Peng and Li [7] proposed the assumption that the angle between the particle chain and the magnetic field obeys the normal distribution, and they proposed describing the shear strain. MRF shear force have expressions that affect the mechanical properties of MRF and other factors such as shear strain rate. Ciocanel et al. [8] considers the nonlinear magnetization of ferromagnetic particles in an external magnetic field. Considering the influence of magnetic force and fluid viscous resistance, the constitutive equation of MRF is established. Yi et al. [9] proposed a more precise dipole model by the same method and obtained the corresponding shear yield stress expression. Zhang et al. [10] proposed a Gaussian distribution model to study the properties of anisotropic magnetorheological elasticity, and they obtained the expression of magnetorheologically induced shear stress. The model improved the prediction of the properties of magnetorheological elastomers. Although some progress has been made in the above research, among the many models, there is no consensus that can accurately and systematically express the rheological properties of MRF. Therefore, the rheological properties of MRF need to be further studied.

In this paper, the chaining process of MRF is analyzed from the microscopic point of view. Firstly, the influence of particle size and particle volume fraction on the MRF microstructure is simulated by numerical simulation. At the same time, the static and dynamic shear observation devices developed by ourselves were used to observe the MRF samples and the influencing factors were analyzed. Finally, the numerical simulation results are compared with the experimental observations, and the microstructural chaining process of MRF can be effectively simulated, which has important guiding significance for the practical application of MRF.

#### 2. Simulation Calculation and Experiment

##### 2.1. Numerical Simulation Method

At present, numerical simulation can simulate the microstructure of MRF using multiple variables and is closer to the real model. Among them, molecular dynamics simulation is one of the most important methods for studying the microstructure of MRF. The numerical calculation based on the finite difference method is commonly used, and the velocity-Verlet algorithm is adopted in this paper. In the simulation, the initial position of particles is randomly generated by a computer, the initial velocity is zero, and the simulation time step is . The calculation formulas of the algorithm are as follows: (1)Location of moment(2)Speed of hours

Formula (1) and formula (2) are solved by the iteration program written in MATLAB, and the iteration is terminated after the number of iterations. In the process of numerical simulation, it takes a lot of time to simulate a complete iteration, especially when calculating the force between particles, because the force of a particle needs to consider the influence of other particles in the system on the particle. For an MRF system with particles, if an efficient algorithm is not used, it is necessary to calculate the interaction between the pairs of particles in each incremental step, the force acting on the particles. The calculation time is proportional to . The Verlet list method and the cell list method can accelerate the calculation of the force, so that the calculation time is proportional to . The Verlet list method calculates the interaction force of magnetic particles in order of magnitude, but updates the Verlet list in order of magnitude. The time of the cell list method in calculating the interaction force of the magnetic particles and the time to update the cell list are all orders of magnitude. However, the Verlet listing method has a higher ratio of effective adjacent particle pairs than a cell listing method. Therefore, the Verlet listing method and the cell listing method are combined, as shown in Figure 1.