Numerical Simulation Of The Structure And Dynamics Of Magnetic Fluids Based On Dissipative Particle Dynamics

Magnetic fluids,also called ferrofluids,are a kind of important smart fluids and functional materials and have been applied in various fields of the industrial and agricultural production and social life.Since many applications of magnetic fluids depend on their structures and the corresponding magnetic properties,the study of the structure of magnetic fluids is of great importance from points of view of both engineering application and academic research.Nowadays,the numerical simulation methods for studying the structure of magnetic fluids mainly include molecular dynamics(MD)method,Brownian dynamics(BD)method,Lattice Boltzmann(LB)method,Monte Carlo(MC)method,dissipative particle dynamics(DPD)method,and so on.The DPD method,as a newly developed Lagrangian meshless particle method,is widely used to simulate various complex fluids and has demonstrated its obvious advantages.Nevertheless,the study on the simulation of the structure of magnetic fluids using the DPD method is not mature.The mathematical model of magnetic fluids is established by introducing the DPD method,considering the effect of solvent explicitly,which makes the resulting model of magnetic fluids closely approximate to the real magnetic fluids.In addition,due to the mesoscopic feature,the DPD method with fewer magnetic particles can achieve the same simulation effect achieved by the MD method with a huge number of particles.Therefore,this paper is devoted to studying several mathematical models of magnetic fluids in two-dimensional(2D)and three dimensional(3D)space using the DPD method.The effects of the key factors of controlling the structures of magnetic fluids on the aggregate structure of magnetic particles are investigated,and the formation mechanism of the magnetic particle chain structure is analyzed in detail.The main contributions are summarized as follows:(1)The 2D structure of magnetic fluids is studied by using a efficient algorithm for updating the trajectories of particles.First,instead of using the Euler scheme to update the trajectories of two kinds of particles in the literature,the modified velocity-Verlet algorithm is employed to update the trajectories of dissipative particles.Under the condition of the weak magnetic dipolar interaction,most magnetic particles are in dissociated state in the present simulations,while these phenomena haven't been reported in the relevant literature.This indirectly shows that the present algorithm is effective.Second,the numerical results show that the proposed algorithm has high accuracy in terms of the mean equilibrium temperature of the system and the mean equilibrium velocities of the particles of two kinds.Furthermore,the 2D structures of magnetic fluids are studied quantitatively by using the radial distribution function.(2)The effects of the two crucial factors(the magnetic dipolar interaction strength and the area fraction of magnetic particles)for controlling the structure of magnetic fluids on the aggregate structures of magnetic particles are studied for the2 D case.The numerical results show that the magnetic dipolar interaction strength plays a crucial role in the formation of the chain-like structures of magnetic particles,and that increasing the area fraction of magnetic particles is not conducive to the formation of longer chain structures.Furthermore,the effects of the periodic boundary size on the radial distribution function and its maximum value are also analyzed.(3)A modified 2D mathematical model of magnetic fluids is employed to simulate the structure of magnetic fluids and the corresponding formation mechanism of the chain-like structure is analyzed further.First,the cubic polynomial spline function is employed as the conservative force potential function,which can provide stronger conservative force weight function than using the traditional potential function.By introducing the generalized dissipative force weight function,the dynamic response of the system is improved.Second,the inherent mechanism of forming better chain-like structures is analyzed by simulating the effects of the magnetic dipolar interaction strength and the area fraction of magnetic particles on the structures of magnetic fluids under the condition of strong conservative force.(4)The 2D mathematical model of magnetic fluids is extended to the 3D case under the condition of a strong external magnetic field.The 3D structures of magnetic fluids are demonstrated by simulating the 3D model.First,the 3D aggregate structures of magnetic particles are simulated for different magnetic dipolar interaction strengths in thermodynamic equilibrium state and the obtained results agree well with the reference data in the literature,which verifies the effectiveness of the present model.Second,by simulating the effects of the volume fraction of magnetic particles on the aggregate structure of magnetic particles,it is shown that the trend of forming chain structure is gradually increasing as the volume fraction of magnetic particles decreases.Last but not least,the numerical results show that the numerical solution of the temperature approaches its corresponding theoretical value by simulating the evolution of the system mean equilibrium temperature,which demonstrates the correctness of the simulated structure of magnetic fluids from one side.(5)The 3D mathematical model of magnetic fluids is established under the condition that the external magnetic field is variable,considering the translational and rotational motions of magnetic particles simultaneously.The 3D structure of magnetic fluids and the dynamics of the magnetic particle are further studied.First,the 3D aggregate structures of magnetic particles are simulated with and without external magnetic fields.In the absence of the external magnetic field,not only the chain-like structure is obtained,but also the ring and the dense globe structures are achieved.In the presence of the magnetic field,both the chain-like and the dense globe structures are obtained.Second,the dynamic behaviors of a single magnetic particle are studied for different values of time step,and the obtained results are in agreement with the reference data in the literature.It is shown that the 3D model is suitable for the study of the dynamics of magnetic particle.Last but not least,through simulating the evolution process of the temperature drift with time,it is shown that the accuracy of the simulation is acceptable.