Techniques of the numerical simulations Essay

The most of researches in MRFs field are including experimental methods, while expensive materials and tools are difficulties of these researches. In the other hand, analytical models can't present complete and closed answers in complex problems. Moreover, structural information helps us to know better this material but both approaches can't present any information about that.
Numerical simulations can cover problems of the previous methods, they solve complex situation and illustrate useful details. Numerical models are mainly divided into two main techniques. The first one is based on equation such as Navier-Stocks which are solved by numerically methods. For example K.P. Gertzos et al used this method to analyze of journal bearing by Bingham lubricate (5). The second numerical approach is the particular method, like molecular dynamics, in this method the motion of each particle is considered to capture macroscopic flow field, this can obtain the most details of phenomena, but this way is too expensive and not suitable for complex fluids. For solve this problem, we can use coarse-grained models, which consider a cluster or group of molecules as a particle, this way decreases computational cost significantly. Dissipative Particle Dynamics (DPD) method, a coarse-grained model, was introduced by Hoogerbrugge and Koelman (1992), then P. Espanol and P. Warren(1995) developed it by introduce an intelligent thermostat. In the method, fluid particles move under Newtonian's second law motion. In the original DPD technique, there are three forces between each pair of particles, a soft repulsion force addition to dissipative and random forces prepared to conserve mass and momentum in the average. These particles, we called "dissipative particles", can form complex system as we like. The DPD method can make strings by connection of dissipative particle to model polymer solutions (), form immiscible droplets to model multiphase fluids, model vapor phase to model liquid/vapor interaction (), simulate suspensions ()(phan-book) and applied in bioengineering.
The DPD is a strong method to simulation of suspensions, because it doesn't need special technique to model multi-body hydrodynamic interactions. A kind of suspensions is MRF that consider solid iron particles and a base fluid. A. Satoh and R.W. Chantrell () have done the first study on magnetic fluids under the applied strong magnetic field in equilibrium situation by DPD. They've shown the method is compatible for this kind of problems.
In this research, magnetorheological fluid has been investigated at a dynamic mode for the first time. The effect of solid particles volume fraction (15% to 39%), magnetizable of iron particle and viscosity of carrier liquid under shear flow (cuette flow) on the rheological properties of fluid has been studied. The fluid particles have been modeled by DPD method forces, and solid particles by particle magnetization model. Lennard-Jones potential has been applied to modeling of interaction between two kinds of particles. The results of this study, same as the literature, show a shear thinning treatment for MRFs . Furthermore, the velocity profile in transmit mode from solid state to fluid state has been presented for the first time.