Modeling of magnetic particle suspensions for simulations by Akira Satoh

By Akira Satoh

The major aim of the publication is to spotlight the modeling of magnetic debris with various shapes and magnetic homes, to supply graduate scholars and younger researchers info at the theoretical facets and real innovations for the therapy of magnetic debris in particle-based simulations. In simulation, we concentrate on the Monte Carlo, molecular dynamics, Brownian dynamics, lattice Boltzmann and stochastic rotation dynamics (multi-particle collision dynamics) tools. The latter simulation tools can simulate either the particle movement and the ambient circulate box at the same time. more often than not, really good wisdom can simply be received in an efficient demeanour lower than the supervision of knowledgeable.

The current ebook is written to play the sort of position for readers who desire to enhance the ability of modeling magnetic debris and increase a working laptop or computer simulation software utilizing their very own skill. This ebook is accordingly a self-learning ebook for graduate scholars and younger researchers. Armed with this data, readers are anticipated so as to sufficiently increase their ability for tackling any hard difficulties they might come across in destiny.

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32 Forces, Energies and Torques Acting on Magnetic Particles As shown in Fig. 3, it is assumed that a plane wall is coated with surfactant molecules modeled as a rigid rod anchored at the corresponding free hinge at the material surface and these two walls are located in a face to face and parallel situation. Employing the notation δ for the length of the rod, ns for the number of surfactant molecules (or rods) per unit area and s for the distance between the two wall surfaces, then the interaction energy of the two walls in the situation of overlap of the surfactant layers is evaluated from the decrease in the number of available microscopic (orientational) states.

44) Application of this formula to evaluation of integral in Eq. 45) Taking into account the relationship in Eq. 46) This is the expression previously derived by Rosensweig et al. [2] and is widely recognized as being applicable for molecular simulations on ferrofluids that are composed of magnetic spherical particles covered by a steric layer. From an educational point of view, we derive a different expression for a steric repulsive interaction using the theory of statistical mechanics where the number of possible microscopic states is treated for determining 36 Forces, Energies and Torques Acting on Magnetic Particles thermodynamic quantities such as the entropy and interaction energy.

IA-*~ . 6 r *(=r d) . ~ ..... 8. Electric repulsive interaction potential for the two same-sized spherical particles due to the overlap of electric double layers around dispersed particles. 44 Forces, Energies and Torques Acting on Magnetic Particles Moreover, it is noted that this potential does not exhibit the same shortrange order as compared with the following van der Waals attractive interaction. 5 Interaction due to van der Waals attraction Next we show expressions for van der Waals interaction energies.

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