Orientational Distributions and Rheological Properties of a Nondilute Colloidal Dispersion Composed of Ferromagnetic Spherocylinder Particles Subjected to a Simple Shear Flow (Analysis by Means of Mean-field Approximation for the Magnetic Field Direction Parallel to the Shear Flow)

We have studied the influences of the magnetic field, shear rate, and random forces on transport coefficients such as viscosity and diffusion coefficient, and also on the orientational distributions of hematite particles composed of a dilute colloidal dispersion. Hematite particles are modeled as spheroids with a magnetic moment normal to the particle axis. In the present analysis, these particles are assumed to conduct the rotational Brownian motion in a simple shear flow as well as an external magnetic field. The basic equation of the orientational distribution function has been derived from the balance of the torques and solved by the numerical analysis method. The results obtained here are summarized as follows. With increasing the magnetic field, since the magnetic moment is strongly restricted to the magnetic field direction, the motion of the particle is forced to rotate in directions normal to the shear flow direction. In the case of a strong magnetic field and a smaller shear rate, the rodlike particles can freely rotate in the xy-plane with the magnetic moment remaining pointing to the magnetic field direction. On the other hand, for a strong shear flow, the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. Additionaly, the diffusion coefficient gives rise to smaller values than expected, since the rodlike particle sediments with the particle inclining toward directions normal to the moment direction.

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Influences of Magnetic Particle-Particle Interactions on Orientational Distributions and Rheological Properties of a Semi-Dense Colloidal Dispersion Composed of Rod-Like Hematite Particles: Analysis by Means of Mean Field Approximation for an External Magnetic Field Parallel to the Angular Velocity Vector of a Simple Shear Flow

Volume 8: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A and B ◽

10.1115/imece2007-41767 ◽

2007 ◽

Author(s):

Ryo Hayasaka ◽

Masayuki Aoshima ◽

Toshinori Suzuki ◽

Akira Satoh

Keyword(s):

Magnetic Field ◽

Magnetic Moment ◽

Mean Field ◽

Field Approximation ◽

Field Direction ◽

Magnetic Interactions ◽

Mean Field Approximation ◽

Magnetic Field Direction ◽

Orientational Distribution ◽

The Magnetic Field

We have investigated mainly the influences of magnetic particle-particle interactions on orientational distributions and viscosity of a semi-dense dispersion, which is composed of rod-like particles with a magnetic moment magnetized normal to the particle axis. In addition, the influences of the magnetic field strength, shear rate, and random forces on the orientational distribution and rheological properties have been clarified. The mean field approximation has been applied to take into account magnetic interactions between rod-like particles. The basic equation of the orientational distribution function has been derived from the balance of torques and solved by the numerical analysis method. The results obtained here are summarized as follows. For a strong magnetic field, the rotational motion of the rod-like particle is restricted in a plane normal to the shearing plane because the magnetic moment of the particle is restricted in the magnetic field direction. Under circumstances of a very strong magnetic interaction between particles, the magnetic moment is strongly restricted in the magnetic field direction, so that the particle has a tendency to incline in the flow direction with the magnetic moment pointing to the magnetic field direction. For a strong shear flow, a directional characteristic of rod-like particles is enhanced, and this leads to a more significant one-peak-type distribution of the orientational distribution function. Magnetic interactions between particles do not contribute to the viscosity because the mean-field vector has only a component along the magnetic field direction.

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Particle Orientational Properties and Viscosity of a Dense Colloidal Dispersion Composed of Ferromagnetic Spherocylinder Particles: Analysis by Means of Mean Field Approximation for a Simple Shear

Fluids Engineering ◽

10.1115/imece2005-79226 ◽

2005 ◽

Author(s):

Akira Satoh

Keyword(s):

Magnetic Field ◽

Applied Magnetic Field ◽

Mean Field ◽

Magnetic Interaction ◽

Colloidal Dispersion ◽

Field Approximation ◽

Magnetic Interactions ◽

Mean Field Approximation ◽

Particle Interactions ◽

Orientational Distribution

We have theoretically investigated the particle orientational distribution and viscosity of a dense colloidal dispersion composed of ferromagnetic spherocylinder particles under circumstances of an applied magnetic field. The mean field approximation has been applied to take into account the magnetic interactions of the particle of interest with the other ones which belong to the neighboring clusters, besides its own cluster. The basic equation of the orientational distribution function, which is an integro-differential equation, has approximately been solved by Galerkin’s method and the method of successive approximation. Even when the magnetic interaction between particles is of the order of the thermal energy, the effect of particle-particle interactions on the orientational distribution comes to appear more significantly with increasing the volumetric fraction of particles. This effect comes to appear more significantly when the influence of the applied magnetic field is not relatively so strong compared with magnetic particle-particle interactions.

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