Brownian relaxation

Nadler, W. Schulten, K., Generalized moment expansion for Brownian relaxation processes, J. Chem. Phys. 1985, 82, 151-160... 

The magnetization dynamics of ferrofluids is characterized by the distinction between Brownian and Neel relaxations. Brownian relaxation refers to the mechanical rotation... 

Magnetic particles in a solution undergo two types of relaxation Brownian relaxation, in which the entire particle rotates, and Neel relaxation, in which the moment rotates while the particle remains still. The Brownian relaxation time xB is... 

The relaxation rates are affected differently by the immobilization of the nanoparticles. The Brownian relaxation time can be changed by changing the viscosity of the carrier while the Neel relaxation should be independent of the carrier liquid. The relaxation rates also are affected differently by phenomena such as immobilization of a nanoparticle due to endocytosis. 

Since Brownian relaxation times scale as the cube of the particle radius (see Section 6.2.2), a fairly abrupt transition from Brownian to non-Brownian behavior might be expected when the droplet radius increases. Surprisingly, however, Otsubo and Prud homme (1994) observed little dependence on droplet radius over a range of 4-12 /xm, for high-density emulsions of oil droplets in an aqueous phase. Figure 9-24 shows G and G" for various... 

We have mentioned that the question posed above was answered in part by Shliomis and Stepanov [9]. They showed that for uniaxial particles, for weak applied magnetic fields, and in the noninertial limit, the equations of motion of the ferrofluid particle incorporating both the internal and the Brownian relaxation processes decouple from each other. Thus the reciprocal of the greatest relaxation time is the sum of the reciprocals of the Neel and Brownian relaxation times of both processes considered independently that is, those of a frozen Neel and a frozen Brownian mechanism In this instance the joint probability of the orientations of the magnetic moment and the particle in the fluid (i.e., the crystallographic axes) is the product of the individual probability distributions of the orientations of the axes and the particle so that the underlying Fokker Planck equation for the joint probability distribution also... 

In order to illustrate how precession-aided relaxation effects may manifest themselves in a ferrofluid, it will be useful to briefly summarize the differences in the relaxation behavior for axially symmetric and nonaxially symmetric potentials of the magnetocrystalline anisotropy and apphed held, when the Brownian relaxation mode is frozen. Thus only the solid-state (Neel) mechanism is operative that is, the magnetic moment of the single-domain particle may reorientate only with respect to the crystalline axes. 

Thus, the principal effect of the external field in Eq. (121) is to reduce the Brownian relaxation time. 

Dressing surfactant density Magnetic core density Effective relaxation time of magnetization Brownian relaxation time Neelian relaxation time Hydrodynamic volume fraction of the surfactant-dressed nanoparticles Suspension volume fraction of magnetic material embedded in the nanoparticles y-phase-side values of the variable eg on K-phase-side values of the variable eg on Spatial fluctuation of the bounded piecewise continuous scalar field cp around the intrinsic average in u... 

Nanoparticles magnetic heating due to Neel and Brownian relaxation processes... 

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