Relaxation time of particle

Let us calculate the relaxation time of particles in this potential (escape time over a barrier) which agrees with inverse of the lowest nonvanishing eigenvalue Yj. Using the method of eigenfunction analysis as presented in detail in Refs. 2, 15, 17, and 18 we search for the solution of the Fokker-Planck equation in the... 

Exact solution of one-dimensional reversible coagulation reaction A+A A was presented in [108, 109] (see also Section 6.5). In these studies a dynamical phase transition of the second order was discovered, using both continuum and discrete formalisms. This shows that the relaxation time of particle concentrations on the equilibrium level depends on the initial concentration, if the system starts from the concentration smaller than some critical value, and is independent of the tia(0) otherwise. 

It is important from a practical viewpoint to predict the shear viscosity of mixtures from those of pure melts. For alkali nitrate melts, a linear dependence has been found between the reorientational line width obtained by Raman measurements and the ratio of temperature divided by shear viscosity.For NO3 ions, the depolarized Raman scattering from 1050cm" total stretching vibrational mode (Al) has a contribution to the line width L, which is caused by the reorientational relaxation time of the Csv axis of this ion. The Stokes-Einstein-Debye(SED) relation establishes a relation between the shear viscosity r of a melt and the relaxation time for the reorientation of a particle immersed in it ... 

Akaganeite particles The first inflection point corresponds to a correlation time larger at 37°C (2.28 ns) than at 5°C (1.76 ns). This temperature dependence is typical of an electronic relaxation time (of Fe " "). The difference between the calculated correlation time and the theoretical relaxation time... 

Any paramagnetic (or ferromagnetic) metal complex or particle that decreases the relaxation times of nuclei detected in an image. 

Fig. 7.13 The size and shape dependence of superparamag-netic (SP), multi-domain (MD) and single-domain particles (SD) as a function of the axial shape ratio The times x refer to relaxation times of 4 10 a and 100 s (from Butler, Banerjee, 1975, with permission).

As justification for the third point we cite some typical figures we define the relaxation time of a process in the gas as the ratio of the width of the zone of temperature change to the velocity of the gas. In other words, we define the relaxation time as the time during which a certain particle of gas travels from the interface to the place where the reaction ends. 

The dimensionless variable St is not always useful in the analysis because the relaxation time of the particle trp in the expression depends on the particle Reynolds number Rep in a general form... 

The elapsed time for particles to pass through the shock front may be approximated by dv/U. Since U is of the same order of magnitude as the speed of sound in the gas, the ratio of the flying time to the Stokes relaxation time of a particle can be expressed by... 

Therefore, for the internal (Neel) relaxation the parameter, r m plays the same role as the fluid viscosity r in the mechanism of the external (Brownian) diffusion. Note that the density of the anisotropy energy K is not included in x. This means that xD can be considered as the internal relaxation time of the magnetic moment only for magnetically isotropic particles (where K = a = 0). The sum of the rotations—thus allowing for both the diffusion of the magnetic moment with respect to the particle and for the diffusion of the particle body relative to the liquid matrix—determines the angle ft of spontaneous rotation of the vector p at the time moment t ... 

It is clear that the rotation relaxation time of the particles cannot be evaluated using only the quasistatic (coxB l) measurements. However, with the aid of the series (4.378) and (4.379), one can manage to find xB employing a minimal amount of additional experimental data. Let us assume that we have measured... 

The temperature at the maximum in the zero field dc susceptibility measurement determines the blocking temperature TB (Fig. 3). It was found to increase with the average diameter of the clusters of a given sample. The simplest model to explain superparamagnetism assumes that each particle has a uniaxial anisotropy with a direction independent of that of the other particles. The energy that is needed to reverse the magnetization U, determines the relaxation time of this process,... 

It is evident that the dipolar interaction increases the activation energy and slows the relaxation time of moment reversal. To explain the dependence quantitatively a simple model was proposed [26], inspired by the references contained in [22], where the relaxation time considered is for independent clusters and the dipolar interaction modifies Ueff. In the model, a test cluster of uniaxial anisotropy is surrounded by clusters with their anisotropy axis randomly oriented. The susceptibility is dominated by the largest particles in a sample since it is proportional... 

The situation looks simpler, if one assumes that relaxation times of the surrounding can be neglected, and one obtains for the collective motion of the entire set of macromolecules, considered as a set of Brownian particles, a system of stochastic Markovian equations... 

Hydration of HPP. All factors mentioned above affect the T i value, showing the change in the state of water to be the result of a change in the composition of the water and the surface properties of the disperse phase. Aluminium hydrolysis products are mostly particles of Al(OH)3 with aluminium hydroxyl complexes adsorbed on them, so the change in T can be associated with an altered nature and number of hydrophilic centres. It has been shown5,6 that in all cases the spin-spin relaxation time of water protons decreases with increasing OH/A1 ratio in the coagulant molecule. This is an evidence of increased hydration of particles surface in this direction. 

---