Stokes relaxation time

The Basset force may be negligible when the fluid-particle density ratio is small, e.g., in most gas-solid suspensions, and the time change is much longer than the Stokes relaxation time or the acceleration rate is low. 

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... 

At infinite dilution, the assumption of a constant relaxation time is reasonable and, using Stokes law as well, we have... 

The relation between the microscopic friction acting on a molecule during its motion in a solvent enviromnent and macroscopic bulk solvent viscosity is a key problem affecting the rates of many reactions in condensed phase. The sequence of steps leading from friction to diflfiision coefficient to viscosity is based on the general validity of the Stokes-Einstein relation and the concept of describing friction by hydrodynamic as opposed to microscopic models involving local solvent structure. In the hydrodynamic limit the effect of solvent friction on, for example, rotational relaxation times of a solute molecule is [ ]... 

Stopping distance The maximum distance a moving particle will travel in still air after all the external forces are removed. In the Stokes region it is the velocity of the particle times the relaxation time. 

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 ... 

Droplet suspensions (gas-liquid, two-component system) Since the inertia of a liquid suspended in the gas phase is higher than the inertia of the gas, the time for the displacement of liquid under the pressure waves should be considered. Temkin (1966) proposed a model to account for the response of suspension with pressure and temperature changes by considering the suspensions to move with the pressure waves according to the Stokes s law. The oscillatory state equation is thereby approximated by a steady-state equation with the oscillatory terms neglected, which is valid if the ratio of the relaxation time to the wave period is small, or... 

Chromium(III) has a ground state in pseudo-octahedral symmetry. The absence of low-lying excited states excludes fast electron relaxation, which is in fact of the order of 10 -10 ° s. The main electron relaxation mechanism is ascribed to the modulation of transient ZFS. Figure 18 shows the NMRD profiles of hexaaqua chromium(III) at different temperatures (62). The position of the first dispersion, in the 333 K profile, indicates a correlation time of 5 X 10 ° s. Since it is too long to be the reorientational time and too fast to be the water proton lifetime, it must correspond to the electron relaxation time, and such a dispersion must be due to contact relaxation. The high field dispersion is the oos dispersion due to dipolar relaxation, modulated by the reorientational correlation time = 3 x 10 s. According to the Stokes-Einstein law, increases with decreasing temperature, and... 

The water proton NMRD profile of Cu(II) aqua ion at 298 K [108] (Fig. 5.36) is in excellent accordance with what expected from the dipole-dipole relaxation theory, as described by the Solomon equation (Eq. (3.16)). The best fitting procedure applied to a configuration of 12 water protons bound to the metal ion provides a distance between water protons and the paramagnetic center equal to 2.7 A, and a correlation time equal to 2.6 x 10 11 s, which defines the position of the cos dispersion. The correlation time is determined by rotation as expected from the Stokes-Einstein equation (Eq. (3.8)). The electron relaxation time is in fact expected to be one order of magnitude longer (see Table 5.6). This also ensures... 

F. Ingrosso, B. Mennucci and J. Tomasi, Quantum mechanical calculations coupled with a dynamical continuum model for the description of dielectric relaxation time dependent Stokes shift of coumarin Cl53 in polar solvents, J. Mol. Liq., 108 (2003) 21 -6. 

S nuclear quadrupole coupling constants have been determined from line width values in some 3- and 4-substituted sodium benzenesulphonates33 63 and in 2-substituted sodium ethanesulphonates.35 Reasonably, in sulphonates R — SO3, (i) t] is near zero due to the tetrahedral symmetry of the electronic distribution at the 33S nucleus, and (ii) qzz is the component of the electric field gradient along the C-S axis. In the benzenesulphonate anion, the correlation time has been obtained from 13C spin-lattice relaxation time and NOE measurements. In substituted benzenesulphonates, it has been obtained by the Debye-Stokes-Einstein relationship, corrected by an empirically determined microviscosity factor. In 2-substituted ethanesulphonates, the molecular correlation time of the sphere having a volume equal to the molecular volume has been considered. 

---