Local viscosity coefficient

When normal sites in a crystal structure are replaced by impurity atoms, or vacancies, or interstitial atoms, the local electronic structure is disturbed and local electronic states are introduced. Now when a dislocation kink moves into such a site, its energy changes, not by a minute amount but by some significant amount. The resistance to further motion is best described as an increase in the local viscosity coefficient, remembering that plastic deformation is time dependent. A viscosity coefficient, q relates a rate d8/dt with a stress, x ... 

It will be recalled that in Fig. 28 we found that for the most mobile ions the mobility has the smallest temperature coefficient. If any species of ion in aqueous solution at room temperature causes a local loosening of the water structure, the solvent in the co-sphere of each ion will have a viscosity smaller than that of the normal solvent. A solute in which both anions and cations are of this type will have in (160) a negative viscosity //-coefficient. At the same time the local loosening of the water structure will permit a more lively Brownian motion than the ion would otherwise have at this temperature. Normally a certain rise of temperature would be needed to produce an equal loosening of the water structure. If, in the co-sphere of any species of ion, there exists already at a low temperature a certain loosening of the water structure, the mobility of this ion is likely to have an abnormally small temperature coefficient, as pointed out in Sec. 34. 

X 10 cm by measuring molecularly dispersed water in toluene and by correcting for local viscosity differences between toluene and these microemulsions [36]. Values for Dfnic were taken as the observed self-diffusion coefficient for AOT. The apparent mole fraction of water in the continuous toluene pseudophases was then calculated from Eq. (1) and the observed water proton self-diffusion data of Fig. 9. These apparent mole fractions are illustrated in Fig. 10 (top) as a function of... 

One difficulty of connecting theory and experiment arises from the fact that the relation between the microscopic coupling parameter between the reaction coordinate and the medium (the friction coefficient) and the macroscopic observables is not well understood. The usual rule of thumb follows Stokes s law and states that the friction is proportional to the macroscopic bulk viscosity however, this may be grossly incorrect. It would be advantageous to use a local viscosity obtained from the measurement of some sort of molecular relaxation phenomenon, but this is not always available. 

The rotational friction coefficient of a spherical molecule in solution is calculated applying the Navier-Stokes equation for a continuum solvent with a position-dependent viscosity as a model of "microscopic viscosity." The rotational friction coefficient decreases with decreasing surface viscosity. The results are compared with the translational fnction and viscosity B coefficients which are previously obtained from the same model. The B coefficient is most sensitive to a local viscosity change The Gierer-Wirtz model overestimates the effect of the "microscopic viscosity" on the translational friction coefficient comparing with the present results... 

The first result agrees with what solution chemists expect for the effect of the "microscopic viscosity " The second result tells us that the sensitivity of the friction coefficients on a local viscosity change largely depends on the mode of solvent motions. The shear mode (the viscosity B coefficient) is the most sensitive of the three It is to be noted that these results do not depend on the particular choice of the functional form of the position-dependent viscosity as expected. 

Gurney considered that the negative B coefficient is an indication of the local loosening of the solvent structure in the vicinity of the solute molecule and can be used as a measure for the structure breaking effect. The present quantitative analysis of the effect of the local viscosity change supports this idea. 

In Figure 2 (b), the correlation between B and Cr examined for each functional form of the "microscopic viscosity " Two different correlation curves suggest that the viscosity B coefficient is sensitive to the functional forms of the local viscosity change. This corresponds to the sensitivity of B on the parameter a as pointed out above. 

The velocity dependence for the partly retarded section follows a linear law with a coefficient comparable to the ratio between the local retardation coefficient and the viscosity of water. The higher the degree of bubble surface retardation, the less is the possibility of detaehment of particles in non-contact flotation. Therefore, the question about the degree of surface retardation is of great interest. 

Many of the mixing simulations described in the previous section deal with the modeling of mass transfer between miscible fluids [33, 70-77]. These are the simulations which require a solution of the convection-difliision equation for the concentration fields. For the most part, the transport of a dilute species with a typical diSusion coeflEcient 10 m s between two miscible fluids with equal physical properties is simulated. It has already been mentioned that due to the discretization of the convection-diffusion equation and the typically small diffusion coefficients for liquids, these simulations are prone to numerical diffiision, which may result in an over-prediction of mass transfer efficiency. Using a lattice Boltzmann method, however, Sullivan et al. [77] successfully simulated not only the diffusion of a passive tracer but also that of an active tracer, whereby two miscible fluids of different viscosities are mixed. In particular, they used a coupled hydrodynamic/mass transfer model, which enabled the effects of the tracer concentration on the local viscosity to be taken into account. 

The local viscosity also depends on concentration and temperature, but the details depend on the polymer and the solvent. Experiments carried out with high-molecular-weight chains as a function of chain length verify the 1 /N dependence for the self-diffusion coefficient in well-entangled solutions. The concentration dependence is much harder to verify because of the issue of local viscosity, but the decrease of the self-diffusion coefficient with concentration is dramatic for all solutions in tiiis regime. 

The concentration dependence of D (c) in the concentrated regime depends on the solvent quality and the local viscosity. It is often observed to go through a maximum with concentration due to a large increase of local viscosity with concentration. However, if the polymer is well above its glass-transition temperature, the mutual-diffusion coefficient can even increase throughout the concentrated regime. Solutions of poly(dimethyl siloxane) in dioxane exhibit a continuously increasing mutual-diffusion coefficient. 

Fluorescence anisotropy studies of concentrated solutions are important for two reasons. Firstly, they bridge the gap between the results for dilute solutions, which can be interpreted relatively easily on the basis of the existing models, and the practically important dynamic behavior of bulk polymers, which is very complicated and its theoretical description and appropriate analysis are difficult. SecOTidly, they elucidate the contribution of the local frictirai to the macroscopic viscosity rj c,T,M) of concentrated polymer solutions. The viscosity coefficient where c is the polymer concentration, M is its molar mass, and T is temperature, can be expressed as... 

In the case under investigations, which includes nematic (anisotropic) phase environments, we shall assume the usual approximation of considering isotropic local friction, and the macroscopic local viscosity is taken equal to half of the fourth Leslie-Ericksen coefficient 1/4 [92-95]. The diffusion tensor of the system is obtained, neglecting translational contributions, as a 4 x 4 matrix, that is. 

The viscosity coefficient A4 is related to the rotation of the local smectic layer normal a and is the only rotational viscosity to appear in the SmA classification on page 297. The key rotational viscosity in SmC is A5, with the coefficients Ae and re being ac-coupling rotational viscosities. 

An explicit expression for the coefficient of shear viscosity can be obtained by assuming the system is in local themiodynamic equilibrium and using the previously derived expression for X and v. Thus we obtain... 

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 [ ]... 

X = distance film has fallen g = gravitational constant Pi = liquid density = latent heat of vaporization JL = liquid viscosity k = liquid thermal conductivity AT = temperature difference = (Tb bbi,p i -NrUj = local Nusselt number, h x/k, h = local heat transfer coefficient... 

---