Mobility of Particles

It is clear that tire rate of growdr of a reaction product depends upon two principal characteristics. The first of these is the thermodynamic properties of the phases which are involved in the reaction since these determine the driving force for the reaction. The second is the transport properties such as atomic and electron diffusion, as well as thermal conduction, all of which determine the mobilities of particles during the reaction within the product phase. 

Electrokinetic studies revealed that the mobilities of particles with pre-adsorbed anionic polymer in the presence of surfactant were controlled by the charge associated with the polymer, while the mobilities were unaffected by the presence of pre-adsorbed nonionic polymer. 

According to the conventional expression, the survival probability depends on the mobility of particles and traps only via the sum of their diffusion... 

In calculations presented below we assume first one kind of defects to be immobile (Da = 0, k = 0) and their dimensionless initial concentration n(0) = 0.1 is not too high it is less than 10 per cent of the defect saturation level accumulated after prolonged irradiation [41]. Its increase (decrease) does not affect the results qualitatively but shorten (lengthen, respectively) the distinctive times when the effects under study are observed. To stress the effects of defect mobility, we present in parallel in Sections 6.3.1 and 6.3.2 results obtained for immobile particles A (D = 0, asymmetric case) and equal mobility of particles A and B (Da = Dq, symmetric case). In both cases only pairs of similar particles BB interact via elastic forces, (6.3.5), but not AA or AB. The initial distribution (t = 0) of all defects is assumed to be random, Y(r > 1,0) = -X (r,0) = 1 i/ = A,B. 

The electrophoretic mobilities of particles in concentrated dispersion have been measured using (a) a relatively simple moving boundary technique185 and (6) a mass transport method186. The interpretation of such measurements may be complicated by electric double layer... 

In conclusion it should be noted that the indicated lowering of the dimension of the system of equations in the quasi-chemical approximation can be used not only in problems describing the equilibrium and kinetics of surface processes for the rapid surface mobility of particles in steady-state conditions, but also in non-steady conditions. In the latter case, the derivatives of the functions Y j(r) or Y j(r) °n the left-hand sides of the equations are linearly related to one another, and for integration of the system of equations with respect to time they must be determined preliminarily from the relevant system of equations. Notwithstanding this circumstance, the indicated replacement of the variables noticeably diminishes the calculation difficulties in solving the problem. 

In relaxation processes of the macromolecular coil to equilibrium, the competing mechanisms of mobility of particles are present simultaneously. However, in the region of weakly entangled macromolecules, relaxation occurs due to isotropic mobility of particles of the chain - the diffusive mechanism -... 

The reptation diffusion is connected with the local anisotropy of mobility of particles, which can be confirmed by investigation of equations (3.37). As an example, Fig. 11 contains the results for displacement of a macromolecule of length M = 25Me (value of parameter x = 0.04) due to numerical integration... 

Liquid systems occupy a special place between gaseous and solid phases. The high mobility of particles in a liquid and the values of diffusion coefficients falling in a narrow range supports the assumption of a free volume of about 1 cm3moL (see Section 6.3.3) as a prerequisite for the manifestation of the typical properties of a liquid phase. 

Figure 10. Dependence of mobility of particles versus viscosity and activation energy of diffusion.

The influence of major variables indicated above on the electrokinetic potential and degree of hydration of AS, BAS and BAC hydrolysis product particles has been studied in detail. The electrophoretic mobility of particles was measured by microelectrophoresis. As a measure of hydration of HPP the time of spin-spin relaxation of protons of adsorbed/adherent water (7j) was used. The 7j values were measured by NMR with a pulse relaxometer by the null method.5 The results obtained can be summarised as follows. 

Nearly all aspects of physical ageing can be explained by means of the "free volume" concept, i.e. the hypothesis that the mobility of particles (atoms, molecules) is mainly determined by their packing density. 

Figure 2. Electrophoretic mobilities of particles in seven4on (l t) and natural sea water (right). Tie lines connect values for the same kind of particle. Data from Ref. 15.

Qi(x) Qx, Cumulative volume or mass distribution Cumulative volume distribution till class i — — Z(x) Electrical mobility of particle size x c G... 

For smaller particles, an indirect method is required to measure the particle velocity. The easiest is phase amplitude light scattering. An alternating electric field with a frequency of a few Hertz is applied. The phase shift of scattered light is dependant on the applied electric field and is proportional to the mobility of particles causing the scattering. 

The movement of colloidal particles in an electric field is termed electrophoresis. Most commercially available zetameters are designed to measure the electrophoretic mobility of particles. The potential is not measured directly, but is calculated from u. The Smoluchowski equation... 

The electrophoretic mobility of particles having a cylindrical or ellipsoidal shape was studied theoretically by Stigter, " van der Drift et al., " and Ohshima. The polyelectrolytes and the spherical particles covered by a layer of polymer " - (or of polyelectrolyte) are two other types of systems that have been matters of great interest. In a recent series of papers Ohshima and... 

In deriving equation 32 or equation 33, it is assumed that 0max is the solid volume fraction at which the suspended particles cease moving. Thus, the forces, such as shearing, that can disturb the suspension structure and hence improve the mobility of particles will have an effect on the value of max. This is confirmed by the fact that a value of kH = 6.0 is observed at low shear limit, that is, y 0 and at high shear limit, y - oo, kH = 7.1 is found. Typical values of max have been found with the use of Quemada s equation as 0max = 0.63 0.02 in the low shear limit and high shear limit for submicrometersized sterically stabilized silica spheres in cyclohexane (72, 85, 88). 

Fluid velocity, y component, normal to channel walls or plate surface Mobility of particle in solution Specific volume Mobility tensor, Eq. (5.1.3b)... 

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