Particles tumbling

Figure 6-32, taken from Govier and Aziz, schematically indicates four flow pattern regions superimposed on a plot of pressure gradient vs. mixture velocity = Vl -t- V5 = Qj + ( s)/A where and Vs are the superficial liquid and solid velocities, Qi, and ( 5 are liquid and solid volumetric flow rates, and A is the pipe cross-sectional area. is the transition velocity above which a bed exists in the bottom of the pipe, part of which is stationary and part of which moves by saltation, with the upper particles tumbling and bouncing over one another, often with Formation of dunes. With a broad particle-size distribution, the finer particles may be fully suspended. Near V 4, the pressure gra-... 

Relative motion can be induced, for example, as a pile is being formed, as particles tumble and slide down a chute. The result of sifting/percolation segregation is usually a side-to-side variation of particles. In the case of a bin, the smaller particles will generally be concentrated under the fill point, with the coarse particles concentrated at the outside of the pile (Fig. 4). 

Wetting liquid (distilled water) was supplied by two pneumatic nozzles to the bed of fine particles tumbling in the drum (the wetting stage). Operating parameters of the nozzles were constant ... 

Rotational diffusion of individual molecules in the fluid phase and particle tumbling of the solid particle matrix lead to more or less efficient motional averaging and directly affect NMR data in the time and frequency domain (Fig. 1). Each of the experiments mentioned above has its individual preference for a certain fraction of system components depending on their molecular dynamics. 

The combination of direct excitation or cross-polarization NMR experiments with off-MAS sample spinning seems to be the most powerful approach for the study of rotational diffusion of all system constituents. It allows for a chemical identification of all organic system components and simultaneously yields data on their rotational diffusion. Hence, for detailed studies on particle tumbling in complex systems, it represents the preferred experimental condition for all particle dispersions which are stable enough to survive the inertial field during sample spinning for an adequate period of time. ... 

The unique capability of NMR spectroscopy to differentiate by means of molecular mobility makes it a perfect tool to assign chemical constituents to structural elements of a particle dispersion. This is most straightforward in the case of dispersed nanospheres every constituent which is part of the solid matrix will exhibit the slow particle tumbling, while all components of the liquid continuous phase undergo rapid rotational diffusion. 

Numerical simulation of the ( H)- C spectra based on the given particle tumbling conditions allows for the quantitative analysis on a system which has undergone a partial phase transition. An example for the poly-e-caprolactone particles is shown in Fig. 24. 

The experimental spectrum, which has been taken after a single 12 h freezing step, shows narrow lines superimposed on a solid-state spectrum for the polymer. The result was reproduced by a simulated spectrum based on data for an aliphatic chain (Table 1) assuming two fractions of different mobility. Fraction A represents the dehydrated solid and is merely subject to particle tumbling at a rate which is expected for particles of a = 50-70 nm in aqueous dispersion (r = 0.1 ms). Fraction B represents the particles with the gel matrix in this case, the molecular reorientation is dominated by the internal mobility which is assumed to be equivalent to an isotropic tumbling of a short correlation time... 

Deviations from spherical shape can be modeled as a growth into prolate or oblate shapes. The area enclosed volume ratio constraint implies a constraint in the possible values of the two semiaxes describing the particle size. Halle [62] calculated the correlation functions for the combined particle tumbling and surface diffusion of prolate and oblate particles. His results have, for example, been applied to microemulsion systems [48,58], focusing on the ratio yVpr(0)// 5,sph(0). where the subscripts pr and sph refer to prolate and spherical particles, respectively. For a given ratio of interfacial area to enclosed volume, which specifies the radius R of the sphere, y, pr(0)//. sph(0) is a function of the prolate axial ratio, Diat, and R. Knowing Djat and R from other experiments, it is possible to determine the aggregate axial ratio from the relaxation experiment. 

Abrasive particles tumble across hard regions of the disk surface, as in normal lapping. Abrasive particles become embedded in softer regions of the disk surface, as in grinding disks. 

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