Particle deposition relaxation time

Although most cakes consist of polydisperse, nonspherical particle systems theoretically capable of producing more closely packed deposits, the practical cakes usually have large voids and are more loosely packed due to the lack of sufficient particle relaxation time available at the time of cake deposition hence the above-derived value of 17.6 pm becomes nearer the 10 pm limit when air pressure dewatering becomes necessary. 

In both experimental and theoretical investigations on particle deposition steady-state conditions were assumed. The solution of the non-stationary transport equation is of more recent vintage [102, 103], The calculations of the transient deposition of particles onto a rotating disk under the perfect sink boundary conditions revealed that the relaxation time was of the order of seconds for colloidal sized particles. However, the transition time becomes large (102 104 s) when an energy barrier is present and an external force acts towards the collector. 

Fig. 25. 2-D MR image of the deposition of 80-pm particles (fines) within a bed packed with 5-mm diameter spherical glass beads. The water flow rate was 300mLmin . All images were acquired in 3-D with isotropic spatial resolution of 188 pm x 188 pm x 188 pm. Two local regions associated with a buildup of fines are highlighted and are identified by the low apparent H spin density from these regions resulting from low voidage and relaxation time effects. Flow was in the + z direction. Reprinted from reference (54), with permission of Springer Science and Business Media.

When the Reynolds number based on tube diameter is greater than 2100, the boundary layer becomes turbulent at some distance from the inlet. The transition usually occurs at a Reynolds number, based on distance from the entrance, Rcj, of between 10 and 10, depending on the roughness of the wall and the level of turbulence in (he mainstream. As shown in Fig, 4,11, the deposition rate tends to follow the development of the turbulent boundary layer. No deposition occurs until Re is about 10- the rate of deposition then approaches a constant value at Re = 2 x 10 in the region of fully developed turbulence. On dimensional ground.s. the deposition velocity at a given pipe Reynolds number can be assumed to be a function of the friction velocity, if, kinematic viscosity, v, and the particle relaxation time, m/f ... 

The data suggest that both the initial deposition rate and the asymptotic deposit mass are both dependent upon the bulk velocity u raised to the power 0.6 - 0.7. The results were also compared with the mass transfer rates of Cleaver and Yates [1975] and Metzner and Friend [1958]. Although the dimensionless particle relaxation times (see Section 7.3) were below 0.1, the inertial deposition rates calculated from the theory of Cleaver and Yates were of an order of magnitude higher than the difiusional rates calculated and indeed measured. The measured power on velocity of 0.7 compared to a theoretical value of 0.875 for difrusion and 2 for inertial particle transfer, suggest a diffiision controlled mechanism. 

Shear stress or particle relaxation time Dimensionless particle relaxation time Rate of deposition Particle flux Particle volume... 

Dangling bonds related to structural defects in a DND particle have a nonzero spin and are revealed with the use of the EPR and NMR (nuclear magnetic resonance) techniques by measuring the spin-lattice relaxation times. Their number is estimated as 1-40 per one DND particle. Experiments performed with copper ions deposited on the surface of DND particles suggest that these defects are located inside the particle at a distance of 0.8-1.5 nm from its surface. ... 

Reason 2 has a large body of experimental evidence (e.g. Figure 9.15 and other references reported in chapter 9) and the physical reason is that higher feed concentrations reduce the time available for particle relaxation when particles hit the top of the cake. Each particle just deposited on the cake is locked into position by other particles in its vicinity before it has time to roll and fill the open crevices in the cake. Thus, at high concentrations, the cake formed is more open and, consequently, it has more voids within it. This has been proved experimentally as well as in a modeUing exercise by Walker . ... 

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