Relaxation time, particles

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. 

This effect of concentration is particularly pronounced with irregularly shaped particles. A possible explanation of the variation in the specific resistance is in terms of the time available for the particles to orient themselves in the growing cake. At higher concentrations, but with the same approach velocities, less time, referred to as particle relaxation time, is available for a stable cake to form and a low resistance results. 

Trp Particle relaxation time the curved pipe axis, defined... 

Laser Doppler velocimetry has been combined with acoustic excitation to allow the derivation of the relaxation time for particles, from which the aerodynamic diameter can be calculated [132-136], The particle relaxation time is derived from the velocity amplitude of the aerosol particle and that of the medium while the aerosol is subjected to acoustic excitation of a known frequency. A differential laser Doppler velocimeter is used to measure the velocity amplitude of the particle, and a microphone is used to measure the velocity amplitude of the medium. The aerodynamic diameter of the particle can be derived from the relaxation time and the known particle density. The method can be applied to real-time in situ measurement of the size distribution of an aerosol containing both solid and liquid droplets in the diameter range of 0.1 -10 pm. 

In the formulation of the transport equations, several characteristic time scales are defined. In this framework these time scales are considered fundamental in the classification and the understanding of the dominant mechanisms in the suspension flow. The particle relaxation time Tgp was already defined in (10.98). The particle-particle collision time t, is defined by ... 

However, in the PGT model the drift velocity is neglected and set to zero. The average particle relaxation time Tgp) pPp is obtained from (10.102). 

Lagrangian micro time scale, or Lagrangian microscale (s) particle relaxation time (s)... 

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 ... 

For laminar flow, the characteristic time of the fluid phase Tf can be deflned as the ratio between a characteristic velocity Uf and a characteristic dimension L. For example, in the case of channel flows confined within two parallel plates, L can be taken equal to the distance between the plates, whereas Uf can be the friction velocity. Another common choice is to base this calculation on the viscous scale, by dividing the kinematic viscosity of the fluid phase by the friction velocity squared. For turbulent flow, Tf is usually assumed to be the Kolmogorov time scale in the fluid phase. The dusty-gas model can be applied only when the particle relaxation time tends to zero (i.e. Stp 1). Under these conditions, Eq. (5.105) yields fluid flow. This typically happens when particles are very small and/or the continuous phase is highly viscous and/or the disperse-to-primary-phase density ratio is very small. The dusty-gas model assumes that there is only one particle velocity field, which is identical to that of the fluid. With this approach, preferential accumulation and segregation effects are clearly not predicted since particles are transported as scalars in the continuous phase. If the system is very dilute (one-way coupling), the properties of the continuous phase (i.e. density and viscosity) are assumed to be equal to those of the fluid. If the solid-particle concentration starts to have an influence on the fluid phase (two-way coupling), a modified density and viscosity for the continuous phase are generally introduced in Eq. (4.92). 

TABLE 2 Particle Relaxation Times (r, ms) of /3-FeOOH Particles at Different NaPSS Concentrations... 

Stoimenova M, Radeva Ts. Electro-optics of semidilute dispersions influence of electrostatic interactions on colloid particles relaxation times. J Colloid Interface Sci 1995 169 329-334. 

From Fig. 12.3.1 we see that the CHCla single-particle relaxation time is constant at constant solution viscosity. The light-scattering reorientation time extrapolated to infinite dilution is in excellent agreement with this single-particle time. Thus the concentration dependence of xt at higher concentrations is due to the increasing importance... 

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