Hydrodynamic particle diameter

While dynamic light scattering revealed an average apparent hydrodynamic particle diameter of about 200 20 nm, transmission electron microscopy gave a more realistic image of the shape and the size distribution of the nanoMIPs. Figure 9 shows that spherical particles with a rather broad size distribution were formed. They had a diameter of 50 nm up to 300 nm with an average particle diameter around 110 nm and the absence or presence of the template molecule... 

FIGURE 12.14 Effect of functional monomer on hydrodynamic particle diameter measured by quasi-elastic light scattering (QELS) at 20°C. (Erom Duracher, D. ta.., Macromol. Symp., 150, 297, 2000. With permission.)... 

The particle size is obtained from the translational diffusion cocflicicm l)y and particle shape information. For a spherical particle, the StokeS Einsuin rch-iionship is used to calculate the hydrodynamic particle diameter r/f,... 

Table 7.1 z-Average hydrodynamic particle diameter, different kinds of CNTs as a function of the ultrasonic treatment time. 

Ultrasonic treatment time (min) z-Average hydrodynamic particle diameter dh,z ave (DLS) (nm)... 

The HdC calibration curves of different particle sizes, as shown in Fig. 22.12 (30), are similar to the calibration curves of different pore size columns the separation ranges of MW due to hydrodynamic chromatography depend on particle size. The larger the particle size, the higher the MW ranges. Stegeman et al. (30) proposed that a smooth calibration curve may be achieved by proper ratio of the particle diameter to the pore diameter. 

The equilibrium particle diameter in the case of non agglomerate particle systems or the enzyme activity of immobilised enzymes after a certain exposure of time is entirely due to the reactor-specific comminution process, and conclusions can therefore be drawn regarding the maximum intensity of hydrodynamic stress. 

This new particle diameter represents the separation at which the hydrodynamic stress balances with the thermal and thermodynamic stresses ... 

Maiorella et al. [93] observed that fouhng behavior was dependent on cell size. For smaller cells or suspensions containing significant levels of debris, high flux rates could not be maintained without inducing high transmembrane-pressures. This behavior is in qualitative agreement with the hydrodynamic hft theory, since lift velocity is predicted to increase with particle diameter to the second [100] or third power [101]. 

This set of equations is sufficient to characterize a particulate matrix which should be used in fluidized bed adsorption regarding its fluidization behavior. It has to be noted, however, that the correlations have been developed for the fluidization of spherical particles of uniform diameter. In reality, most adsorbents are provided with a certain distribution of particle diameter. In this case, classified fluidization occurs and a modified equation should be used to describe the hydrodynamics of bed expansion [21]. For an estimation of the suitability of a certain matrix for fluidized bed adsorption the correlations shown above are convenient to use and provide sufficient information. The minimum fluidization velocity may be calculated using an average particle diameter as recommended by Couderc [22], In the next section, conventional as well as new matrices shall be described under this respect. 

As a first step, the hydrodynamics in the studied geometry is analyzed using periodic boundary conditions, except for the main flow direction. In the CFD simulations, water at 20°C is used as a model fluid. The results are illustrated in Fig. 9 with an example given for a bcc-packing with a 6.4 mm particle diameter. In this example, the velocity specified at the inlet is 5 mm/s resulting in a superficial velocity of 2.05 mm/s, this yields the Reynolds number Re=13.1. 

Recent systematic studies used steric-S-FFF with well-characterized latex beads of diameters 2-50 pm where the sedimentation force was adjusted to exactly counterbalance the lift force FL [79,301] to provide a measure of FL. This has led to a more subtle view of the hydrodynamic lift forces than expressed by Eq. (85). There are indications that the hydrodynamic lift force is presumably composed of two different contributions (a) the lift force due to the fluid inertial effect ly., which may be described by the theory of hydrodynamic lift forces [289-291], and (b) the hydrodynamic lift force by a near-wall effect ly [61,62,79,301,302]. The latter was experimentally found to be a function of particle diameter dH, the distance of the particle bottom from the wall 8, the fluid shear rate s0, and the fluid viscosity T by ... 

The behavior of particles under the simultaneous effect of field forces and lift forces can vary with the nature of different applied primary field forces [298]. The force acting on the particles is proportional to the third power of the particle diameter in S-FFF, but only to the first power of the particle diameter in Fl-FFF thus indicating that S-FFF is probably best suited for a fine balance between the external field and hydrodynamic lift forces. 

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