Hydrodynamic mean diameter

Li, J. Z., Yang, L., and Liu, W. Hydrodynamic mean diameter of multisized particles, in "Proceeding of CJChEC, p. 754. Tianjin University Press, 1991c. 

The surface mean diameter is the diameter of a sphere of the same surface area-to-volume ratio as the actual particle, which is usually not a perfect sphere. The surface mean diameter, which is sometimes referred to as the Sauter mean diameter, is the most useful particle size correlation, because hydrodynamic forces in the fluid bed act on the outside surface of the particle. The surface mean diameter is directly obtained from automated laser light diffraction devices, which are commonly used to measure particle sizes from 0.5 to 600 p.m. X-ray diffraction is commonly used to measure smaller particles (see Size TffiASURETffiNT OF PARTICLES). 

Glicksman and McAndrews (1985) determined the effect of bed width on the hydrodynamics of large particle bubbling beds. Sand particles with a mean diameter of 1 mm were fluidized by air at ambient conditions. The bed width ranged from 7.6 cm to 122 cm while the other cross sectional dimension remained constant at 122 cm. Most experiments were carried out with an open bed. The bubble rise velocity increased with the bed width, in the representation of bubble velocity as... 

As an example, the dependence of hydrodynamic parameters of critical regime for the sand-water mixture and sand-glycol (80 % glycol solution in water) mixture is illustrated in Figure 1. The volumetric concentration C of the mixtures varied from 5 to 30 %, a mean diameter of sand was d = 0.25 mm and a pipe diameter was D = 50.4 mm. The values of the critical velocity VCr and critical pressure gradient ICr differ substantially according to the used carrier liquid. 

The polystyrene seed latex was monodispersed. Even after several grow-ups (polymerizations) the final 1650 A latex was monodispersed. Hydrodynamic chromatography on the 1650 A latex gave a mean diameter of 1660 a with a size variance as small as for normal polystyrene latex standards (typical standard of 1760 8 with a standard deviation of 23 a). The final latex particle size could be accurately predicted from the initial particle size and the total amounts of monomer and polymer used. 

The proportionality constant typically is close to unity [Seibert and Fair, Ind. Eng. Chem. Res., 27(3), pp. 470-481 (1988)]. Note that Eq. (15-42) indicates the maximum stable drop diameter and not the Sauter mean diameter (although the two are proportionally related and may be close in value). Smaller drops may be formed at the distributor due to jetting of the inlet liquid through the distributor holes or by mechanical pulsation of the liquid inside the distributor [Koch and Vogelpohl, Chem. Eng. Technol., 24(12), pp. 1245-1248 (2001)]. In static extractors, hydrodynamic stresses within the main body of the... 

The papers by Okada et al. (1990a, 1990b) can be estimated as an important novelty in the experimental investigation of the elementary microflotation act and the role of hydrodynamic and surface forces. The mean diameter of bubbles fed into the cell was 33pm. Three kinds of uniform latex particles of different diameter (0.9,2.9, and 6.4pm) were used as model particles. In order to change the surface charges of bubbles and particles three types of surfactants (cationic, anionic and nonionic) and AlCl, were used. The electrokinetic potentials of bubbles... 

In gas-liquid spray towers the liquid is atomized and enters as a fine spray at the top and the gas is introduced at the bottom. The gas flow rate has to be kept sufficiently low to permit the liquid to fall. It is generally chosen in such way that the liquid drops of mean diameter fall at 20 percent of their free-fall velocity, as calculated from Stokes law. An efficient dispersion of the liquid requires the openings of the distributor to be small and the pressure high. Thereby a fraction of the drops hits the wall and flows down the wall as a film. Furthermore, a certain degree of coalescence of the drops is inevitable, so that the drop size, velocity, and therefore residence time vary strongly with position. A rigorous hydrodynamic analysis of such a situation is extremely complicated so that only the overall behavior has been studied. 

Based on the solution of the velocity field, the force and torque acting on the aggregates can be calculated and the hydrodynamic equivalent diameters for translation (xh,t) and rotation (xi -) can be derived. They scale with the aggregate mass via a power law that reflects the stmctural properties of the aggregate. That means, while for hep aggregates the aggregate mass (N) is proportional to the third power of Xh, there is a fractal-tike relationship for DLCA aggregates with a hydrodynamic dimension 4i close to the fiactal dimension (Fig. 4.17, left cf. discussion to Kirkwood-Riseman theory on pp. 164). This fractal relationship... 

Intensity weighted harmonic mean size from DLS experiments (m) Hydrodynamic (equivalent) diameter of translation/rotation (m) Stokes diameter or sedimentation equivalent diameter (-)... 

Micelle hydrodynamic diameters are measured using dynamic light scattering with a Coulter N4 nanosizer. The analyses are performed at scattering angle of 90° at 20°C (Zhang et al. 2004). Mean diameters are calcnlated according to the formula ... 

Werther (1974) measured the bubble characteristics in cylindrical beds of diameters 100,200,450, and 1000 mm for fine partieles with a mean diameter of 83 pm. He showed that for bed diameters eommonly used for laboratory experiments, 200 mm or smaller, the bed diameter had a strong effeet on the bed hydrodynamics. There was a zone of preferred bubble flow near the bed walls at lower elevations. Fig. 6. The... 

The discussion of electrolyte solutions requires the estimation of the Reynolds number for the particular case where L is of the order of the mean diameter of the particles, i.e. 0.1 nm. All liquids commonly used as solvents show dynamic viscosities of the order of 1 cPoise and densities of the order of 1 g cm . Then the order of magnitude of Re can be evaluated if for U an estimate of the hydrodynamic velocity of the sphere in the liquid can be made. The order of magnitude of U can be derived from the linear transport theory, where the motion of a particle in a liquid is described at a local level by the action of a friction force F (eq 1.1). In the steady state of motion this force is supposed to equilibrate the thermodynamic force ... 

The dAc/dz term is usually zero since tubular reactors with constant diameter are by far the most important application of Equation (3.7). For the exceptional case, we suppose that Afz) is known, say from the design drawings of the reactor. It must be a smooth (meaning differentiable) and slowly varying function of z or else the assumption of piston flow will run into hydrodynamic as well as mathematical difficulties. Abrupt changes in A. will create secondary flows that invalidate the assumptions of piston flow. 

Moissis and Berenson (1962) also derived the pool boiling CHF on horizontal surfaces by means of hydrodynamic transitions. Instead of taking 0 between values of f and d, they used the most unstable wavelength as proportional to the jet diameter, DJt... 

The incorporation of comonomers increases the mean hydrodynamic diameter of EUP-micelles, dz (Fig. 16). Contrary to CMC, the dz of micelles resp. microemulsion droplets increases with the concentration of an external electrolyte. 

Hydrodynamic diameters dh and corresponding Gaussian width c of block copolymer micelles in solvents of decreasing polarity. None means that no micelles could be detected by DLS. 

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