Critical Peclet number

The dependence of P (PeL) and g (PeL) is shown in Fig. 11.4. The parameter P (PeL) is a parabola with an axis of symmetry left of the line Pcl = 0. Since the Peclet number is positive, for any value of the operating parameters, the physical meaning is that only for the right branch of this parabola, which intersects the axis of the abscissa at some critical value of Peclet number, Pcl = Peer- The vertical line PeL = Peer subdivides the parametrical plane P - Pcl into two domains, corresponding to positive (PeL < Peer) or negative (PeL > Peer) values of the parameter P . The critical Peclet number is... 

The effect of convection on the pitting behaviour of stainless steel 304 is in total contrast to that of pure iron, in that removal of the metal salt film leads to the repassivation of the metal surface. Harb [113] has recently investigated the pitting-convection behaviour of single pits in a pH 3.5 solution of 0.1 M Na2S04 and 0.2 M NaCl. Basing his analysis on the concept of a critical Peclet number [113], he showed that high Peclet numbers (Pe > 10) favour removal of the dissolution products from the pit surface and subsequent repassivation, whilst for flow rates and/or pit radii for which... 

Peclet number (Pe) Ratio of convection flow velocity to the characteristic diffusion velocity. The critical Peclet number for a flame velocity and characteristic pore size inside a fire-resistant barrier specifies the conditions for flame break through a screen. For example, at Pe < (40-100) the flame is quenched. 

In the domain of a very small Peclet number the growth rate of fiow oscillations is negative at any values of flow parameters. In the vicinity of the critical point (Pcl = POcr, P 0) the sign is determined by Eq. (11.82). An increase in (other... 

Chemical reaction coefficient, 25 281,283, 290 combinations of, 25 293t effect on critical value of mass transfer Peclet number, 25 284t Chemical reaction engineering (CRE), 22 330... 

Mass transfer Peclet number (PeMT), 25 270, 279, 280, 281, 283, 285, 311, 316. See also Peclet numbers (Pe) critical value of, 25 283-285 effect on dimensionless reactant molar densities, 25 289t, 294-295 particle-based, 25 291 Mass-transfer rate, in liquid-bquid extraction, 10 751... 

The conditions presented above have been formulated for the case that the values of the Peclet numbers for heat and mass dispersion in a bed are indentical. However, recent experimental research on axial heat dispersion in packed beds has indicated that the values of the Peclet number for heat transfer may be different from those for mass transfer (48). Fortunately, the aforementioned conditions are still valid, however, the critical values of B and Pe as well as the bounds Dan,in and Da x are dependent on the ratio q = PeH/PeM. From the theoretical results may be inferred that for highly exothermic reactions multiple steady states may... 

To determine the critical shear stress, %, we note that the translational Peclet number Pet[= 6iTr)ga yJkBT] - 8, allowii the calculation of the critical shear stress ... 

When y is given in dimensionless form as the translational Peclet number, the dimensionless critical shear rate Peclet number, y, is 8, as given in the following equation ... 

Dimensional analysis implies that for a given value of , all monodisperse hard-sphere suspensions ought to show an onset of shear thickening at a universal value of the Peclet number Pe, or reduced stress Or. Thus, the critical shear rate Yc foi shear thickening ought... 

Shear thinning sets in at a critical value of the Peclet number, Pe = Pe. = r],y a /ksT. Hence, the critical shear rate yc must be inversely proportional to the cube of the particle radius. Thus, using the answer in part (a), we obtain... 

CCT, critical cracking thickness Boltzmann constant (1.381x10 local permeability [m ] fracture resistance [N m ] average permeability in/of compact [m ] particle shape factor compact thickness [m] initial particle number concentration [m refractive index of particle material refractive index of dispersion material number density of ion i dimensionless number dimensionless number Stokes number Peclet number capillary pressure [N-m ] dynamic pressure [N m ] local liquid pressure in the compact [N-m local solid pressure in the compact [N-m ] superficial fluid velocity [m-s q gas constant [J K ] centre to centre distance [m]... 

Assuming that this result is correct, it is very important because comparison with (9-230) or (9-274) shows that the rate of heat transfer from a particle (or heated body) to a surrounding fluid at high Peclet numbers depends critically on whether the streamlines (or stream surfaces) near the heated surface are open or closed. 

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