Peclet number change

The rod is visualised as being constrained to a tube in a similar fashion to entanglements constraining a polymer in reptation theory. So for a finite concentration our diffusion coefficient and rotary Peclet number changes ... 

The development of the two-phase flow in a heated capillary at different Peclet number is illustrated in Fig. 9.13. It shows that different mechanisms of two-phase flow formation may occur depending on the value of Peu. At small Pcl the fine bubble formation (on the micro-channel wall) plays a dominant role. Growth of these bubbles leads to a blockage of the micro-channel, to a sharp change of the hydraulic... 

Chapter 11 consists of following Sect. 11.2 deals with the pattern of capillary flow in a heated micro-channel with phase change at the meniscus. The perturbed equations and conditions on the interface are presented in Sect. 11.3. Section 11.4 contains the results of the investigation on the stability of capillary flow at a very small Peclet number. The effect of capillary pressure and heat flux oscillations on the stability of the flow is considered in Sect. 11.5. Section 11.6 deals with the study of capillary flow at a moderate Peclet number. 

The electroviscous effect present with solid particles suspended in ionic liquids, to increase the viscosity over that of the bulk liquid. The primary effect caused by the shear field distorting the electrical double layer surrounding the solid particles in suspension. The secondary effect results from the overlap of the electrical double layers of neighboring particles. The tertiary effect arises from changes in size and shape of the particles caused by the shear field. The primary electroviscous effect has been the subject of much study and has been shown to depend on (a) the size of the Debye length of the electrical double layer compared to the size of the suspended particle (b) the potential at the slipping plane between the particle and the bulk fluid (c) the Peclet number, i.e., diffusive to hydrodynamic forces (d) the Hartmarm number, i.e. electrical to hydrodynamic forces and (e) variations in the Stern layer around the particle (Garcia-Salinas et al. 2000). 

For turbulent flow in single-phase systems, the predicted temperature profile is not changed significantly if the Peclet number is assumed to be infinite. Therefore, in turbulent two-phase systems the second-order terms in Eqs. (9) probably do not have a significant effect on the resulting temperature profiles. In view of the uncertainties in the present state of the art for determining the holdups and the heat-transfer coefficients, the inclusion of these second-order terms is probably not justified, and the resulting first-order equations should adequately model the process. 

If the right side of this equation is plotted versus dimensionless time for various values of the group Q)JuL (the reciprocal Peclet number), the types of curves shown in Figure 11.8 are obtained. The skewness of the curve increases with 3) JuL and, for small values of this parameter, the shape approaches that of a normal error curve. In physical terms this implies that when 3JuL is small, the shape of the axial concentration profile does not change... 

Values of Dr can be calculated from the change in shape of a pulse of tracer as it passes between two locations in the bed, and a typical procedure is described by Edwards and Richardson(27). Gunn and Pryce(28), on the other hand, imparted a sinusoidal variation to the concentration of tracer in the gas introduced into the bed. The results obtained by a number of workers are shown in Figure 4.6 as a Peclet number Pe = ucd/eDL) plotted against the particle Reynolds number (Re c = ucdp//j ). 

For large values of the Peclet number, Eq. (38) reduces to Eq. (11) and the exit concentration is strongly influenced by the dimensionless group BN kp/L (Fig. 7). On the other hand, at low values of the Peclet number the exit concentration is hardly influenced by this dimensionless group, which means that the exit concentration is relatively insensitive to changes in the flow rate and screw speed. We shall return to this point momentarily. 

A second factor which may have played a role in the conclusions drawn by Latinen was that a low Peclet number ( 10) was also required to obtain agreement with the theory. As pointed out earlier, the lower the Peclet number the less sensitive is the exit concentration to changes in the screw speed, and this could bring into question any conclusion regarding the linear dependence on the square root of screw speed. 

Remember that according to the approximation made for the dispersion coefficient, dis (Eq. 25-12), the Peclet Number does not depend on it. Therefore, the influence of the pump regime on the concentration at the well is not caused by a change of the transport conditions in the aquifer (e.g., flow time tw), but simply by the fact that more dinitrophenol enters the groundwater during the passage of the pollution cloud if u is large. 

The Peclet number, DGC/k = GC/(k/D) and its modification, the Graetz number wC/kL, are ratios of sensible heat change of the flowing fluid to the rate of heat conduction through a film of thickness D or L. 

As the diameter is decreased, the heat transfer from a unit volume intensifies because of the increase in the ratio of surface to volume (d-1) heat exchange per unit surface also intensifies. For a constant value of the Nusselt number the heat exchange coefficient is proportional to d l. Under the rough assumption that Tc and E change little from one case to the next, we come to the conclusion that at the limit the Peclet number (numerically equal for gases to the Reynolds number), based on the flame velocity (or adiabatic flame velocity u0) has a specific value... 

Changes in microstructure of the suspension become important when the diffusion time fj becomes long compared to the characteristic time of the process, fp. This number hcis been discussed earlier as the De number. The importance of convection relative to diffusion is compared in the Peclet number Pe (in which u is the fluid velocity). The importance of convection forces relative to the dispersion force is compared in Nf just as the dispersion force compared to the Brownian force. The electrical force compared to the dispersion or Brownian force is given by N. The particle size compared to the range of the electrical force is compared in UK. 

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