Dimensionless number Peclet

The parameter D is known as the axial dispersion coefficient, and the dimensionless number, Pe = uL/D, is the axial Peclet number. It is different than the Peclet number used in Section 9.1. Also, recall that the tube diameter is denoted by df. At high Reynolds numbers, D depends solely on fluctuating velocities in the axial direction. These fluctuating axial velocities cause mixing by a random process that is conceptually similar to molecular diffusion, except that the fluid elements being mixed are much larger than molecules. The same value for D is used for each component in a multicomponent system. 

The dynamical regimes that may be explored using this method have been described by considering the range of dimensionless numbers, such as the Reynolds number, Schmidt number, Peclet number, and the dimensionless mean free path, which are accessible in simulations. With such knowledge one may map MPC dynamics onto the dynamics of real systems or explore systems with similar characteristics. The applications of MPC dynamics to studies of fluid flow and polymeric, colloidal, and reacting systems have confirmed its utility. 

Dijfusional dimensionless numbers The Peclet, Prandtl, Schmidt, Sherwood, and Nusselt number are the most common ones. 

In Equation (4.9) the balance between convective transport and diffusive transport in the membrane boundary layer is characterized by the term JvS/Di. This dimensionless number represents the ratio of the convective transport Jv and diffusive transport Dj/8 and is commonly called the Peclet number. When the Peclet number is large (./ 5>> D,/S), the convective flux through the membrane cannot easily be balanced by diffusion in the boundary layer, and the concentration polarization modulus is large. When the Peclet number is small (Jv <5C D,/8), convection is easily balanced by diffusion in the boundary layer, and the concentration polarization modulus is close to unity. 

Dimensionless numbers help in convection heat transfer engineering Used to compare relative values in the practice of engineering In convection, there is the Eckert number and the Prandtl number, There is also the Reynolds number, Peclet number and Nusselt number. 

NGf gas flow number [= xl/(/img)], dimensionless NPe Peclet number for axial dispersion (uGd0/DeE for liquid vtH/De for solids), dimensionless NKc Reynolds number (= aid2p/p in stirred tank) (= uGdcpJpL in bubble columns), dimensionless... 

D. dimensionless HTU Peclet number, see equation 75 Peclet number specifically defined for phase A orJ, see equation 77... 

Ferry (1992) and Ague (1994b) used the dimensionless thermal Peclet number (B) of Brady (1988) to assess whether or not the large fluxes needed to make regional quartz vein sets elsewhere in the Acadian orogen of New England may have also transported heat ... 

Peclet Number, Pe dimensionless number appearing in enthalpy or species mass conservation equations (defined for heat transfer and mass transfer, respectively). It is interpreted again as the ratio of the convective transport to the molecular transport and is defined as... 

If these Peclet numbers are divided by the Reynolds number, the resulting dimensionless numbers are called the Pradtl number, Pr and Schmidt number. Sc, respectively. The Prandtl number (Pr) is the ratio of momentum diffusivity and thermal diffusivity. The Schmidt number (Sc) is the ratio of momentum diffusivity and mass diffusivity. These five dimensionless numbers can convey very useful information about the relative contributions of convective and molecular transport and relative magnitudes of momentum, heat and mass transfer. 

In summary, chromatographic batch separation depends on the following dimensionless parameters Peclet and Stanton numbers, dimensionless injection time, Henry coefficients and dimensionless Langmuir parameters. 

Peclet number, Pe A dimensionless number used frequently by chemical engineers. Pe = (ux)/Dm, where x is a characteristic length, u the mobile phase velocity, and Dfn the molecular diffusivity. In chromatography, there are two Peclet numbers, defined by respect to the column length and to the particle size. The former must be large (i.e., 100 or more) for the simple models of chromatography to be valid. The second is known by chromatographers as the reduced mobile phase velocity. 

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]... 

Dimensionless group Dimensionless group Dimensionless concentration Peclet number for mass transfer Peclet number for heat transfer Dimensionless temperature Dimensionless length Activation energy group Dimensionless time... 

A numerical study of the free-radical polymerization of styrene (Scheme 6.15) compared the behavior of an interdigital micromixer with a T-junction and a straight tube [37, 48], The diffusion coefficient of the reactive species was varied to simulate the viscosity increase during a polymerization. The performance of the polymerization turned out to be largely dependent on the radial Peclet number. This dimensionless number is defined as the ratio of the characteristic time of diffusion in the direction perpendicular to the main flow to the characteristic time of convection in the flow direction (i.e., the mean residence time) and, therefore, is directly proportional to the characteristic length of the reactor. 

Number of particles Ny, total number N , number per unit mass Peclet number for axial mixing, UL/E, dimensionless Number of increments or screens number of particles in spot sample also, exponent in equation for flow from bins... 

The product of the Reynolds and Schmidt numbers, which counts as one dimensionless number, is equivalent to the Peclet number for mass transfer, PeMx- The Peclet number represents the ratio of the convective mass transfer rate process to the diffusion rate process of component, and it appears on the left-hand side of the dimensionless mass transfer equation for component i. The remaining r dimensionless transport numbers can be treated simultaneously because they represent ratios of scaling factors for the reactant-product conversion rate due to the jth independent chemical reaction relative to the rate of diffusion of component I. Hence,... 

For unsteady-state diffusion into a quiescent medium with no chemical reaction, the mass transfer Peclet number does not appear in the dimensionless mass transfer equation for species i because it is not appropriate to make variable time t dimensionless via division by L/ v) if there is no bulk fluid flow (i.e., (d) = 0). In this case, the first term on each side of equation (10-11) survives, which corresponds to the unsteady-state diffusion equation. However, the characteristic time for diffusion of species i over a length scale L, given by L /50i,mix. replaces L/ v) to make variable time t dimensionless. Now, the accumulation and diffusional rate processes scale as CAo i.mix/A, with dimensions of moles per volume per time. Since both surviving mass transfer rate processes exhibit the same dimensional scaling factor, there are no dimensionless numbers in the mass transfer equation which describes unsteady-state diffusion for species i in nonreactive systems. 

All dimensionless numbers that are required to analyze mass transfer in packed catalytic tubular reactors can be expressed in terms of three time constants t, CO, and d. For example, the mass transfer Peclet number is... 

Answer The mass transfer Peclet number scales as Lpfr, and the interpellet Damkohler number scales as Lpp,. Therefore, PeMi = 150 and A mterpeiiet = 60. The other three dimensionless numbers are unaffected when the reactor length is doubled. 

The relative importance of the advective transport compared to diffusion is measured by calculating the Peclet number. This dimensionless number is defined as... 

The Peclet number (Pe), a dimensionless number that characterizes the relative importance of diffusion to convection, is often used in the context of mixing of continuously flowing streams. The Peclet number is given by... 

Peclet number is a dimensionless number relating the rate of advection of a flow to its rate of thermal diffusion. 

In this equation there is a dimensionless number, the so-called Bodenstein number. Bo (sometimes also called Peclet number, especially when a diameter is taken as characteristic length) ... 

The characteristic dimensionless numbers such as Reynolds number (Re) and Peclet number (Pe) are very suitable for discussing the operating conditions for micromixers. From the definitions in Equations (7.1) and (7.2), the relation... 

---