Péclet number

About: Péclet number is a research topic. Over the lifetime, 2487 publications have been published within this topic receiving 56276 citations. The topic is also known as: Pe & Peclet number.

Heat and mass transfer in packed beds

Abstract: Eddy mass diffusivities, effective thermal conductivities, and wall heat transfer coefficients were measured in an 8-in. tube packed with 1/2- and 3/4-in. glass spheres. Superficial mass velocities ranged from 110 to 1,640 Ib./(hr.) (sq. ft.), corresponding to modified Reynolds numbers of 100 to 2,000. Air was the main stream fluid in all cases. The modified Peclet group (DpV/E*td) was found to be constant at a value of about 12 in the region of fully developed turbulence. At lower Reynolds numbers this group varied with the flow rate. Effective thermal conductivities were correlated by an equation. Modified Peclet numbers for heat transfer were about 25% less than those for mass transfer. The wall heat transfer coefficient varied with the superficial mass velocity as hw = 0.090 (Go0.75). An explanation is suggested for the similarity in velocity dependence between these values and those for turbulent flow in an empty tube, based on channeling at the wall.

The rheology of Brownian suspensions

Abstract: The viscosity of a suspension of spherical Brownian particles is determined by Stokesian dynamics as a function of the Peclet number. Several new aspects concerning the theoretical derivation of the direct contribution of the Brownian motion to the bulk stress are given, along with the results obtained from a simulation of a monolayer. The simulations reproduce the experimental behavior generally observed in dense suspensions, and an explanation of this behavior is given by observing the evolution of the different contributions to the viscosity with shear rate. The shear thinning at low Peclet numbers is due to the disappearance of the direct Brownian contribution to the viscosity; the deformation of the equilibrium microstructure is, however, small. By contrast, at very high Peclet numbers the suspension shear thickens due to the formation of large clusters.

Dispersion in fixed beds

Abstract: A macroscopic equation of mass conservation is obtained by ensemble-averaging the basic conservation laws in a porous medium. In the long-time limit this ‘macro-transport’ equation takes the form of a macroscopic Fick's law with a constant effective diffusivity tensor. An asymptotic analysis in low volume fraction of the effective diffusivity in a bed of fixed spheres is carried out for all values of the Peclet number ℙ = Ua/Df, where U is the average velocity through the bed. a is the particle radius and Df is the molecular diffusivity of the solute in the fluid. Several physical mechanisms causing dispersion are revealed by this analysis. The stochastic velocity fluctuations induced in the fluid by the randomly positioned bed particles give rise to a convectively driven contribution to dispersion. At high Peclet numbers, this convective dispersion mechanism is purely mechanical, and the resulting effective diffusivities are independent of molecular diffusion and grow linearly with ℙ. The region of zero velocity in and near the bed particles gives rise to non-mechanical dispersion mechanisms that dominate the longitudinal diffusivity at very high Peclet numbers. One such mechanism involves the retention of the diffusing species in permeable particles, from which it can escape only by molecular diffusion, leading to a diffusion coefficient that grows as ℙ2. Even if the bed particles are impermeable, non-mechanical contributions that grow as ℙ ln ℙ and ℙ2 at high ℙ arise from a diffusive boundary layer near the solid surfaces and from regions of closed streamlines respectively. The results for the longitudinal and transverse effective diffusivities as functions of the Peclet number are summarized in tabular form in §6. Because the same physical mechanisms promote dispersion in dilute and dense fixed beds, the predicted Peclet-number dependences of the effective diffusivities are applicable to all porous media. The theoretical predictions are compared with experiments in densely packed beds of impermeable particles, and the agreement is shown to be remarkably good.