Packed beds dimensionless variables

X/i o. Dimensionless axial variable = X/L. Dimensionless axial variable Dirac delta function, see reference (S20) Fraction voids in packed bed Eigenvalue in Eq. (67c), (68c), and (69c) Mean of tracer curve at measurement point (dimensionless) Difference in means of the tracer curves at the two measurement points Xm and Xa Kinematic viscosity of fluid... 

In this chapter generalized mathematical models of three dimensional electrodes are developed. The models describe the coupled potential and concentration distributions in porous or packed bed electrodes. Four dimensionless variables that characterize the systems have been derived from modeling a dimensionless conduction modulus ju, a dimensionless diffusion (or lateral dispersion) modulus 5, a dimensionless transfer coefficient a and a dimensionless limiting current density y. The first three are... 

A number of experimental and theoretical studies of mass transfer in solution processes have been published. Since this literature is fairly well known, it will be mentioned briefly, but not analyzed in detail. Most of the earlier work in agitation employed dissolution rates as performance criteria (H6, H8, W5). Experimental studies of dissolution itself have employed suspended solute plates (B7, Wl), single crystals (M12, P5), revolving crystals (D2), and packed beds (Gl, L3, M5, V4). Recently, several theoretical analyses of literature data have appeared (El, HI, R3). A number of Russian investigators have also studied dissolution (N6, Zl) they prefer to correlate data in terms of individual variables rather than the dimensionless groups customary in English and American literature. 

When the SEC of lignins is performed on an open column packed with soft gels, such as Sephadex G, the elution volume of the same solute size varies slightly between runs due to small fluctuations in the flow rate and ambient temperature that may disturb the void volume and total permeation volume of the gel bed. Moreover, a new column has to be packed every three months for a Sephadex G gel/aqueous 0.1 M NaOH system because reproducible column performance can be maintained only for a finite period of time as a result of slow decomposition of the packing material. Thus, the variation in the elution volume between columns can be considerably large because of variation in the height of the gel bed from one column to another. To overcome uncertainty arising from these potential sources, the elution volume is often converted to a dimensionless variable prior to y-axis... 

A common approach is to model a packed bed reactor as a system of partial differential equations and in order to investigate the behaviour of such a reactor numerically, these model equations have to be discretized. For all four methods discussed in this section, first the space variable of the dimensionless equations is discretized. This leads to a large system of N (where JV depends on the space discretization) time periodic ordinary differential equations. This system can be written as... 

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