Chemical and Biological Engineering ETDs

Publication Date

4-13-1979

Abstract

A different approach to the problem of mass transfer to a rotating disk, employing less restrictive assumptions, has been undertaken to quantify the phenomenon of mass transfer at the disk's edge. Experimental work in support of theor­etical conjectures was performed as part of this work.

In order to include the effect of mass transfer at the edge on mass transfer to the entire disk, the equation of convective diffusion was solved in two dimensions over a region that extended beyond physical projection of active area of the disk. A synthesis of experimental results and theoret­ical considerations was used to specify and locate the boundary conditions.

The solution of the equation of convective diffusion was accomplished by expressing the derivative terms as finite differences, thus transforming the partial differential equa­tion into a set of linear equations. Solving these linear equations by a modified Gauss-Seidel relaxation method, yielded a two-dimensional concentration profile in the region about the disk. This concentration profile was a function of both the axial and radial coordinate as compared with the profile, previously solved for by Levich, which is radially invariant. The concentration profiles were used to calculate a radial enhancement factor which is the ratio of the flux to the disk, calculated from the two dimensional profiles, to that calculated using the one dimensional profile.

The radial enhancement factor was found to be a function of Schmidt and Reynolds numbers. At Reynolds numbers approach­ing turbulence the radial enhancement factor ranges from 1.005 to 1.002 for Schmidt numbers between 4 and 1000. As the Reynolds number goes to zero the radial enhancement factor increases rapidly.

Since the established velocity profiles for fluid flow at a rotating disk were derived for an infinite disk, a model fluid flow beyond the edge pf a finite disk was developed. This model, based on a variation of the VonKarmann integral momentum balance, was incor1porated into the mass transfer model and a second set of solutions to the equation of con­vective diffusion was made.

The inclusion of hydrodynamic effects increased the radial enhancement factor at low Schmidt number.

Experimental determinations of zinc deposited at limiting current were made using rotating disk electrodes with and without insulating shrouds. The deposit distributions were used to calculate radial enhancement factors which correlated well with those calculated from the solution of the equation of convective diffusion. Determinations of limiting currents at low Reynolds number also corroborated the results derived from the mass transfer model.

The experimental results also indicate the superior repro­ducability of results obtained using a streamlined, shrouded rotating disk electrode.

Document Type

Dissertation

Language

English

Degree Name

Chemical Engineering

Level of Degree

Doctoral

Department Name

Chemical and Biological Engineering

First Committee Member (Chair)

Richard Wilson Mead

Second Committee Member

Chen-Yen Cheng

Third Committee Member

Su-Moon Park

Fourth Committee Member

Thomas Evan Jones

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