The data of Eisenberg¹ and of Mohr² provide an excellent basis for examining mass transfer in the system where the inner cylinder rotates within a larger stationary cylinder.  The data are here correlated more carefully with respect to the dependence of the Stanton number on the Reynolds number, the Schmidt number, and the geometric ratio k of the inner cylinder radius to that of the outer cylinder.  Three methods are deployed in this endeavor.  Simple empiricism involves fitting the data according to the equation below where the parameters A, n, and p are functions of k.  Enlightened empiricism expands on the traditional method of fitting the eddy viscosity as a function of the distance from the wall in the form of y⁺ = (y/n)(t₀/r)^0.5, where t₀is the shear stress at the solid wall.  This method does not work well in a predictive manner for rotating systems or systems where the flow is in the direction of the curvature of the surface (as with Goertler vortices).  Dissipation theory relates the local dissipation to its generation, transport, and decay, involving a parameter for the decay constant of the dissipation.

The electrochemical data of Eisenberg (with 1-k values from 0.1723 to 0.871) seem to be in the regime of wide gaps, while Mohr focused on thin gaps (1-k ranging from 0.0172 to 0.0839) to explore the failure of Eisenberg’s data to show an expected behavior where thin gaps blend into turbulent Couette flow.  The dissipation theorem should provide a new method of understanding turbulent shear flow and a way of predicting the effect of varying the radius ratio.

^*The author of this work is an Electrochemical Society Honorary Member

 

 

References

1. Morris Eisenberg, “Studies of Rates of Solid Dissolution and of Electrode Reactions at Rotating Cylindrical Bodies,” dissertation (Berkeley: University of California, 1953).

2a.  Charles Milton Mohr, Jr., Mass Transfer in Rotating Electrode Systems, dissertation (Berkeley: University of California, 1975).

2b.  Charles M. Mohr, Jr., and John Newman, Mass Transfer in Turbulent Flow between Rotating Cylinders with Small Separation Gaps.  Berkeley: Lawrence Berkeley Laboratory, 1976.  LBL-5136.  Apparently never published.