Current Flow in Cylinders

Abstract

Effect of electrical conductivity and a viscous flow on the stability of a currentcarrying hollow cylinder of fluid Phys.The mixed b:mndary value problem arising from the flow of current into a right circular cylinder of radius a through a perfectly conducting coaxial disk electrode at one end is solved approximately. The boundary conditions are met rigorously except that the electrode is not quite plane. A solution valid for all values of the disk radius is given for which in the worst case the deviation from flatness is nearly O.01a. More exact solutions are worked out for disk radii la, !a, and fa and the first forty coefficients in the Bessel function series for the potential in the cylinder are tabulated. A cylinder whose diameter is eight times its length is also treated for disk radii la and !a and the first forty coefficients in the potential series are tabulated. The probable errors in the resistance formulas derived from these solutions are given.

Effect of local Peclet number on mass transfer to a heterogeneous surface

“…The unit cell in this case was the (approximately) circular region surrounding a single pore. Many other similar unit cell analyses exist in the literature (Dudukovic and Mills, 1985; Nanis and Kesselman, 1971;Reller et al, 1982;Smythe, 1953;Wakeham and Mason, 1979). The effects of a nonuniform spatial distribution of sites have also received some consideration (Brunn, 1984;Prager and Frisch, 1975).…”

“…Most previous analyses of mass transfer to heterogeneous surfaces have envisioned a regular distribution of active sites and have focused on diffusion within a representative unit cell surrounding a single active site (Dudukovic and Mills, 1985; Keller and Stein, 1967;Nanis and Kesselman, 1971; Reller et al, 1982;Smythe, 1953;Wakeham and Mason, 1979). In all of these models the stagnant film approximation has been used.…”

Electrochemical measurements of mass transfer at surfaces with discrete reactive areas

“…If fluid flow is ignored, symmetry ensures that there is no mass transfer between adjacent unit cells, and a two-dimensional or axisymmetric diffusion problem is obtained (Dudukovic and Mills, 1985;Keller and Stein, 1967;Nanis and Kesselman, 1971;Reller et al, 1982;Smythe, 1953;Wakeham and Mason, 1979). Convective transport is often incorporated indirectly in such models by assuming that bulk fluid concentrations are reached at a specified distance from the surface.…”

Perspective on Electrospray Ionization and Its Relation to Electrochemistry

“…The author also divides the total current into the skin current that flows along the Taylor cone skin and the bulk current that flows through a body of liquid. Gañan-Calvo et al's detailed model [55,[105][106][107][108] of total electrospray current is based on an extension of the classic work by Melcher and Warren [109][110][111][112] of the electric field surrounding the jet. The analysis leads to two limiting formulas for total electrospray current: one is for liquids of high conductivity and high viscosity [107]:…”