Zur Kenntnis der natürlichen Konvektion bei der Elektrolyse. 4. Mitteilung. Polarographische Untersuchung der Konzentrationsabhängigkeit des Grenzstroms

Abstract

The validity range of the boundary layer theory of mass transfer by natural convection has been studied. Limiting currents were measured for deposition of Cd, Tl and Cu on vertical cathodes in unstirred solutions. The concentration ranged from 10−4 to 10−1 molar. Two kinds of electrodes were used: plane electrodes with heights varying from 0,1 to 4 cm and microwires of the type used in the polarography with solid electrodes.

Kinetics of Metal Deposition

“…However, Levich (9) and Agar (10) deduced from theoretical grounds that for vertical macro plate electrodes convective processes should operate and limiting current densities be proportional to concentration raised to a power of five-fourths. This has been confirmed theoretically and experimentally for macro systems (11)(12)(13)(14)(15)(16).…”

Mass Transfer and Current Distribution under Free Convection Conditions

“…A diffusion layer formed around a body is generally thicker with increasing distance from the frontal edge of the body. Hence, under limiting current conditions the current density (or the reciprocal of the thickness of the diffusion layer) is inversely proportional to the fourth root of the distance from the bottom of the cathode, as confirmed by Wagner (3), Ibl (8), and Wilke (11).…”

“…This gives a differential equation: =--(90t--30)/(15t+2) [8] In Eq. [8], ~ is the kinematic viscosity, g the acceleration of gravity, t the transference number of H +, fl, and fl~ the density coefficients (i.e., the relative increase in density caused by unit increase in the concentrations of CuSO, and H=SO,, respectively), and ~ *C and D refer to Cu ++. Equation [8] was solved for the following three cases, with the boundary condition for F:…”

“…The rate of metal deposition may be controlled mainly or partly by the rate of transfer of ions to the cathode. In the absence of agitation, ions are usually transferred by free convection, a process which has received much theoretical and experimental investigation (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). Owing to depletion of reactive ions, the density of the cathodic region becomes lower than that of the bulk of the solution; an upward flow of solution then results.…”

Current Distribution in Galvanic Cells Involving Natural Convection

“…Under these conditions, cation concentration at the electrode is virtually equal to zero, and the current reaches a limiting value Im~. Approximate solutions of the differential equations for the concentration and the velocity distribution in the boundary layer have been obtained by using solutions for the analogous heat transfer problem (1)(2)(3)(4)(5)(6)(7). For a laminar boundary layer, the local limiting current density is proportional to the fourth root of the distance from the leading edge of the electrode in accord with experimental results (3,(5)(6)(7).…”