Enhanced mass transfer using roughened rotating cylinder electrodes in turbulent flow

Cylindrical electrodes have been roughened by machining groove patterns, pyramidal knurling, and superimposing wires and meshes for which the degree of roughness has been calculated. By rotating the electrodes in a turbulent regime, mass transfer for cathodic copper electrodeposition has been measured and the degree of consequent enhancement (relative to an equivalent smooth cylinder) calculated. Typically, the surface area has been increased by 10–40% and the mass transfer rate by 100–300% for turbulent flow defined by 7000<Re<80 000.Nomenclature A (A_R) area of cathodic (rough) cylinder (cm²) - C exponent - C_B metal ion concentration in bulk solution (mol cm^–3) - d_s (d_R) diameter of smooth (rough) cylinders (cm) - D diffusion coefficient of metal ion (cm²s^–1) - F Faraday's constant - I_L limiting current density (mA cm^–2) - j₀ dimensionless mass transfer factor (=ShSc^c) - k_L mass transfer coefficient (=I_L/zFC_B) - k_s,k_R k_L values for smooth and rough cylinders - m, n exponents - P pitch, or roughness element spacing (cm) - Re Reynolds number (=Ud/v) - Ré d_RU_R/v - Re_s dU_s/v - Sc Schmidt number (=v/D) - Sh Sherwood number (=k_Ld/D) - St Stanton number (=k_L/U) - U_s (U_R) peripheral velocity at smooth (rough) cylinders (cm s^–1) - U₀ friction velocity (cm s^–1) - w width of wire mesh opening (cm) - z valency change, number of electrons - groove depth (cm) - kinematic viscosity (cm² s^–1) - groove width