Fluctuating flow with mass transfer induced by a rotating disk electrode with a superimposed time-periodic modulation

Fluctuating flow with mass transfer induced by a rotating disk electrode with a time-periodic angular velocity Ω0[1+α cos(pτ)]b is analyzed by solving numerically the time-dependent von Kármán self-similar form of the Navier–Stokes and convective diffusion equations when the electrochemical reaction at the disk electrode is mass transfer limited. Results are presented for the full frequency range for several values of the waveform parameter b and α<1. At the intermediate frequency p=1.24 (with α=0.9, b=1), the time-periodic flow undergoes a transition from a quasisteady von Kármán flow to a double boundary layer structure. The transition, which is characterized by an abrupt shift from phase lead (p<1.24) to phase lag (p>1.24) in the far-field angular velocity, is discussed in terms of a viscous wave confined to the Stokes layer by axial inflow. The numerical results for b=1 are compared to the low- and high-frequency asymptotic theories of Chawla and Verma [Proc. R. Soc. London Ser. A 386, 163 (1983)], and it is shown that terms of O(p−5/2) neglected by Chawla and Verma are required in the high-frequency expansion to describe the flow in the far field. Electrochemical measurements of the fluctuating mass transfer limited flux induced by the modulating disk electrode are in excellent agreement with the numerical results. The low-frequency calculations show that a judicious choice of b results in the cancellation of all harmonics other than the fundamental near the disk surface for certain field variables. The implications for electrochemical studies are discussed.