Steady-State Voltammetry Using Microwire Electrodes under Microfluidic Control Nicholas P. C. Stevens, Qiu Fulian, Kerry A. Gooch, and Adrian C. Fisher* Department of Chemistry, UniVersity of Bath, ClaVerton Down, Bath, BA2 7AY, UK ReceiVed: December 6, 1999; In Final Form: March 3, 2000 The development and application of a new hydrodynamic electrochemical device is described. This novel technique is based on a microwire electrode with approximate dimensions of 25 μm, sited centrally within a rectangular duct (of 800 μm height and 0.05-0.02 m width), subjected to fluid flow under well-defined mass transport conditions. Finite element simulations are presented to model the solution velocity profiles within the cell and around the microwire electrode. The results of these calculations were employed to characterize the concentration distribution of a reactant within the cell, which is undergoing a transport-limited reaction at the electrode/solution interface. Experimental studies using the new technique were performed using aqueous and organic solutions containing ferrocene and potassium ferrocyanide to establish the variation of electrolysis current as a function of the solution flow rate. The experimental results are compared to those predicted numerically and good agreement is noted. Introduction The general area of microelectrode research has grown rapidly in recent years and has been successfully combined with hydrodynamic techniques to provide powerful new diagnostic tools in the field of electrochemistry. 1-7 In addition, the research area of microreactors and microfluidics has also created significant interest due to the potential of creating new analytical and synthetic devices on a physically smaller scale than has been possible previously. 8-10 In this article, we present the numerical and experimental characterization of an electrochemi- cal device that unites the benefits of these two significant research topics. Hydrodynamic techniques have been extensively exploited in electrochemical measurements previously. However, it is usually to employ an analytical approximation to the velocity profile within the solution. 11 This has significantly restricted the development of more general hydrodynamic techniques due to the necessity to use geometries that are accessible to mathematical approximation. More recently, we have demon- strated that this limitation may be overcome by the application of fluid dynamic simulations that enable the velocity profiles in geometries of arbitrary dimensions to be calculated. 12-14 In addition, our approach also permits the design of new electro- chemical devices on PC level computers, thus removing much of the laborious laboratory studies that are usually required for geometry optimization. In this paper, we develop our previous approach to predict the fluid dynamics around a microwire electrode sited within a narrow rectangular duct. The velocity profiles predicted by the calculations are used to solve the mass transport expressions for an electrochemically active material undergoing a transport- limited reaction at the electrode/solution interface. Predictions of the transport-limited current as a function of the solution flow rate are compared to those observed experimentally for the device and good agreement is observed. Theory. In this section, we describe the model of the transport characteristics for the microwire device shown in Figure 1. The cell was constructed from two rectangular ducts with the metallic wire held in the center of the cell. The cylinder was insulated at the regions close to the cell walls, so that only the central portion of the cylinder was employed for electrochemical measurements. Under these conditions, the mass transport limited one electron reduction of (A) can be simulated using the following transport equation assuming migration to be insignificant because of the use of high background electrolyte concentrations and the cell width to be much smaller than the height. In eq 1, c is the reactant concentration (A), D is the reactant diffusion coefficient, and V x and V z are the velocities in the x and z directions, respectively (Figure 1). Finite element simulations were performed to establish the velocity profile (V x , V z ) throughout the cell by solution of the two-dimensional form of the Navier-Stokes equations and the continuity equation where the normalized variables (denoted by primes) are x′ ) x/l, z′ ) z/l, u′ ) u/l, V′ )V/l and p′ ) p/l. The variables p, l, and u 0 are the pressure characteristic, length, and applied velocity, respectively. F x and F are the force and viscosity, respectively. For further details on the numerical construction, readers are directed to the text of Taylor. 15 A(s) + e - (m) f B(s) ∂c ∂t ) D ( ∂ 2 c ∂x 229 + D ( ∂ 2 c ∂z 229 -V x ( ∂c ∂x 29 -V z ( ∂c ∂z 29 ) 0 (1) u′ ( ∂u′ ∂x′ 29 +V′ ( ∂V′ ∂x′ 29 ) F x l Fu o 2 - ( ∂p′ ∂x′ 29 + V u 0 l ( ∂ 2 u′ ∂x 2 + ∂ 2 u′ ∂z 2 29 (2) u′ ( ∂u′ ∂x′ 29 +V′ ( ∂V′ ∂x′ 29 ) F x l Fu o 2 - ( ∂p′ ∂z′ 29 + V u 0 l ( ∂ 2 V′ ∂x 2 + ∂ 2 V′ ∂z 2 29 (3) ( ∂u′ ∂x′ ) + ( ∂V′ ∂z′ ) ) 0 (4) 7110 J. Phys. Chem. B 2000, 104, 7110-7114 10.1021/jp994264n CCC: $19.00 © 2000 American Chemical Society Published on Web 07/07/2000