Reconstruction of hydrodynamic flow profiles in a rectangular channel using electrochemical methods of analysis

We propose a theoretical method for reconstructing the shape of a hydrodynamic flow profile occurring locally within a rectangular microfluidic channel based on experimental currents measured at double microband electrodes embedded in one channel wall and operating in the generator–collector regime. The ranges of geometrical and flow parameters providing best conditions for the flow profile determination are indicated. The solution of convection–diffusion equation (direct problem) is achieved through the application of the specifically designed conformal mapping of spatial coordinates and an exponentially expanding time grid for obtaining accurate concentration and current distributions. The inverse problem (the problem of flow profile determination) is approached using a variational formulation whose solution is obtained by the Ritz's method. The method may be extended for any number of electrodes in the channel and/or different operating regimes of the system (e.g. generator–generator).