The effect of an external boundary and diffusive interaction between reactants on the rate constant for diffusion-controlled bulk reactions in an external electric field is considered. Appropriate boundary-value problems for ''wall-sink'' and ''sink-sink'' systems in an electric field are solved approximately by the method of reflections. Mainly we are interested in calculation of the deviation of the reaction rate constant from the value calculated by Smoluchowski approach. A thorough analysis is made of the time-dependent case of ''wall-sink'' system in absence of an electric field. It has been shown that the wall effect leads to a nonexponential long time tail for the bulk concentration of diffusing particles. Special attention is given also to the investigation of competitive effect between two sinks which is found to be of interest for many applications. The rigorous theoretical study of this problem provides a way of quantitative estimation of the shadow effect. Drift of diffusing particles in some arrays of ideal sinks is treated as well. (C) 1997 American Institute of Physics. [S0021-9606(97)50146-2].