  We present an efficient point-particle approach to simulate
reaction-diffusion processes of spherical absorbing particles in the
diffusion-limited regime, as simple models of cellular uptake. The exact
solution for a single absorber is used to calibrate the method, linking the
numerical parameters to the physical particle radius and uptake rate. We study
configurations of multiple absorbers of increasing complexity to examine the
performance of the method, by comparing our simulations with available exact
analytical or numerical results. We demonstrate the potentiality of the method
in resolving the complex diffusive interactions, here quantified by the
Sherwood number, measuring the uptake rate in terms of that of isolated
absorbers. We implement the method in a pseudo-spectral solver that can be
generalized to include fluid motion and fluid-particle interactions. As a test
case of the presence of a flow, we consider the uptake rate by a particle in a
linear shear flow. Overall, our method represents a powerful and flexible
computational tool that can be employed to investigate many complex situations
in biology, chemistry and related sciences.
