Notes on the implementation of brownian motion in mesoscopic fluid-particle models

Mesoscopic simulation of nucleic acids transport can prove extremely beneficial to the growing field of mi-crofluidic DNA biosensors. In microfluidic devices, unlike macroscopic ones, the diffusive transport becomes relevant as it is no longer overwhelmed by convection. Diffusion of colloid-sized particles is caused by their brownian motion in solution, whose modelling is therefore crucial for the correct description of diffusive effects. It is known that the random displacement and velocity perturbations follow a multivariate Gaussian distribution. We analyse the explicit form of the covariance matrix and show a decomposition that factorizes the probability density function into three pairs of bivariate distributions. A preliminary model is implemented and validated for a simple test case.