We investigate the kinetics of irreversible adsorption under the van der Waals regime, i.e. weakly Brownian polydisperse colloidal suspensions injected into shallow microchannels at high ionic strengths, where each suspension is represented by populations of particles with different particle sizes. We find that each population size of the particle in the suspension can be treated independently using an analytical solution based on the advection-diffusion equation and that the distribution of the adsorbed particles along the channel axis behaves according to a power law. The experimental measurements agree with Langevin simulations and are well accounted for by theory valid in the van der Waals regime. Operating in the van der Waals regime permits the present study to confirm the use of microfluidics as an effective in situ method to measure the Hamaker constant of particles under aqueous conditions.