Contact between particles and motile cells underpins a wide variety of biological processes, from nutrient capture and ligand binding, to grazing, viral infection and cell-cell communication. The window of opportunity for these interactions depends on the basic mechanism determining contact time, which is currently unknown. By combining experiments on three different species -Chlamydomonas reinhardtii, Tetraselmis subcordiforms, and Oxyrrhis marina-simulations and analytical modelling, we show that the fundamental physical process regulating proximity to a swimming microorganism is hydrodynamic particle entrainment. The resulting distribution of contact times is derived within the framework of Taylor dispersion as a competition between advection by the cell surface and microparticle diffusion, and predicts the existence of an optimal tracer size that is also observed experimentally. Spatial organisation of flagella, swimming speed, swimmer and tracer size influence entrainment features and provide trade-offs that may be tuned to optimise the estimated probabilities for microbial interactions like predation and infection. * A.M. and R.J. contributed equally to this work and are joint lead authors. A.M., R.J. and M.P. designed the study, analysed results, developed the theory, wrote the manuscript; R.J. performed the experiments; A.M. developed the model, performed simulations. † R.J. Current Address: IMEDEA, University of the Balearic Islands, Carrer de Miquel Marquès, 21 07190 Esporles, Illes Balears ‡ Correspondence: M.Polin@warwick.ac.uk (S) J above the length L (S) M at the peak of the distribution. Exponential fits to these curves give L (CR) J = 9.2 ± 0.6 µm for CR, L (TS) J = 7.4 ± 1.2 µm for TS and L (OM) J = 11.7 ± 1.4 µm for OM, while we find L (CR) M ≈ 6.7 µm, L (TS) M ≈ 8.6 µm and L (OM) M ≈ 7.5 µm. Unexpectedly, the characteristic entrainment length L (S) J