The flow and saliva particulate transport dynamics during normal human breathing through the mouth are simulated numerically using an Eulerian large-eddy simulation (LES) approach for the flow coupled with a Lagrangian approach for the transport of saliva particles. The coupled Eulerian–Lagrangian (EL) simulation results reveal new striking insights into the rich dynamics of the Lagrangian coherent structures (LCS) that arise from saliva particles during normal breathing. Specifically, they uncover a new time-periodic mechanism via which particles are introduced into the flow as individual breathing pulses and accumulate to form a slowly propagating vortex front that persists long distances away from the source. The simulated LCS reveal a wealth of recurrent material motion through which the biosols propagate forward while their cloud expands laterally with a slowly evolving vortex front. Also, the finite-time Lyapunov exponent (FTLE) field of human breathing was calculated using the flow map from the LES velocity field. The ridges of the calculated FTLE field revealed distinct hyperbolic LCS, which closely resemble trajectories of saliva particles obtained from the coupled EL simulation. Finally, simulation results for normal breathing with a non-medical face mask show that the mask can effectively disrupt the formation of coherent particle surfaces and, thus, effectively limit saliva particle propagation.