E ective viscosity of puller-like microswimmers: a renormalization approach

E ective viscosity (EV) of suspensions of puller-like microswimmers (pullers), such as the Chlamydamonas algae, is di cult to measure or to simulate for all swimmer concentrations. Although there are good reasons to expect that the EV of pullers is similar to that of passive suspensions, analytic determination of the passive EV for all concentrations remains unsatisfactory. At the same time, the EV of bacterial suspensions is closely linked to collective motion in these systems and is biologically signi cant. We develop an approach to determining analytic EV estimates at all concentrations for suspensions of pullers as well as for passive suspensions.The proposed methods are based on the ideas of renormalization group theory (RG) and construct the EV formula based on the known asymptotics for small concentrations and near the critical point (i.e., approaching dense packing). For passive suspensions the method is veri ed by comparison against known theoretical results. We nd that the method performs much better than an earlier RG-based technique. For pullers the validation is done by comparing to experiments conducted on Chlamydamonas suspensions.