Polyethylene glycol-modified vesicles (liposomes) encapsulating hemoglobin (HbV) are artificial oxygen carriers that have been developed as a transfusion alternative. The HbV suspension in an albumin solution is nearly Newtonian; other biopolymers, hydroxyethyl starch (HES), dextran (DEX), and modified fluid gelatin, induce flocculation of HbVs through depletion interaction and render the suspensions as non-Newtonian. The flocculation level increased with hydrodynamic radius (R-h) or radius of gyration (R-g) of series of HES or DEX with different molecular weights at a constant polymer concentration (4 wt %). However, the flocculation level differed markedly among the polymers. A crowding index (C-i) representing the crowding level of a polymer solution is defined as (excluded volume of one polymer) x (molar concentration) x Avogadro's number, using R-h or R-g. All polymers' flocculation level increases when C-i approaches 1: when the theoretical total excluded Volumes approach the entire solution Volume, the excluded HbV particles are forced to flocculate.