  Centrifugation of erythrocytes (aka Red Blood Cells, RBCs) in a self-forming
Percoll gradient is a protocol often used as a way to sort RBCs by age.
However, a pattern formation of discrete bands is systematically observed along
the continuous density gradient. Although early studies mentioned that
aggregation between cells might modify their spatial distribution, it is
debated whether a population with continuous density distribution can form
discrete bands. Here, we develop a continuity equation, considering the
aggregation of cells with a continuous density distribution, which describes
the macroscopic evolution of the RBC volume concentration in a density
gradient. The numerical solutions demonstrate that the competition between
iso-density distribution and aggregation is sufficient to create band patterns.
Our model reproduces the temporal evolution observed in the conventional
experimental protocol, but also predicts several types of bifurcation-like
behaviors for the steady-state patterns in constant gradients, when the volume
fraction and aggregation energy of the cells are varied. We threrefore
discovered that the competition between RBC aggregation and iso-density
distribution is a novel physical mechanism leading to pattern formation.
