Abstracting the essence of the confinement effect on crowding microspheres: Mean-field theory and numerical simulation

A mean field theory is developed to quantify the simulated fraction N1/N of hard spheres (diameter σ) around the rim region (V1) against the size of spherical cavity Rcav for packing fraction η = 0.3 (open circles) and 0.15 (solid circles) with the characteristic length of depletion forces for rim particles (dotted circle) zc as an adjustable parameter. For large Rcav, N1/N obeys a power law: N1/N∼Rcav-1. Investigated densities are similar to crowded biological cells.47