Sphere caging by a random fibre network

We analyse the remarkable efficiency of a random distribution of rigid thin rods (with diameter σ) to ‘cage’ a test sphere (with diameter D σ) by purely geometric hindrance due to rod–sphere contacts. The average number of random contacts which traps a sphere in three dimensions corresponds to a volume fraction φc=7(D/σ)2 of very long rods or fibres. Some implications for confinements and dynamics of (colloidal) particles in fibre structures are discussed.