Mucus clearance is the primary defense mechanism that protects airways from inhaled infectious and toxic agents. In the current Gel-on-Liquid mucus clearance model mucus gel is propelled on top of a “watery” periciliary layer surrounding the cilia. However, this model fails to explain the formation of distinct mucus layer in health or why mucus clearance fails in disease. We propose a Gel-on-Brush model in which the periciliary layer is occupied by membrane spanning mucins and mucopolysaccharides densely tethered to the airway surface. This brush prevents mucus penetration into the periciliary space and causes mucus to form a distinct layer. The relative osmotic moduli of the mucus and periciliary brush layers explain both the stability of mucus clearance in health and its failure in airway disease.

We use scaling theory to derive the time dependence of the mean-square displacement 〈Δr2〉 of a spherical probe particle of size d experiencing thermal motion in polymer solutions and melts. Particles with size smaller than solution correlation length ξ undergo ordinary diffusion (〈Δr2 (t)〉 ~ t) with diffusion coefficient similar to that in pure solvent. The motion of particles of intermediate size (ξ < d < a), where a is the tube diameter for entangled polymer liquids, is sub-diffusive (〈Δr2 (t)〉 ~ t1/2) at short time scales since their motion is affected by sub-sections of polymer chains. At long time scales the motion of these particles is diffusive and their diffusion coefficient is determined by the effective viscosity of a polymer liquid with chains of size comparable to the particle diameter d. The motion of particles larger than the tube diameter a at time scales shorter than the relaxation time τe of an entanglement strand is similar to the motion of particles of intermediate size. At longer time scales (t > τe) large particles (d > a) are trapped by entanglement mesh and to move further they have to wait for the surrounding polymer chains to relax at the reptation time scale τrep. At longer times t > τrep, the motion of such large particles (d > a) is diffusive with diffusion coefficient determined by the bulk viscosity of the entangled polymer liquids. Our predictions are in agreement with the results of experiments and computer simulations.

We propose a hopping mechanism for diffusion of large nonsticky nanoparticles subjected to topological constraints in both unentangled and entangled polymer solids (networks and gels) and entangled polymer liquids (melts and solutions). Probe particles with size larger than the mesh size ax of unentangled polymer networks or tube diameter ae of entangled polymer liquids are trapped by the network or entanglement cells. At long time scales, however, these particles can diffuse by overcoming free energy barrier between neighboring confinement cells. The terminal particle diffusion coefficient dominated by this hopping diffusion is appreciable for particles with size moderately larger than the network mesh size ax or tube diameter ae. Much larger particles in polymer solids will be permanently trapped by local network cells, whereas they can still move in polymer liquids by waiting for entanglement cells to rearrange on the relaxation time scales of these liquids. Hopping diffusion in entangled polymer liquids and networks has a weaker dependence on particle size than that in unentangled networks as entanglements can slide along chains under polymer deformation. The proposed novel hopping model enables understanding the motion of large nanoparticles in polymeric nanocomposites and the transport of nano drug carriers in complex biological gels such as mucus.