It has been observed that the transportability of mucus by cilial mats is dependent on the rheological properties of the mucus. Mucus is a non-Newtonian fluid that exhibits a plethora of phenomena such as stress relaxation, tensile stresses, shear thinning, and yielding behavior. These observations motivate the analysis in this paper that considers the first two attributes in order to construct a transport model. The model developed here assumes that the mucus is transported as a rigid body, the metachronal wave exhibits symplectic behavior, that the mucus is thin compared to the metachronal wavelength, and that the effects of individual cilia can be lumped together to impart an average strain to the mucus during contact. This strain invokes a stress in the mucus, whose non-Newtonian rheology creates tensile forces that persist into unsheared regions and allow the unsupported mucus to move as a rigid body whereas a Newtonian fluid would retrograde. This work focuses primarily on the Doi-Edwards model but results are generalized to the Jeffrey's and Maxwell fluids as well. The model predicts that there exists an optimal mucus rheology that maximizes the shear stress imparted to the mucus by the cilia for a given cilia motion. We propose that this is the rheology that the body strives for in order to minimize energy consumption. Predicted optimal rheologies are consistent with results from previous experimental studies when reasonable model parameters are chosen.

• Received 12 September 2010
• Publisher error corrected 24 February 2011

DOI:https://doi.org/10.1103/PhysRevE.83.011921