A lubricant boundary condition for a biological body lined by a thin heterogeneous biofilm. (English) Zbl 1406.92134
Summary: We study the asymptotic behavior of an incompressible viscous fluid flow in a biological body lined by a thin biological film with a cellular microstructure, varying thickness, and a heterogeneous viscosity regulated by a time random process. Letting the thickness of the film tend to zero, we derive an effective biological slip boundary condition on the boundary of the body. This law relates the tangential fluxes to the tangential velocities via a proportional coefficient corresponding to the energy of some local problem. This law describes the ability of the biological film to function as a lubricant reducing friction at the wall of the body. The tangential velocities are functions of the random trajectories of a finely concentrated biological particle.
MSC:
| 92C35 | Physiological flow |
| 76Z05 | Physiological flows |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
Keywords:
biological body; incompressible viscous flow; thin biofilm flow; random structural evolution; asymptotic analysis; lubricant effective boundary conditionReferences:
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