An Effective Model for Flows over Flexible Hairy Surfaces

  • Colaco, Flasio (Indian Institute of Technology Goa)
  • Yogaraj, Sudhakar (Indian Institute of Technology Goa)

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The coupled interaction of fluid flows with solid surfaces coated with flexible, hairy filaments is prevalent in a wide array of biological systems. Notable examples include miniature hairs on blood vessels and hairy projections from the epithelial cells of the intestines, which aid in nutrient transport and absorption. Geometry-resolved simulations (DNS) of such a phenomenon are highly expensive due to two reasons: (i) the length scale of the filament is usually much smaller than the characteristic scale of the problem, and (ii) the elastic deformation of each filament should be tracked using coupled fluid-structure interaction analyses. Thus, it is a multiscale and multiphysics problem. Using dimensional analysis and conservation laws, we derive an effective model for this coupled fluid-solid interaction, when fluid and solid inertia are negligible. The resulting conditions to be enforced on a nominal interface are analogous to the classical Beavers-Joseph condition [1,2] for flows over porous media. The key feature is that in the effective model, the solid filaments are absent; the influence of the geometry and deformation of hairy filaments is embedded in the interface conditions, leading to a single-scale and single-physics problem. The coefficients appearing in the interface conditions are computed by solving inexpensive auxiliary problems over a single filament. The comparison of the velocity profile in a Couette flow with an applied pressure gradient shows the accuracy of the effective model. In addition, we validated the effective model on a two-dimensional cavity problem in which each filament deflects differently owing to the respective shear and pressure forces acting on them. The model results match those from the geometry-resolved simulations accurately for various values of the filaments' geometrical and material properties. References 1. Beavers G.S., Joseph, D.D., Boundary conditions at a naturally permeable wall, Journal of fluid mechanics, 30(1), 197-207, 1967. 2. Sudhakar Y., Lacis U., Pasche S., Bagheri S., Higher-order homogenized boundary conditions for flows over rough and porous surfaces, Transport in Porous Media, 136(1), 1-42, 2021.