Immersed boundary simulations of fluid shear-induced deformation of a cantilever beam

A biofilm is a colony of microorganisms that adheres and grows on a surface typically in contact with a stagnant or flowing fluid environment. The hydrodynamic interaction between the fluid and the film structure plays a key role in the various phases of the biofilm life-cycle — formation, growth, detachment, and reestablishment. The fluid-flow conditions determine the shear stresses exerted upon the film structure causing it to deform up to a critical point, beyond which the biofilm is uprooted from the surface into a planktonic state in the flowing fluid. To develop a fundamental understanding of the effects of the fluid-flow parameters on the mechanics of the biofilm, this work considered an ideal 2D model scenario of ‘a rectangular cantilever beam immersed in a channel filled with viscous, incompressible fluid, where one end of the beam is fixed to the channel wall, bending in response to a shear flow.’ The Immersed boundary (IB) method was employed to simulate numerically the fluid–structure interaction. The effect of physical parameters of the problem — stiffness and height of the cantilever and flow velocity, along with the numerical parameters on the equilibrium structure of the elastic beam was investigated and the simulation results were qualitatively compared with respect to linear beam theory. A careful analysis of the “corner effects” — irregularities in beam shape near the free and fixed ends, has been presented. It was shown that this issue can be effectively eliminated by smoothing out the corners with a “fillet” or rounded shape. Finally, the IB formulation was extended to include porosity in the beam to investigate the effect of the resultant porous flow on the beam deflection.