A bifurcation occurs when an elastic filament rotates in a viscous fluid at frequency ω (bifurcation parameter). We use the immersed boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier–Stokes equations, and to determine the nature of the bifurcation, which turns out to be subcritical.

When an elastic filament spins in a viscous incompressible fluid it may undergo a whirling instability, as studied asymptotically by Wolgemuth, Powers, Goldstein [1]. We use the Immersed Boundary (IB) method to study the interaction between the elastic filament and the surrounding viscous fluid as governed by the incompressible Navier-Stokes equations and to determine the nature of the bifurcat...

In this paper, we study flow through thin porous media as in, e.g. seals or fractures. It is often useful to know the permeability of such systems. In the context of incompressible and iso-viscous fluids, the permeability is the constant of proportionality relating the total flow through the media to the pressure drop. In this work, we show that it is also relevant to define a constant permeabi...

Potential flows u = ∇φ are solutions of the Navier–Stokes equations for viscous incompressible fluids for which the vorticity is identically zero. The viscous term μ∇u = μ∇∇φ vanishes, but the viscous contribution to the stress in an incompressible fluid (Stokes 1850) does not vanish in general. Here, we show how the viscosity of a viscous fluid in potential flow away from the boundary layers e...

Electrostatically actuated microbeams have been studied by many researchers in the last few years. The aim of this study is to present an improved numerical analysis of the dynamic instability of a cantilever microbeam immersed in an incompressible viscous fluid. The finite element method is used for solving the vibrational equation of the microbeam and the potential functions of the fluids in ...

Steady hydromagnetic Couette flow of class-II of a viscous, incompressible and electrically conducting fluid through a porous medium in a rotating system taking Hall current into account is investigated. Heat transfer characteristics of the fluid flow are considered taking viscous and Joule dissipations into account. It is noticed that there exists flow separation at the moving plate in the sec...