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Influence of flow confinement on the drag force on a static cylinder

The influence of confinement on the drag force $F$ on a static cylinder in a viscous flow inside a rectangular slit of aperture $h_0$ has been investigated from experimental measurements and numerical simulations. At low enough Reynolds numbers, $F$ varies linearly with the mean velocity and the viscosity, allowing for the precise determination of drag coefficients $λ_{||}$ and $λ_{\bot}$ corresponding respectively to a mean flow parallel and perpendicular to the cylinder length $L$. In the parallel configuration, the variation of $λ_{||}$ with the normalized diameter $β= d/h_0$ of the cylinder is close to that for a 2D flow invariant in the direction of the cylinder axis and does not diverge when $β= 1$. The variation of $λ_{||}$ with the distance from the midplane of the model reflects the parabolic Poiseuille profile between the plates for $β\ll 1$ while it remains almost constant for $β\sim 1$. In the perpendicular configuration, the value of $λ_{\bot}$ is close to that corresponding to a 2D system only if $β\ll 1$ and/or if the clearance between the ends of the cylinder and the side walls is very small: in that latter case, $λ_{\bot}$ diverges as $β\to 1$ due to the blockage of the flow. In other cases, the side flow between the ends of the cylinder and the side walls plays an important part to reduce $λ_{\bot}$: a full 3D description of the flow is needed to account for these effects.