Study of Cylinder Movement Near a Surface at Low Reynolds Numbers*

The movement of a cylinder near a surface is a fundamental problem in fluid dynamics, extensively studied by researchers such as Teng et al. [1] and Houdrage et al. [2]. This study focuses on the behavior of an infinite 2D cylinder in close proximity to a wall under force-free conditions at low Reynolds numbers. Our objective was to correlate cylinder sliding behavior with surrounding conditions.

Simulations were conducted using COMSOL 6.2 with the creeping flow and ODE module. A P2+P2 discretization scheme was employed for fluid discretization, and quadratic Lagrange shape functions were used for curved mesh elements. Weak constraints were applied to the cylinder's boundary.

The results indicate that cylinder sliding depends significantly on boundary conditions. Specifically, when the top of the bounding box remained open, sliding occurred when the aspect ratio (width to height) was less than 2.5. Conversely, with the sides of the bounding box open and the top closed, sliding occurred for aspect ratios greater than or equal to 2. These findings were consistent across varying distances from the cylinder's radius, where sliding behavior persisted until contact-like interactions were observed.