Finite Element Analysis of the Lift on a Slightly Deformable and Freely Rotating and Translating Cylinder in Two-Dimensional Channel Flow

Motivated by the lateral migration phenomena of fresh and glutaraldehyde-fixed red blood cells in a field flow fractionation (FFF) separation system, we studied the transverse hydrodynamic lift on a slightly flexible cylinder in a two-dimensional channel flow. The finite element method was used to analyze the flow field with the cylinder at different transverse locations in the channel. The shape of the cylinder was determined by the pressure on the surface of the cylinder from the flow field solution and by the internal elastic stress. The cylinder deformation and the flow field were solved simultaneously. The transverse lift exerted on the cylinder was then calculated. The axial and angular speed of the cylinder were iterated such that the drag and torque on the cylinder were nulled to represent a freely translating and rotating state. The results showed that the transverse lift on a deformable cylinder increased greatly and the equilibrium position moved closer to the center of the channel compared to a rigid cylinder. Also, with the same elastic modulus but a higher flow rate, a larger deformation and higher equilibrium location were found. The maximum deformation of the cylinder occurred when the cylinder was closest to the wall where a larger shear rate existed. The numerical results and experimental studies are discussed.