Numerical simulation and scaling analysis of elasticity-induced lift force in a viscoelastic fluid between confining surfaces

How to accurately characterize the lift force on the particles near the solid surfaces is an ongoing challenge in fluid mechanics and microfluidic techniques, especially in a complex system with viscoelastic fluid or/and soft surface that is commonly encountered in a biological system. The motions of the particles in vicinity of a surface can be simplified to be a rigid cylinder surrounded by the viscoelastic fluid moving along a substrate which can be rigid or soft according to different cases. In such an inertial free system with a wide range of Weissenberg number (Wi < 5.00, representing the ratio of the elastic force to the viscous force), firstly we numerically evaluate the influence of the systematic parameters, including the polymer viscosity, the geometry and Wi, on the net normal force for a cylinder closely moving along a rigid substrate, and the elasticity-induced lift force in a scaled form. It is shown that a strong shear arises in the viscoelastic confinement between the moving cylinder and the rigid substrate, it leads to the asymmetry of the first normal stress distribution around the cylinder, and thus the lift force. Then, the influence of a soft substrate on the lift force is considered, and we find that the lift force induced by the viscoelastic fluid always dominates in magnitude over that induced by the soft substrate deformation. This work provides a reliable scaling that can be utilized to quantify the elasticity-induced lift force on the particles in a viscoelastic system, such as the micro- and nanofluidic systems in biological applications.