Numerical simulations of the dynamics of a deformable particle in a viscoelastic liquid subjected to Poiseuille flow in a cylindrical microcapillary at non-negligible inertia

Abstract

The manipulation and control of particles in microfluidic devices through non-intrusive methods is pivotal in many application fields, e.g., cell focusing and sorting. Inertial microfluidics is rapidly gaining attention in the scientific community because of the considerable advantages in terms of throughput. In addition to inertia, other factors can trigger the cross-stream migration of particles in liquids undergoing pressure-driven channel flows, such as the deformability of the particles themselves and/or the viscoelasticity of the carrier fluid. For this reason, the dynamics of an initially spherical elastic particle suspended in a viscoelastic liquid subjected to pressure-driven flow in a cylindrical channel at non-negligible inertia is studied through three-dimensional arbitrary Lagrangian–Eulerian finite-element numerical simulations. The mechanical behavior of the particle is described through the neo-Hookean hyper-elastic constitutive equation, whereas the rheological behavior of the carrier liquid is described through the Giesekus model. The Reynolds number Re, measuring the relative importance of inertial and viscous forces in the tube, the elastic capillary number Cae, measuring the relative importance of liquid viscous stress and solid elastic stress, and the Deborah number De, measuring the ratio of the liquid relaxation time and the flow characteristic time, are varied. The particle migrates transversally to the flow direction until reaching a radial equilibrium position depending on Re, Cae, and De. Different dynamics are observed depending on the interplay among inertia and elasticity of both the liquid and the solid phase: one, two, or even three stable equilibrium positions can be found along the tube radius.