  The manipulation and control of microparticles through non-intrusive methods
is pivotal in biomedical applications such as cell sorting and cell focusing.
Although several experimental and numerical studies have been dedicated to
single suspended particles or clusters of rigid spheres, analogous cases with
deformable particles have not been as thoroughly studied, especially when the
suspending liquid exhibits relevant viscoelastic properties. With the goal of
expanding the current knowledge concerning these systems, we perform a
computational study on the hydrodynamic interactions between two neutrally
buoyant initially spherical elastic particles suspended in Newtonian and
shear-thinning viscoelastic matrices subjected to pressure-driven flow in a
cylindrical microchannel. Due to the well-known focusing mechanism induced by
both particle deformability and fluid elasticity, the two particles are assumed
to flow at the axis of the tube. The rheological behavior of the viscoelastic
continuous phase is modelled via the Giesekus constitutive equation, whereas
the particles are assumed to behave as Neo-Hookean solids. The problem is
tackled by employing a mixed finite element method. The effects of particle
deformability, fluid elasticity, confinement ratio, and initial interparticle
separation distance on the pair dynamics are investigated. The main outcome of
this study is a quantitative indication of the flow conditions and spatial
configurations (initial distances) under which the particles will spontaneously
form organized structures. Such results are helpful to design efficient
microfluidic devices with the aim of promoting particle ordering.
