Simulations of deformable systems in fluids under shear flow using an arbitrary Lagrangian Eulerian technique

• We study the deformation of soft systems in fluids under unbounded shear flow.
• The study is done with a finite element method based code for viscoelastic fluids.
• To track the interface, a finite element method is defined on it.
• Deformed shape of drops and elastic particles are nearly ellipsoidal.
• Results on elastic particles in viscoelastic fluids are shown for the first time.

An arbitrary Lagrangian Eulerian finite element method based numerical code for viscoelastic fluids using well-known stabilization techniques (SUPG, DEVSS, log-conformation) is adapted to perform a 3D study of soft systems (drops, elastic particles) suspended in Newtonian and viscoelastic fluids under unbounded shear flow. Since the interface between the suspended objects and the matrix needs to be tracked, a finite element method with SUPG stabilization and second-order time discretization is defined on the interface, with the normal velocity of the interface equal to the normal component of the fluid velocity and a tangential velocity such that the elements on the interface are evenly distributed. This allows the mesh to get rid of the tank-treading motion of the particle. Both drops and elastic particles deform because of the flow and attain stationary deformed shape and orientation with respect to the flow direction. The effects of the physical parameters of the system on the phenomenon are investigated. The code is validated for drops and elastic particles in a Newtonian fluid through comparison with data from literature. New results on the deformation of elastic particles in an Upper Convected Maxwell fluid and a Giesekus fluid are presented.