Dynamics of soft elastic particles in viscous flows

This work focuses on the dynamics of rubber-like elastic particles (e.g., microgel particles) in viscous flows. The solid phase is represented by an incompressible, Mooney-Rivlin type model. Instead of solving the displacement field in the solid, evolution equations for the extra elastic stress tensor are derived to describe the elastic deformation. Therefore, the governing equations in both the fluid and the solid phase are written consistently in the current configuration (Eulerian representation). First of all, to compare the linear/nonlinear behaviors for different constitutive models, the instability of a Newtonian Couette flow past an elastic solid is tested. Next, to resolve the fluid/elastic particle interactions, a monolithic finite element solver which uses the Arbitrary Lagrangian-Eulerian moving mesh technique is implemented to solve the velocity, pressure and stress in the two phases simultaneously. When the velocity gradient of the external flow is constant (i.e., simple flow), it is demonstrated that an ellipsoidal particle will undergo a homogeneous deformation with a uniform field of stress and pressure. An analytical theory has been developed to describe the finite-strain, time-dependent response of the neo-Hookean elastic particles by using a polarization technique originally developed for the classical Eshelby problem in the linear elasticity. Under the simple flow conditions, we then studied the dynamical behaviors of a single elastic particle as well as the rheology of a dilute suspension of soft particles. When subjected to an extensional flow, an initially ellipsoidal (elliptical) elastic particle simultaneously stretches and rotates, tending to deform into a stable, ellipsoidal shape with the initial major axis aligned with the extension direction. However, steady-state solutions may not exist when the particle stiffness is lower than a certain critical value. By using the solution of a single particle, the macroscopic rheological properties are evaluated for a dilute suspension of elastic particles in an extensional flow. Somewhat counterintuitively, softer particles lead to a larger viscosity for the suspension. In an unbounded simple shear flow, three types of motion—steady-state, trembling and tumbling—are observed, depending on the shear rate in the flow, the elastic shear modulus and the initial particle shape. The steady-state motion is found to be always stable. The existence of a trembling regime is documented for the first time in non-vesicle systems, and a complete phase diagram is developed. The rheological properties of a dilute suspension of such soft particles generally exhibit shear-thinning behavior, and can even display negative intrinsic viscosity for sufficiently soft particles. In the end, we extended the finite element solver to simulate electrophoretic motion of a neo-Hookean particle where a coiling deformation a long ellipsoidal elastic particle is observed. After transient deformation, the particle eventually migrates at a constant Helmholtz-Smoluchowski velocity with a fixed, deformed shape