Modulating 3D rectified flows via body elasticity

Rectified flows associated with the oscillatory motion of immersed rigid boundaries, known as viscous streaming flows, represent an efficient way of manipulating and controlling fluids via inertial effects. Despite recent progress, little is known about the role of body compliance, particularly when 3D settings are considered, a situation frequently encountered in microfluidics and biology. Motivated by this, we conduct a theoretical investigation into compliance-induced 3D streaming, via the minimal case of an oscillating, hyperelastic sphere immersed in a viscous fluid. We confirm our findings against direct numerical simulations and demonstrate the existence of new elasticity-induced streaming regimes, unavailable in the case of rigid bodies.