Modulating rectified flows via elastohydrodynamic effects

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 their potential, we know surprisingly little about streaming when body compliance is involved, a situation frequently encountered in microfluidic and biological settings. Motivated by this, we conduct the first theoretical investigation into body compliance-induced streaming, via the minimal case of an oscillating, hyperelastic cylinder immersed in a viscous fluid. Further, we confirm our findings against direct numerical simulations. Our study demonstrates the existence of a new elasticity-induced term, allowing forms of inertial flow control, even in the Stokes limit, unavailable in the case of rigid bodies.