Time-Asymptotic (Floquet) Linear stability of pulsatile particle-laden channel flows*

Pulsatile flows have significant applications in microfluidics, including mixing, particle separation, and clog mitigation, as well as in biological systems, such as cardiovascular flows. Linear stability analysis of particle-laden flow with uniform distribution is investigated for a pulsatile flow in a channel. The time- asymptotic (Floquet) stability and modal transient growth during pressure-modulation cycle of pulsatile plane Poiseuille flow is investigated to study the dynamics of the coupled fluid-particle system, where disturbances are decomposed into a product of exponential growth and a sum of harmonics. The coupling between the fluid flow and particles is modeled using Stokes drag, with the particles assumed to be solid, spherical, and heavy. A parametric study of stability in the non-dimensional parameter space, primarily defined by Reynolds number, Womersley number, and the amplitude of the applied pressure modulation, is conducted for different particle relaxation times and mass fractions. Results show that for an S (particle relaxation time) 5x10^-5  and f (mass fraction) of 5%, the addition of a pulsating component promotes instability by reducing the critical Reynolds number. Furthermore, it is observed that for S = 5x10^-5 and f = 5%, at large frequencies (measured by Womersley number), increasing the amplitude of the oscillating component has a stabilizing effect, while it destabilizes the system at lower frequencies.