Floquet stability analysis of pulsatile particle-laden channel flow

Abstract

We investigate the linear stability of particle-laden pulsatile channel flow using Floquet analysis within a two-phase dusty-gas framework. Uniformly distributed spherical particles are coupled to an incompressible Newtonian fluid through Stokes drag, and the governing equations are linearized about a time-periodic base flow driven by a sinusoidally varying pressure gradient. The effects of Reynolds number, Womersley number, pulsation amplitude, particle relaxation time, and particle mass fraction on temporal instability are examined. In the steady limit, particles with very short relaxation times destabilize the flow, whereas finite relaxation times introduce interphase slip and drag-mediated damping that stabilize disturbances. Under pulsatile forcing, increasing pulsation amplitude destabilizes the flow at low Womersley numbers but stabilizes it at sufficiently high Womersley numbers. This transition is governed by the penetration depth of oscillatory motion and is systematically shifted by particle relaxation time and mass loading through interphase momentum exchange. A critical corresponding value remains small throughout, indicating strong particle-fluid coupling and ruling out resonance-like particle dynamics. These findings provide a unified physical framework for the stability of pulsatile particle-laden flows relevant to physiological and periodically forced multiphase systems.