Faraday instability in shallow particle-laden liquids under vertical vibration

The Faraday instability of shallow particle-laden liquids under geometric confinement was investigated through combined experimental and theoretical analyses. Water-based suspensions containing micrometer-sized magnetite particles were vertically excited in a cylindrical container, and the effects of particle mass, particle size, and fluid depth on the threshold acceleration and axisymmetric modal responses were examined. Particle loading increased the instability threshold, with the threshold acceleration increasing by up to 29% as the particle mass was increased from 0.05 to 0.15 g. Although the overall particle volume fraction was low, sedimentation formed a basal particle layer near the container bottom. A modified baseline force-detuning-based model with nominal effective-property corrections captures the modal ordering and the overall instability characteristics of shallow particle-laden liquids. Comparison with the experimental results further suggests that sedimented-particle-bed dissipation contributes to the additional threshold increase observed at larger particle masses, larger particle sizes, and higher-order modes.