  This study investigates the phenomenon of the early-stage dynamics of
impact-induced hardening in dense suspensions, where materials undergo
solidification upon impact. While Stokes flow theory traditionally applies to
suspensions with micrometer-sized particles due to their low Reynolds numbers,
suspensions containing larger particles defy such idealizations. Our work
focuses on the early-stage impact-induced hardening of suspensions containing
millimeter-sized particles through dynamic impact experiments. We are
particularly interested in the maximum drag force $F_\mathrm{max}$ acting on
the projectile as a function of the impact speed $u_0$. We successfully
conducted experiments using these suspensions and confirmed the relation
$F_\mathrm{max}\sim u_0^{3/2}$ for relatively large $u_0$ as observed in the
previous studies suspensions of micrometer-sized particles. Our findings reveal
that the early-stage behaviors of millimeter-sized particle suspensions align
well with predictions from the floating model, typically applicable under
Stokes flow conditions. This research sheds light on the complex dynamics of
impact-induced hardening in dense suspensions, particularly with larger
particles, advancing our understanding beyond conventional micrometer-sized
systems.
