= Solution
For fluid <density> $\rho_f$, speed $U$ and characteristic length $d$, inertial kinetic <energy> scales as $\rho_fd^3U^2$ while viscous work over distance $d$ scales as $\eta Ud^2$. Their ratio is the \b[<Reynolds number>],
$$
\boxed{\mathrm{Re}=\frac{\rho_fUd}{\eta}.}
$$
Smaller particles at a fixed speed have smaller Re, so viscous stresses dominate fluid inertia when $\mathrm{Re}\ll1$. Increasing speed increases Re and eventually makes inertia more important, rather than making viscous dominance stronger.
Particle inertia is a separate issue. Its <particle velocity-relaxation time> is $\tau_p=\rho_pd^2/(18\eta)$; comparing it with a travel time $d/U$ gives a <Stokes number> $\tau_pU/d$. This uses particle <density> $\rho_p$, whereas the fluid <Reynolds number> uses fluid <density> $\rho_f$.
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