= Solution
At a micrometre scale, <viscous forces> normally dominate inertia. As an illustrative Newtonian estimate, $L=1\,\mathrm{\mu m}$, $U=10\,\mathrm{\mu m\,s^{-1}}$, $\rho=10^3\,\mathrm{kg\,m^{-3}}$ and $\eta=10^{-3}\,\mathrm{Pa\,s}$ give a <Reynolds number> $\rho UL/\eta=10^{-5}$. The surrounding flow is approximately a <Stokes flow>, satisfying $-\nabla p+\eta\nabla^2\mathbf u=0$ and $\nabla\cdot\mathbf u=0$.
A body of radius $0.5\,\mathrm{\mu m}$ translated at that speed in an unbounded Newtonian liquid would need <Stokes drag> $6\pi\eta aU\simeq9.4\times10^{-14}\,\mathrm N$. It stops almost immediately when propulsion stops. The <scallop theorem> rules out propulsion by a single reciprocal stroke in this ideal regime; a rotating helix or a nonreciprocal cycle of shapes can propel it. <Brownian motion> also randomizes position and orientation: <Stokes–Einstein relation> scales as $a^{-1}$ and <rotational diffusion> as $a^{-3}$, so retaining heading becomes harder as size decreases.
The Newtonian calculation is a scale estimate, not a complete model of blood. Vessel walls alter drag, the imposed flow advects the body, and nearby <red blood cells> make the medium heterogeneous at this scale. <Non-Newtonian fluid> effects and deformable obstacles can matter; steering must be assessed against those effects rather than inertial coasting.
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