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How does gravity affect the settling rate of silica nanoparticles in water?

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Gravity exerts a downward force on silica nanoparticles in water, causing them to settle, though this process is extremely slow for particles of this size. For example, a 10-nm-diameter silica nanosphere has a sedimentation rate of approximately 0.01 mm/day in water.1

The settling rate is governed by the balance between gravitational forces and the drag force exerted by the fluid. This relationship is described by Stokes’s law, which defines the terminal velocity ( $v$ ) of a spherical particle as:

$v = \frac{2}{9} \frac{(d_{1} - d_{2}) g r^{2}}{η}$

In this equation, $d_{1}$ is the density of the particle, $d_{2}$ is the density of the liquid, $g$ is the acceleration due to gravity, $r$ is the radius of the sphere, and $η$ is the viscosity of the liquid. Because nanoparticles are highly mobile and have such small radii, their settling rate under gravity alone is negligible compared to larger particles, often requiring more powerful force fields, such as those generated by an ultracentrifuge, to achieve effective separation.213