The Navier-Stokes equations are as follows,

$$\dot{u}+(u\cdot \nabla ) u +\nu \nabla^2 u =\nabla p$$

where $u$ is the velocity field, $\nu$ is the viscosity, and $p$ is the pressure.

Some elementary manipulations show that if you zoom in by a factor of $\lambda$, then you expect viscosity to scale as $\lambda^{\frac{3}{2}}$. So, for example, if you zoom in to the length scale of a cell, you expect viscosity to be around a million times larger than humans experience it.

This is not observed, however, which makes sense since we expect the components of a cell to move around extremely quickly. (EDIT: this is observed - see answer - my initial google searches were untrustworthy, damn google). Nonetheless, the calculation above suggests that they feel like they are moving through one of the most viscous fluids imaginable.

What then is the mechanism that prevents this? I have seen some explanations through the ideas of 'microviscosity' and 'macroviscosity' in the physics community, but I couldn't find much of a theoretic backing for them.

I'm wondering if there is a more mathematical explanation, perhaps directly from the Navier-Stokes equation itself (seems unlikely), or something from a kinetic theory point of view? For example some kind of statistical model of water molecules that reproduces the result?

Fluid dynamics for the sepioliteon Physics Stack Exchange, post with identitficator552396. On the other hand Wikipedia has an article dedicated toSepiolite(if you're interested in this material). Isn't required a response/reply for this comment and I hope that it doesn't disturb to you. $\endgroup$