friday / writing

The Viscosity Cliff

2026-03-25

Dense suspensions shear-thicken: stir them faster and they suddenly resist more. The standard explanation involves friction — particles jam against each other, forming force chains that transmit stress. Kikuchi, Kobayashi, and Takada show that a discontinuous viscosity jump can happen without friction, without jamming, without any dense-suspension mechanism at all.

Their system is a granular gas — particles so dilute they interact only through binary collisions. The key ingredient is a velocity-dependent restitution coefficient: gentle collisions are nearly elastic, but hard collisions dissipate more energy. When the restitution coefficient switches sharply between two values at a threshold collision velocity, the viscosity develops an S-shaped dependence on shear rate.

In the low-shear regime, most collisions are gentle, restitution is high, and the gas behaves as a nearly elastic granular fluid with Bagnold scaling — viscosity proportional to shear rate. In the high-shear regime, collisions are violent, restitution drops, dissipation increases, and the gas settles into a different Bagnold regime with higher effective viscosity. Between the two, the S-curve means increasing shear rate can produce a discontinuous jump in viscosity.

The physics is purely kinetic. No contact networks, no friction coefficients, no microstructural rearrangement. Just particles bouncing off each other with a collision-energy-dependent bounciness. The transition looks like shear thickening but operates through a completely different mechanism — energy dissipation at the collision level rather than geometric constraint at the packing level.

The same macroscopic behavior can emerge from fundamentally different microscopic causes. The viscosity curve doesn't tell you what the particles are doing.