Potato Starch and Water

A shear-thickening suspension – not thixotropic

The starch grains in potato starch are 15–100 µm across and do not dissolve in cold water. So the mixture is a suspension: solid particles in a liquid. An emulsion is droplets of one liquid in another, like mayonnaise, and a solution is a substance spread out as individual molecules, like sugar in water.

The mixture is shear-thickening (also called dilatant): the harder you push, the thicker it gets, and beyond a certain limit it becomes solid. It is often called thixotropic, but that is actually the opposite. A thixotropic substance gets thinner the longer you stir it, and thickens slowly again when it stands still. Ketchup and paint are examples.

Friction between the grains: the Wyart–Cates model

The grains are surrounded by a thin film of water. At low stresses they slide past each other on the film, and the mixture is a thick liquid. If they are pressed together harder, the film is squeezed away, the grains touch directly, and friction arises. Friction makes the grains lock together at a lower packing density.

Matthieu Wyart and Mike Cates described it in 2014 with three equations. The fraction of frictional contacts grows with the stress $\sigma$:

$$f(\sigma)=1-e^{-\sigma/\sigma^*}.$$

The packing density at which the grains lock falls from $\phi_0$ (without friction) to $\phi_m$ (full friction):

$$\phi_J(\sigma)=f\,\phi_m+(1-f)\,\phi_0 .$$

And the viscosity tends to infinity as the volume fraction of the grains $\phi$ approaches $\phi_J$:

$$\eta(\sigma)=\frac{\eta_s}{\left(1-\phi/\phi_J(\sigma)\right)^{2}} .$$

The simulation uses $\phi_0=0.60$, $\phi_m=0.44$, $\sigma^*=600$ Pa and $\eta_s=0.1$ Pa·s. If $\phi$ lies between $\phi_m$ and $\phi_0$, there is a stress $\sigma_J$ at which $\phi_J(\sigma_J)=\phi$:

$$\sigma_J=-\sigma^*\ln\!\left(1-\frac{\phi_0-\phi}{\phi_0-\phi_m}\right).$$

This is where the mass becomes solid. The flow rate $\dot\gamma=\sigma/\eta(\sigma)$ at first grows with the stress, reaches a greatest value $\dot\gamma_{\max}$ and then falls to zero at $\sigma_J$. That is the graph above. It explains everything on the page: the mass cannot flow faster than $\dot\gamma_{\max}$. If you force it faster, it jumps up onto the solid branch.

That is why the mixture has to be right

If there is too little starch, $\phi<\phi_m$, the grains can never lock. The mixture gets thicker when you push, but remains a liquid. If there is too much, $\phi>\phi_0$, it is solid already at rest and crumbles like wet sand. Only in between does it behave as it should. The slider for the mixture shows it: try 100 g and 220 g per 100 ml of water.

The phenomena

Slow press and quick strike

A finger of radius $a$ pushed down at speed $v$ shears the mass at $\dot\gamma\sim v/a$. With the standard mixture $\dot\gamma_{\max}\approx 6\ \mathrm{s^{-1}}$, so a finger of 0.9 cm can sink at no more than just over 5 cm/s. Any faster, and the mass beneath the finger locks. The solid region spreads out from the finger as a front, much faster than the finger itself moves. In 2012 Scott Waitukaitis and Heinrich Jaeger measured that the front runs about ten times as fast as whatever strikes. That is why you can run across a pool of cornflour but sink if you stand still.

The matt surface

When the grains lock, they have to push each other slightly apart to get past each other. The packing expands, the water is drawn in between the grains, and the surface turns dry and matt. Osborne Reynolds called it dilatancy in 1885 and saw it in wet sand: the sand around a foot turns pale and dry when you step on it. In the simulation the surface changes from shiny to matt when the mass becomes solid.

Squeeze and release

When you squeeze and roll a lump, the stress is held above $\sigma_J$, and the lump is solid. When you let go, the stress drops to gravity's modest contribution, the lump melts and runs out over your hand with the low viscosity at rest, $\eta_0$.

The drip that snaps

A thread of radius $r$ carrying a drop of volume $V$ has the stress $\sigma=\rho gV/(\pi r^2)$ at the top. The thread is stretched at the rate $\dot\varepsilon=\sigma/(3\eta)$, gets thinner, and the stress rises. When it reaches $\sigma_J$, the thread locks and snaps like a solid instead of pinching off like water. The drop falls as a solid lump, shatters when it hits the table, and then melts into little puddles. With a thinner mixture the thread gets longer before it snaps.

What you need

A bowl, 100 ml of cold water, 150–200 g of potato starch (about 200 ml) or cornflour, a spoon, a little food colouring if you like, and a newspaper under the bowl.

What to do

1. Pour the water into the bowl, and sprinkle in the starch a little at a time while stirring slowly.
2. Stir with a spoon until it gets heavy to stir. When the spoon almost stops if you stir fast, but the mass slides when you tilt the bowl, the mixture is right.
3. If it is too thin, sprinkle in more starch. If it crumbles, add water a teaspoon at a time.

Experiments

Finger and strike. Push a finger slowly into the mass, and pull it slowly out. Then strike the surface quickly with your knuckles. It feels like a table, and nothing splashes.

Squeeze and release. Pick up a handful, and roll it quickly between your hands into a ball. Stop, and watch it melt and run out between your fingers.

Drip. Let the mass run out over the edge of your hand or a spoon. Look for where the stream snaps instead of forming drops.

The ball. Lay a small ball gently on the surface, and watch it sink. Then drop it from a height of 20 cm: it bounces or stays on top of the mass for a moment. Bury it, and try to jerk it out: the whole bowl comes with it.

For the brave. Lay a plastic bag on a loudspeaker, pour in the mass, and play a loud, low tone of around 40–80 Hz. Fingers and holes grow up out of the surface.

Clearing up

Never pour the mass down the sink or the toilet. It settles and can block the drain. Let it dry out or put it in the bin, and wash the bowl afterwards. Potato starch is completely harmless, but it is dusty, so avoid stirring it up into the air.

References

• M. Wyart & M. E. Cates, ‘Discontinuous shear thickening without inertia in dense non-Brownian suspensions’, Phys. Rev. Lett. 112, 098302 (2014).
• R. Seto, R. Mari, J. F. Morris & M. M. Denn, ‘Discontinuous shear thickening of frictional hard-sphere suspensions’, Phys. Rev. Lett. 111, 218301 (2013).
• S. R. Waitukaitis & H. M. Jaeger, ‘Impact-activated solidification of dense suspensions via dynamic jamming fronts’, Nature 487, 205 (2012).
• M. I. Smith, R. Besseling, M. E. Cates & V. Bertola, ‘Dilatancy in the flow and fracture of stretched colloidal suspensions’, Nature Communications 1, 114 (2010).
• O. Reynolds, ‘On the dilatancy of media composed of rigid particles in contact’, Philosophical Magazine 20, 469 (1885).
• E. Brown & H. M. Jaeger, ‘Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming’, Rep. Prog. Phys. 77, 046602 (2014).
• F. S. Merkt, R. D. Deegan, D. I. Goldman, E. C. Rericha & H. L. Swinney, ‘Persistent holes in a fluid’, Phys. Rev. Lett. 92, 184501 (2004).