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Here is one of the many videos on youtube showing how a cornstarch and water mixture can become very hard when put under stress. I haven't found a good explanation of why it behaves the way it does. Is there any paper that has been published on this that explains the weird properties of the liquid? If not, could someone here try to explain what is going on?

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The addition of polymers into a solvent (in this case water) changes its properties dramatically, in particular viscosity. It's a delicate balance of energetic and entropic considerations due to the long chains of the polymers.

As for the explicit why, I cannot formulate a coherent answer now. But maybe you could read about Non-Newtonian fluids (the general concept of non idea fluids) and in particular Shear thickening describing the phenomena of cornstarch.

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