Adding cornstarch to the mud used for the Top Kill would have changed the mud so that it would have not broken up when trying to suppress the high pressure oil.
Jonathan Katz website.
Arxiv - Viscoelastic Suppression of Gravity-Driven Counter
The effect of cornstarch for this process is described at physorg
To work for the top kill, the mud would need to behave less like ketchup and more like quicksand.
Ketchup is what is known as a shear-thinning fluid. Initially it resists flowing. It begins to flow only when the pressure of your fingers on the bottle produces a stress on the condiment that is greater than what is called the yield stress. But after that, it flows freely.
Or as they used to say in the ketchup commercial “Anticipation is making me wait.”
Other examples of shear-thinning fluids are toothpaste, mayonnaise, mustard, and –crucially-- drilling mud, which is typically a slurry, or watery mixture, of clay and other minerals.
To suppress instability the mud needed to be a shear-thickening rather than a shear-thinning fluid--like the quicksand. As every reader of the Worst Case Scenario Survival Handbook knows, when you fall into quicksand, it is important to move slowly. The faster you move, the more the quicksand resists your movement.
The additive Katz suggested wasn’t esoteric or expensive. It was the kitchen staple cornstarch.
If you mix cornstarch and water, pour it in a cookie pan and slap it with your open hand, it doesn’t spatter. You can let your hand sink into it but you can’t easily jerk it out. Children play with it, and recipes for cornstarch "oobleck" can be found on the web.
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