This is an interesting question because a marshmallow is a complicated system which involves multiple phases. Furthermore, none of the phases readily separate from the other under normal conditions (room temperature, atmospheric pressure, etc.).
So lets examine the parts of the marshmallow. The white goo that gives the marshmallow its taste is a very viscous liquid. However, marshmallows have gelatin in them. Adding this ingredient provides collagen fibers which interlock with one another to form a solid support system that tightly encloses the liquid goo. Additionally, marshmallows have air whipped into them during the manufacturing process, so they actually contain a solid, a liquid, and a gas.
Each phase makes the composite system behave differently than any one single phase. For example, the marshmallow is highly compressible while most solids and liquids are, at best, weakly compressible. This is due to the gaseous content within the marshmallow. However, without gelatin, the marshmallow would exhibit continuous deformations under applied stresses. To illustrate the effect of gelatin on the final product structure, just compare the ingredients in a bag of marshmallows and those in a jar of fluff. Youll see that the ingredients are more or less identical except that the fluff lacks gelatin. If you take a scoop out of the fluff, the atmospheric stresses will cause flow that tends to flatten the fluff. On the other hand, the marshmallow stands upright and maintains its structure in the atmosphere.
One final note is that while the collagen structural fibers are essentially a solid at room temperature, they are not covalently bound to one another. The links between fibers are almost like knots in a rope and it is possible to disentangle them and get somewhat more fluid properties. This can happen under mechanical stress (such as pulling the marshmallow) or at high temperatures (like over a campfire).
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