A Complex Fluid is defined as a mixture which has a coexistence between two phases: solid–liquid (suspensions or solutions of macro-molecules such as polymers), solid–gas (granular), liquid–gas (foams) or liquid–liquid (emulsions).

Examples include paint, pediatric liquid medicines, laundry detergent, cell membranes and mayonnaise.

Although many materials found in nature can fit into the class of complex fluids, very little is well understood about them. Inconsistent and controversial conclusions concerning their material properties still persist. The careful study of these systems may lead to “new physics” and new states of matter. For example, it has been suggested that these systems can jam and a “jamming phase diagram” can be used to consider how these systems can jam and unjam. It is not known whether further research will demonstrate these findings, or whether such a theoretical framework will prove useful. As yet this large body of theoretical work has been poorly supported with experiments.

Source : Wikipedia

Another poorly understood aspect is the phenomenon of Dilatancy - first described in 1886 - whereby some complex fluids increase their volume when deformed. It's believed to be linked to the 'jamming' cited in the above quote.

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