The propensity of reacted materials to become mixed with unreacted materials that are fed to stirred vessels or chemical reactors. The design of continuous stirred-tank reactors (CSTRs) is based on the assumption of instantaneous homogeneity. In reality, the flow of materials short-circuit and leave the vessel or reactor before the expected time, while some reside for longer periods. Back-mixing is a concern in the design of plug flow reactors, which lead to a departure in ideality.