A theory of flow as a cooperative phenomenon

Abstract

This theory may provide a link between the rheology and the microstructure of a flowing substance. Based on the methods of nonequilibrium statistical mechanics a kinetic equation for stress relaxation is derived. It is shown that the flow is largely determined by the coordination number z of cooperative flow units in the structure. A graphical procedure is given from which the coordination number and the strength of the cooperativity can be directly evaluated from experimental stress relaxation data. For flow in the linear regime other instances of flow are calculated and the results are, qualitatively: t 1 z , time dependence of strain in creep; ω 1 z , frequency dependence of dynamic moduli; t 1− 1 2 , time dependence of stress in constant rate of strain experiments. It is further proposed that non-Newtonian steady flow in structured liquids may be explained as a cooperative relaxation phenomenon and it is shown that a region with cooperative flow τ ∼ D 1 z (τ shear stress, D shear rate) exists above the region of Newtonian flow at low shear rates.