Rheological modelling of complex fluids: A transient network model with microstates

In this work, the dynamics of a transient network is analyzed with a model that includes two coupled kinetic processes to describe the rheological behavior of complex fluids. Five microstates are defined, representing the complexity of interactions among the macromolecules suspended in a Newtonian fluid. These microstates represent statistically networks with varying entanglement density, such as a dense entangled network in one extreme, and free chains or dangling ends (pendant chains) on the other extreme. It is assumed that the energy barrier required to modify the complexity of the system can be provided by flow, and that the flow-induced change in the network complexity is modelled as a coupled kinetic scheme constituted by a set of reversible kinetic equations describing the evolution of the microstates. The average concentration of microstates at a given time defines the maximum segment length joining the entanglement points in the transient network. The rheological material functions are calculated according to the classical statistical description of a transient network, but with a variable maximum segment length (variable extensibility), which is a function of the kinetics of the microstates. The model predicts shear banding in steady simple shear and time-dependent non-linear rheological phenomena, such as thixotropy, stretched exponential relaxation and other interesting responses of complex fluids.