A transient-network model describing the rheological behaviour of concentrated dispersions

Attractive forces acting between particles in dispersions may cause a three-dimensional structure to be built up. A temporary-network model is postulated that describes the rheological behaviour of such systems. Chains of particles are assumed to be created and broken by thermal actions and by applied deformation. The relation between the network structure and the macroscopic stress tensor is deduced. One of the main model features is that no use is made of the common assumption of affinity of the motion of the chain vectors with the gradient of the macroscopic velocity field. Instead, the chain deformations are assumed to depend on the forces acting on them, i.e. their deformations depend on their stiffness and on the applied deformation, whereas fracture of chains may cause stress relaxation in the rest of the network. The chains may behave as highly non-linear springs, whereas the probability that the chains will break in some time interval may be an explicit function of the chain length itself. Integral equations are derived, from which the stress-tensor components can be calculated in any flow experiment, that obeys creeping-flow conditions. Analytical expressions are obtained for the relaxation spectrum of such systems in terms of the microscopic parameters.