A ?constrained-chain? network model for viscoelastic fluids

Abstract

The "constrained-chain" theory of rubber elasticity proposed by Crossland and van der Hoffwas found by them to predict quantitatively many salient features of experimental studies.The present work utilized the "constrained-chain" strain-energy function in a development parallel to that of the "rubberlike liquid" model of Lodge to arrive at a naturally strain-dependent integral constitutive equat_ion for viscoelastic fluids. It can be considered as a particular case of the K-BKZ model with part of the memory function arising from a molecular model. The memory function contains the only nonlinear parameter of the model, the maximum extensibility of a network chain. The model gives a singularity in the stress integral when a network chain is streched to its maximum extensibility. To eliminate this singularity, an assumption has been made which reduces the number of fully extended network chains to zero. Alternative approaches are discussed briefly.

A ?constrained-chain? network model for viscoelastic fluids

“…The specific "constrained-chain" model (from here on simply called the "constrained-chain" model) investigated here is given by the following specific choices for the functions fp and gp [1]: The specific "constrained-chain" model (from here on simply called the "constrained-chain" model) investigated here is given by the following specific choices for the functions fp and gp [1]:…”

“…Empirically assuming H 1 = 1, H2 = 0 and using the same memory function as in the "constrained-chain" model, a modified Tanner model is obtained [1]. The original Tanner "rupture" model [3,4] is recovered if we assume {l,t -t'<sc, f=g= O,t-t'>s«~, (8) in the modified Tanner model.…”

“…In Part I [1], a natt/rally strain-dependent constitutive equation for viscoelastic fluids has been developed from the "constrained-chain" theory of rubber elasticity [2]. The general form of the "constrained-chain" model for isothermal, incompressible fiows of viscoelastic ftuids, which is discussed in Part I, is T +p~ = i /z(t, t', 11) [H1 (11,12) C-i _ H2 (11, 12) C] dt', oo (1) …”