Exploring the Existence of Bulk Stress Hysteresis in the Elongational Flow of Polymer Solutions

T. Sridhar¹, R. Prabhakar^1,2, J. Ravi Prakash¹, Duc At Nguyen¹

¹Department of Chemical Engineering, Monash University, Melbourne, VIC 3800, Australia

²Present address: Research School of Chemistry, Australian National University, Canberra

Nearly all currently popular models in polymer rheology assume that the steady state stress in a polymer solution is uniquely determined by the rate of deformation to which the solution is subjected. Yet in a seminal paper in 1974, de Gennes proposed arguments to suggest that in fact, under certain circumstances, the time history of deformation experienced by the solution might have a crucial bearing on the steady state value of stress attained for a given deformation rate. The importance of de Gennes contention has paradigm changing implications for the modelling of polymer rheology, as was recognized at about the same time by Hinch and Tanner. The accurate estimation of the relationship between stress and strain in a solution lies at the heart of being able to develop a realistic description of the flow of polymer solutions. The microfluidics of biopolymer solutions is just one example of a number of current contexts in which such a description is crucial for efficient design. Serious early doubts, however, about the theoretical validity of de Gennes arguments, and the absence until recently of any supporting experimental evidence, has implied that the need for a fundamental change in the modeling of polymer solution rheology has not been widely recognized so far.

In ground breaking experiments on ultra-dilute solutions of DNA molecules subjected to planar elongational flow, Shaqfeh and coworkers have shown recently that even though solutions experience identical rates of deformation, individual DNA molecules can have two widely disparate conformational states (either coiled or highly stretched) depending on the time history of the solutions deformation. Since the stress in a polymer solution has its origin predominantly in the entropic resistance of individual polymer molecules to deformation from their equilibrium coiled state, the Stanford groups results clearly validate De Gennes hypothesis (albeit indirectly) of different deformation histories leading to disparate states of stress.

The design of the flow cell used in the Stanford experiments, while being ideal for the observation of single molecules for extended periods of time, does not currently enable the simultaneous measurement of fluid stresses. Additionally, the existence of disparate conformational states has only been demonstrated unambiguously so far for the particular case of E-Coli DNA in a sucrose-water solution.

In this paper, we report the measurement of bulk stresses in a synthetic polymer solution undergoing uni-axial elongational flow, with appreciably different magnitudes at nearly identical values of strain rate, depending on the time history of the solution's deformation. This demonstration has been achieved by successfully extending the domain of operation of the filament stretching rheometer from its usual constant strain rate mode to a constant stress mode, in which a uniform elongational flow field is generated with a desired value of stress. Computer simulations are shown to reproduce the experimental observations, and indicate as conjectured originally by de Gennes, that the origin of the deformation history dependence of stress lies in the conformation dependence of hydrodynamic forces.