VOLUME 85, NUMBER 9 PHYSICAL REVIEW LETTERS 28 AUGUST 2000 Relating the Microscopic and Macroscopic Response of a Polymeric Fluid in a Shearing Flow Hazen P. Babcock, 1 Douglas E. Smith, 1 Joe S. Hur, 2 Eric S. G. Shaqfeh, 2 and Steven Chu 1 1 Departments of Physics and Applied Physics, Stanford University, Stanford, California 94305 2 Department of Chemical Engineering, Stanford University, Stanford, California 94305 (Received 9 March 2000) The microscopic and macroscopic response of a polymer solution in start-up shear flow was investi- gated using fluorescence microscopy of single molecules, bulk viscosity measurements, and Brownian dynamics simulations. An overshoot in viscosity was observed upon flow inception and understood via the observed molecular extension and by simulation findings. Increasing the polymer concentration up to six times the overlap concentration (C  ) has no effect on the character of the dynamics of individual molecules. PACS numbers: 83.10.Nn, 87.14.Gg, 87.15.–v One of the most important goals in understanding com- plex fluids is to link the macroscopic material proper- ties with microscopic changes. For instance, interesting macroscopic responses of these complex fluids containing large molecules such as polymers, colloids, liquid crystals, micelles, and surfactants have been widely reported in the literature [1–7]. A classic example is the observation that polymeric fluids often display a transient overshoot in vis- cosity upon the inception of a shearing flow [5–7]. Various theories and models predict such an overshoot [8–13] but a clear understanding of how this macroscopic behavior is associated with the changes in microscopic state is lacking. In this work, we made detailed observations of both the molecular dynamics and the macroscopic viscosity of the same polymer solution. The effect of concentration was studied down to nearly infinite dilution in order to distinguish individual chain effects from those due to in- termolecular interactions [14]. Finally, the experimental data were compared to the predictions of molecular mod- els specifically based on the known molecular parameters of the polymer used in the experiments. We used DNA solutions as a model system and made side-by-side com- parison of the single-molecule observations, viscosity mea- surements, and Brownian dynamics simulations. Simple shear flow was created in a 50 mm gap be- tween two parallel glass plates in an apparatus similar to that used previously [15,16]. We measured the maximum extension of the polymers in the flow direction (direc- tion of plate travel) using video fluorescence microscopy. The technique has been improved such that the transient molecular extension could be observed in the center-of- mass frame of a single molecule during the start-up of shear flow. In order to visualize single molecule dynamics at higher polymer concentrations, small fractions of fluo- rescently labeled “probe” molecules were added to so- lutions of unlabeled molecules [17–20]. To determine the statistical properties of the molecular dynamics, these measurements were repeated on an “ensemble” of 60 to 130 identical molecules for each different shear rate and sample concentration. The time-dependent shear viscosity of the same DNA solutions was measured using a rheome- ter (RDA II, RSI Scientific, Piscataway, NJ). By observing the recoil of isolated, stretched molecules after the flow is turned off we measure the longest relaxa- tion time, t , of our polymer [21]. The dimensionless pa- rameter called the “Weissenberg Number” Wi is used to characterize the effective strength of the shear flow. It is the product  gt where  g, the shear rate, is the plate veloc- ity divided by the gap width. In the simplest case of an isolated chain, one generally expects the statistical prop- erties of two data sets, even if they are taken at different solvent viscosities, to match as long as Wi is the same for both [15,22]. At higher concentrations one eventually ex- pects to see deviations due to strong intermolecular inter- actions (in particular, entanglements) which should change the character of the dynamics. First, we considered the limit of infinite dilution in order to examine the polymer response in the absence of any possible interactions between poly- mer molecules. We used a concentration of 10 25 C  [23]. At this concentration the average distance between molecules is much larger than the contour length of a molecule and we expect interactions to be negligible. When there is no applied flow, flexible polymers adopt a random coil state. If a shear flow is suddenly applied the polymers begin to stretch. While the individual polymers display widely different dynamics upon flow inception, the average extension rises smoothly to a constant steady state value [Fig. (1)]. For Wi . 19, we observed a small overshoot in extension. In order to test whether the overshoot in extension was due to an initial time synchronization of coiled molecules, we compared the dynamics of coiled molecules stretch- ing at the inception of flow to the dynamics of tran- siently coiled chains after steady-state conditions had been reached. We set the new time  0 point to be the first point in the time trace after 50 strain units where the polymer extension was less than one standard deviation from the average extension at Wi  0. When these traces were averaged together, there was no evidence of an overshoot. 2018 0031-9007 00  85(9)  2018(4)$15.00 © 2000 The American Physical Society