The coil-stretch transition in the extension of polymers in two-dimensional flows was investigated near a critical boundary defined by simple shear flow. Visualization of individual molecules revealed a sharp coil-stretch transition in the steady-state length of the polymer with increasing Weissenberg number (Wi) in flows where the magnitude of the elongational component (\\E\\) slightly exceeded the rotational component (\\E\\). However, unlike in pure elongational flow, large fluctuations in the length of the polymer were observed near the critical point of the transition. These fluctuations result in a softening of the phase transition between coiled and extended states of the polymer. In flows where \\Omega\\ is slightly greater than \\E\\, significant transient polymer deformation was observed. However, the average length of the polymer as a function of Wi increased much more slowly than in simple shear flow.
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