The effects of slit-like confinement on flow-induced polymer deformation

This paper is broadly concerned with the dynamics of a polymer confined to a rectangular slit of width D and deformed by a planar elongational flow of strength γ̇. It is interested, more specifically, in the nature of the coil-stretch transition that such polymers undergo when the flow strength γ̇ is varied, and in the degree to which this transition is affected by the presence of restrictive boundaries. These issues are explored within the framework of a finitely extensible Rouse model that includes pre-averaged surface-mediated hydrodynamic interactions. Calculations of the chain's steady-state fractional extension x using this model suggest that different modes of relaxation (which are characterized by an integer p) exert different levels of control on the coil-stretch transition. In particular, the location of the transition (as identified from the graph of x versus the Weissenberg number Wi, a dimensionless parameter defined by the product of γ̇ and the time constant τ_p of a relaxation mode p) is found to vary with the choice of τ_p. In particular, when τ₁ is used in the definition of Wi, the x vs. Wi data for different D lie on a single curve, but when τ₃ is used instead (with τ₃ > τ₁) the corresponding data lie on distinct curves. These findings are in close qualitative agreement with a number of experimental results on confinement effects on DNA stretching in electric fields. Similar D-dependent trends are seen in our calculated force vs. Wi data, but force vs. x data are essentially D-independent and lie on a single curve.