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Transient dynamics of a polymer in the start-up of linear-mixed flow

We study the transient dynamics of a polymer chain in the start-up of linear-mixed flow under non-steady-state conditions. We show that in the close vicinity of simple shear flow, when the rotational flow component is slightly in excess of the elongational flow component, the temporal variation of the mean square extension follows oscillatory monotonic decay. The magnitude of the oscillations decreases with an increase in the rotational flow component, crossing over to smooth monotonic decay in the limiting case of a pure rotational flow. In contrast, in simple shear flow, when the amounts of rotational and elongational flow components are exactly the same, the non-normality of the velocity gradient tensor leads to transient amplification of the initial mean square extension, resulting in a non-monotonic temporal decay profile. The transient growth occurs above a critical shear rate and is more pronounced at high shear rates, when the time scale of the applied perturbation due to shear is shorter than the relaxation time of the polymer chain.