Characteristic Times of Polymer Tumbling Under Shear Flow

Abstract

AbstractThe tumbling dynamics of flexible chains in shear flow, analysed by Brownian Dynamics simulations, are found to be ruled by three characteristic times τtumb, τdif and τlag. The average tumbling time τtumb scales with the shear rate with a robust exponent against excluded volume (EV) or hydrodynamic interactions, $\tau _{{\rm tumb}} \approx {\dot {\gamma }}^{{-} 2/3} $. The chain extensions in the flow plane decorrelate in a time τdif determined by the diffusion of the chain configuration in gradient direction, $\tau _{{\rm dif}} \approx Y^{2} /D$. The chain keeps memory of its configuration over a number of tumblings events given by the ratio τdif/τtumb. While for ideal chains $\tau _{{\rm dif}} /\tau _{{\rm tumb}} \approx O(1)$, for expanded (EV) chains we find $\tau _{{\rm dif}} /\tau _{{\rm tumb}} \approx {\dot {\gamma }}^{0.2} $. Hence, EV chains tumble in a more deterministic way as ${\dot {\gamma }}$ is increased. As a consequence, contrary to previous assumptions, the exponential tail of the tumbling time distribution $P(\tau )\approx {\exp} ({-} \nu \tau )$ presents a non‐Poissonian exponent. This exponent ν is found to be determined by a new characteristic time τlag measuring how fast the chain in‐flow elongation X responses to the drag force induced by chain fluctuations in gradient direction Y. PSCS numbers.magnified image