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Dynamics of flexible fibers in shear flow

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 Publication date 2015
  fields Physics
and research's language is English




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Dynamics of flexible non-Brownian fibers in shear flow at low-Reynolds-number are analyzed numerically for a wide range of the ratios A of the fiber bending force to the viscous drag force. Initially, the fibers are aligned with the flow, and later they move in the plane perpendicular to the flow vorticity. A surprisingly rich spectrum of different modes is observed when the value of A is systematically changed, with sharp transitions between coiled and straightening out modes, period-doubling bifurcations from periodic to migrating solutions, irregular dynamics and chaos.



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We use numerical simulations of a bead-spring model chain to investigate the evolution of the conformation of long and flexible elastic fibers in a steady shear flow. In particular, for rather open initial configurations, and by varying a dimensionless elastic parameter, we identify two distinct conformational modes with different final size, shape, and orientation. Through further analysis we identify slipknots in the chain. Finally, we provide examples of initial configurations of an open trefoil knot that the flow unknots and then knots again, sometimes repeating several times. These changes in topology should be reflected in changes in bulk rheological and/or transport properties.
We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well-known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi$_{text c}$, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.
The Boltzmann equation for inelastic Maxwell models is considered to determine the velocity moments through fourth degree in the simple shear flow state. First, the rheological properties (which are related to the second-degree velocity moments) are {em exactly} evaluated in terms of the coefficient of restitution $alpha$ and the (reduced) shear rate $a^*$. For a given value of $alpha$, the above transport properties decrease with increasing shear rate. Moreover, as expected, the third-degree and the asymmetric fourth-degree moments vanish in the long time limit when they are scaled with the thermal speed. On the other hand, as in the case of elastic collisions, our results show that, for a given value of $alpha$, the scaled symmetric fourth-degree moments diverge in time for shear rates larger than a certain critical value $a_c^*(alpha)$ which decreases with increasing dissipation. The explicit shear-rate dependence of the fourth-degree moments below this critical value is also obtained.
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