Dry polymer model for a string of pushers: Nontrivial scaling of tumbling time with shear rate

Understanding the dynamics of active polymers is an important component for modeling the dynamic response of biological cells and microorganisms when subjected to external forces. A minimal computational model of active filaments that captures all the essential features of activity-induced filament motion is required to study large systems of dense suspensions. In this paper we present a model of a dry active polymer, compare its steady-state static and dynamic properties with those of a polymer consisting of extensile stresslets, and show that the two models give very similar results. When subjected to shear flow, both models show two distinct regimes in the tumbling interval as a function of shear rate, with a diffuse crossover regime in between. At high shear rate, the active and passive polymers follow the same power law for the tumbling interval. However, the tumbling interval is smaller than that of the passive polymer for low shear rates and larger for the high shear rate. We show that activity-induced large bends increase the coupling of the polymer with the shear gradient in the low-shear-rate regime, leading to a decrease in the tumbling interval. However, in the high-shear-rate regime, the active forces on the folds at the end of the stretched polymer prevent it from tumbling, leading to a larger tumbling interval. We show that the critical shear rate, at which the tumbling interval versus the shear-rate curve of the active polymer crosses that of the passive polymer, is determined by the balance of bending and shear forces and increases with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>κ</a:mi><a:mo>/</a:mo><a:msup><a:mi>N</a:mi><a:mn>3</a:mn></a:msup></a:mrow></a:math>, where <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mi>κ</b:mi></b:math> is the bending coefficient and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>N</c:mi></c:math> is the length of the polymer. Published by the American Physical Society 2024