  The transition from globular to elongated states of biopolymers in shear flow
occurs at a distinct critical shear rate, $\dot{\gamma }^{*}$. The magnitude of
$\dot{\gamma }^{*}$ depends on the internal potential and the polymer length.
For example, the critical shear is much larger for von Willebrand Factor (vWF)
compared to DNA. Furthermore, it is shown through computational analysis of vWF
(model-vWF) that $\dot{\gamma }^{*}\sim N^{1/3}$, where N is the number of
dimeric units in the vWF. In this study, we show that in the presence of
charged nanoparticles (CNP) and polymer, the critical shear rate scales
differently depending on the polymer length and the charge-strength of the CNP.
It is shown that CNP alter the conformational dynamics of polymers under shear
flow when the polymer beads have an opposite charge. The introduction of CNP
shifts the critical shear rate and alters the scaling. Furthermore, it is shown
that the critical zeta potential of CNP, $\zeta^{*}$, scales linearly with
shear rate, and scales cubically with ratio $\beta$ between final CNP-polymer
composite size and original polymer size, that is $\zeta^{*}\sim \dot{\gamma
}\beta ^{-3}$.
