Shearing Active Gels Close to the Isotropic-Nematic Transition

We study numerically the rheological properties of a slab of active gel close to the isotropic-nematic transition. The flow behavior shows a strong dependence on the sample size, boundary conditions, and on the bulk constitutive curve, which, on entering the nematic phase, acquires an activity-induced discontinuity at the origin. The precursor of this within the metastable isotropic phase for contractile systems (e.g., actomyosin gels) gives a viscosity divergence; its counterpart for extensile suspensions admits instead a shear-banded flow with zero apparent viscosity.

Figure 1

For an extensile nematic ($\phi =3.0$, $\xi =0.7$, $\eta =0.567$, $\zeta =0.1$), as functions of $\dot{\gamma }$ in steady state :(a) Passive order-parameter stress ${\Pi }_{xy}^P={\Pi }_{xy}+\zeta Q_{xy}$; (b) Total passive stress ${\Sigma }_{xy}^P={\Pi }_{xy}^P+\eta \dot{\gamma }$; (c) Order-parameter $Q_{xy}$; (d) Total shear stress $\sigma (\dot{\gamma })$ (dotted curve: the same for $\phi =2.95$).

Figure 2

(a) Apparent zero shear viscosity for an isotropic contractile gel in a slab under shear. Solid curve(s): free-boundary conditions; HLB data are indistinguishable from those derived from the bulk flow curve [13]. Dashed curve: fixed boundaries (director along flow). (b) Apparent viscosity in a linear regime for an active extensile gel in a slab under shear. Solid and dashed curves correspond to systems with free and fixed boundaries, respectively. The insets show plots of $Q_{xy}$ and $u_x$ (solid and dashed lines) in the ${\eta }_{\mathrm{app}}=0$ phase.

Figure 3

${\eta }_{\mathrm{app}}$ vs $\dot{\gamma }$ for $\phi =2.99$ (solid, dashed, and dotted lines) and $\phi =2.8$ (dot-dashed line) for contractile gels under shear. Anchored BCs are considered, with $Q_{\alpha \beta }=0$ (solid, dot-dashed lines) or with $\mathbf{n}\parallel \widehat{\mathbf{x}}$ (long-dashed and dotted lines). For the dotted line, the bulk was initialized with nematic order.

Figure 4

Viscosity and (inset) flow curves for active contractile gels in bulk homogeneous shear: $\phi =2.8$, 2.9, 2.99 (dot-dashed, dashed, solid lines). Vertical line segments signify the end of the I branch and a jump up to N. Data with nematic anchoring as in Fig. 3 are shown for an initially isotropic (squares) or nematic (circles) bulk.

Figure 5

Dynamic phase diagram in the ($\zeta$, $v_0$) plane (with $v_0=\dot{\gamma }L$ the wall velocity; $L=100$) for an active liquid crystal close to the isotropic-nematic transition ($\phi =2.695$, $\eta =0.28$). The phases are labeled as follows: $\mathrm{N}=\mathrm{\text{nematic}}$, $\mathrm{I}=\mathrm{\text{isotropic}}$, $\mathrm{B}1=\mathrm{I}/\mathrm{N}$ banded, $\mathrm{B}2=\mathrm{N}/\mathrm{N}$ banded.