40
2 Active Nematics
Fig. 2.19 (a) Patterns in a 1:1 mixture of phase-separated active polar and passive isotropic fluids.
Left: Low contractile activity with normal anchoring at the active/passive interface. Center: High
contractile activity with no anchoring. Lower panels show blowups with white arrows indicating
the direction of the flow field. Right: Tensile activity, increasing from above to below, with normal
anchoring. The inset in the lower picture shows a blowup of a selected droplet, and spirals show
the polarity pattern in rotating droplets. The active phase is colored red, the passive one, blue, and
a transitional border region, green (Bonelli et al, 2019)
activity and normal anchoring at the active/passive interface, with the alignment
vector pointing toward the passive phase. Quite surprisingly, the pattern becomes
ordered at higher activity, but the order disappears altogether, as shown in the central
panels, when anchoring is removed. The pattern at low tensile activity in the upper
right panel mixes lamellae with droplets of the active phase, but droplets definitely
prevail in the lower right panel as activity increases. Polar droplets with normal
anchoring must contain a vortex defect. Its structure is aster-like in small droplets
but spiral in big ones, which, accordingly, rotate with an angular velocity increasing
with their radius. Given cheap computer power, there is a lot of freedom to modify
patterns, changing activity, alignment strength, and the ratio of active and passive
phases, multiplying the production of colorful pictures.
Unlike a chimeric combination of nematic stress with polar symmetry, chiral
active fluids are straightforward analogues of the passive cholesteric liquid crystals
briefly mentioned in Sect. 2.1. A picture of cholesteric alignment, more detailed
than that in Fig. 2.1, is shown in Fig. 2.20a. A generic hydrodynamic instability of
the cholesteric order is pitch splay, sketched in (Fig. 2.20b). A splay deformation
of the pitch is equivalent to layer undulations with bending of the director field in
normal planes along the pitch axis. When activity is tensile, this deformation mode
gives rise to active flow along the pitch axis, parallel to the bend direction, which
destabilizes the cholesteric order. Pitch orientations have nematic symmetry, and at
high distortions develop pairs of 1/2-charged line defects, called λ-lines. Cholesteric
2 Active Nematics
Fig. 2.19 (a) Patterns in a 1:1 mixture of phase-separated active polar and passive isotropic fluids.
Left: Low contractile activity with normal anchoring at the active/passive interface. Center: High
contractile activity with no anchoring. Lower panels show blowups with white arrows indicating
the direction of the flow field. Right: Tensile activity, increasing from above to below, with normal
anchoring. The inset in the lower picture shows a blowup of a selected droplet, and spirals show
the polarity pattern in rotating droplets. The active phase is colored red, the passive one, blue, and
a transitional border region, green (Bonelli et al, 2019)
activity and normal anchoring at the active/passive interface, with the alignment
vector pointing toward the passive phase. Quite surprisingly, the pattern becomes
ordered at higher activity, but the order disappears altogether, as shown in the central
panels, when anchoring is removed. The pattern at low tensile activity in the upper
right panel mixes lamellae with droplets of the active phase, but droplets definitely
prevail in the lower right panel as activity increases. Polar droplets with normal
anchoring must contain a vortex defect. Its structure is aster-like in small droplets
but spiral in big ones, which, accordingly, rotate with an angular velocity increasing
with their radius. Given cheap computer power, there is a lot of freedom to modify
patterns, changing activity, alignment strength, and the ratio of active and passive
phases, multiplying the production of colorful pictures.
Unlike a chimeric combination of nematic stress with polar symmetry, chiral
active fluids are straightforward analogues of the passive cholesteric liquid crystals
briefly mentioned in Sect. 2.1. A picture of cholesteric alignment, more detailed
than that in Fig. 2.1, is shown in Fig. 2.20a. A generic hydrodynamic instability of
the cholesteric order is pitch splay, sketched in (Fig. 2.20b). A splay deformation
of the pitch is equivalent to layer undulations with bending of the director field in
normal planes along the pitch axis. When activity is tensile, this deformation mode
gives rise to active flow along the pitch axis, parallel to the bend direction, which
destabilizes the cholesteric order. Pitch orientations have nematic symmetry, and at
high distortions develop pairs of 1/2-charged line defects, called λ-lines. Cholesteric