Active nematic defects in compressible and incompressible flows

Supavit Pokawanvit, Zhitao Chen, Zhihong You, Luiza Angheluta, M. Cristina Marchetti, and Mark J. Bowick

Phys. Rev. E 106, 054610 – Published 16 November 2022

Abstract

We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint. Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case, while they become unstable under the incompressibility constraint. For compressible flows at high enough activity, stable arches organize themselves into a smecticlike pattern, which induce an associated global polar ordering of $+ 1 / 2$ nematic defects. By contrast, divergence-free flows give rise to a local nematic order of the $+ 1 / 2$ defects, consisting of antialigned pairs of neighboring defects, as established in previous studies.

Received 27 June 2022
Accepted 25 October 2022

DOI:https://doi.org/10.1103/PhysRevE.106.054610

Physics Subject Headings (PhySH)

Flocking

Active defects Active nematics Collective dynamics

Polymers & Soft Matter

Authors & Affiliations

Supavit Pokawanvit¹, Zhitao Chen², Zhihong You ³, Luiza Angheluta ⁴, M. Cristina Marchetti ², and Mark J. Bowick ^5,*

¹Department of Applied Physics, Stanford University, Stanford, California 94305, USA
²Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA
³Fujian Provincial Key Laboratory for Soft Functional Materials Research, Research Institute for Biomimetics and Soft Matter, Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
⁴Department of Physics, University of Oslo, P.O. Box 1048, 0316 Oslo, Norway
⁵Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA

^*bowick@kitp.ucsb.edu

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Issue

Vol. 106, Iss. 5 — November 2022

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Images

Figure 1
State diagram for (a)–(c) compressible and (d)–(f) incompressible systems. The background color in each snapshot shows the vorticity $ω$ with magnitude corresponding to the color bar on the far right. The black arrows are $+ 1 / 2$ defects, whose heads indicate the defect polarization. Magenta dots are $- 1 / 2$ defects. All simulations start from a uniform director oriented along $x$ with $S = \sqrt{1 / 2}$ . Some small noise is added to the orientation to initiate the instability. For both compressible and incompressible systems, the uniform nematic state is stable at $| α | < 1$ [black dots, panels (a) and (d)]. Then, at $1 < | α | < 1.5$ , the uniform state becomes unstable and both systems develop a parallel band state through the bending instability typically found in active nematics [blue squares, panels (b) and (e)]. At $| α | > 1.5$ , the band state can no longer accommodate the strong activity. In this case, defect flocking emerges in compressible systems while dynamics in incompressible systems becomes chaotic [red triangles, panels (c) and (f)].
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Figure 2
Wave number $k$ corresponding to the peak of the Fourier transform of the nematic order phase field in the arch state as a function of $κ$ on a log-log scale. $k$ is scaled by $k_{0} = π / L$ , which is the minimal wave number allowed by the finite system size. The two insets show typical snapshots from simulations at $κ = 1$ (blue box, corresponding to the blue dot on the plot) and $κ = 8$ (red box, corresponding to the red dot on the plot), respectively, and $α = - 2$ .
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Figure 3
Critical activity above which a solution of uniform arches of arch wave number $k$ becomes linearly unstable for a compressible system. The blue circles are the values obtained from numerical simulations, while the blue solid line shows the prediction from the analytical linear stability analysis in Eq. (17). The black dashed line corresponds to the critical activity above which the uniform state ( $k = 0$ ) becomes unstable. The numerical parameter values are listed in Table 1.
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Figure 4
Defect order: (a) For compressible systems the mean defect polarization $S_{p}$ (solid blue) and mean phase gradient $V_{n}$ (dashed red). Both grow with time and eventually saturate roughly at the same time. The inset shows the probability distribution of the angle between $S_{p}$ and $V_{n}$ , with a strong peak at $π / 2$ (activity $α = - 2$ ). (b) For incompressible systems, in contrast, there is only local (nematic) order and no long-range order. This is evident from the behavior of the correlation function of the defect polarization $C (r)$ for three different activities. The inset shows the same correlation function with distance $r$ rescaled by the mean defect separation, $d_{sep}$ .
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