Nematic ordering in active fluids driven by substrate deformations: Mechanisms and patterning regimes

Abstract

The interplay between active matter and its environment is central to understanding emergent behavior in biological and synthetic systems. Here, we show that coupling active nematic flows to small-amplitude deformations of a compliant substrate can fundamentally reorganize the system's dynamics. Using a model that combines active nematohydrodynamics with substrate mechanics, we find that contractile active nematics-normally disordered in flat geometries-undergo a sharp transition to long-range orientational order when the environment is deformable. This environmentally induced ordering is robust and enables distinct patterning regimes, with wrinkle morphologies reflecting the nature of the active stresses. Our results reveal a generic mechanism by which mechanical feedback from soft environments can lead to ordering in active systems.

Figures (6)

• Figure 1: Emergence of oreintational order in a contractile system coupled to a deformable substrate. (a) A schematic representation of the nematic orientation $\mathbf{Q}$, and the substrate out-of-plane deformation orientation $\omega_z$. (b) Zoomed-in 3D representation of the deformation amplitude field of the region highlighted by the white box in (c), with highlighted $\mathbf{W}$ showing relation between the substrate $\omega_z$ and $\mathbf{W}$. (c) Nematic order parameter in a typical simulation, with the black contour marking zero out-of-plane deformation.
• Figure 2: Extensile and contractile activities respond fundamentally differently to deformable substrates. Nematic order parameter $S$ (a, b) and wrinkle amplitude $A$ (d,e) versus activity $\zeta$ and coupling strength $k_w$. The fixed parameter in (a) and (d) is the coupling strength $k_w = 0.005$; and in (b), (e), the magnitude of the activity $|\zeta| = 0.04$. Phase diagram of $\text{Nematic order}$ (c) and $\text{Amplitude}$ (f). The growth of $\text{Amplitude}$ with activity $(|\zeta|)$ shows square root (contractile) and linear (extensile) scaling (d), while the dependence of $\text{Amplitude}$ to the coupling strengths $(k_w)$ (e) demonstrates opposite coupling responses for extensile and contractile activities.
• Figure 3: Patterns of deformation in contractile and extensile systems distinguish at the local and mesoscale. Histograms for contractile (a) and extensile (b) systems show the director preferentially aligns parallel versus perpendicular to the wrinkle. (c) Snapshot of a typical contractile wrinkle pattern. (d) Magnified view of a region in (c), where colour indicates wrinkle orientation, revealing distinct orientation domains, along with (e) the corresponding structure factor. Panels (f)-(h) show equivalent plots for extensile systems, displaying sparse wrinkles and orientation domains with diffuse boundaries. The parameters are fixed at $|\zeta|=0.05$, $k_w=0.005$.
• Figure 4: Algebraic correlations and system-spanning power-law deformations emerge in contractile active nematics. (a) Time series of largest wrinkle domain size normalized by system size, showing contractile systems form system spanning patterns. (b) Power spectrum of the nematic order. (c,d) Patch size distributions, the number of deformation domains of a given area divided by the system size, reveal that patches in contractile systems exhibit power-law scaling (c), large patches in extensile systems follow an exponential distribution (d). The parameters are fixed at $|\zeta|=0.05$, $k_w=0.005$.
• Figure 5: Contractile activity generates oreintational order and deformations without hydrodynamics, while extensile activity shows no ordering in the absence of hydrodynamics, with $k_w=0.005$