Phase Separation Dynamics and Active Turbulence in a Binary Fluid Mixture

TL;DR

To address how activity and two-fluid hydrodynamics shape phase ordering, we develop a two-fluid model that couples Cahn–Hilliard phase separation for $\phi$ with Beris–Edwards nematohydrodynamics and solves distinct momentum equations for active and passive fluids connected by viscous drag. The model includes active stress $\nabla \cdot(\zeta \phi \mathbf{Q})$ and capillary stress $-\mu \nabla \phi$, with $\mathbf{Q}$ evolving via the Beris–Edwards equation, and is solved using a phase-field lattice Boltzmann method. Simulations show microphase separation coexisting with active turbulence, with $|\zeta|$, $\phi$, $\lambda$, and $K$ governing flow scales and pattern formation; higher activity and active fraction boost energy input and inter-fluid energy transfer, while elastic effects suppress turbulence. The findings illuminate energy exchange between phases in active emulsions and have implications for engineered active materials and understanding biological systems where relative motion between components matters.

Abstract

Active matter, encompassing natural systems, converts surrounding energy to sustain autonomous motion, exhibiting unique non-equilibrium behaviors such as active turbulence and motility-induced phase separation (MIPS). In this study, we present a novel two-fluids model considering dynamics of the Cahn-Hilliard (CH) model for phase separation with Beris-Edwards nematohydrodynamics equation for orientational order and two distinct momentum equations for active and passive fluids coupled by viscous drag. A phase field-based lattice Boltzmann method is used to investigate the existence of active turbulence and phase separation in the binary mixture. We analyze micro-phase separated domain under extensile and contractile stresses, long the statistical properties of turbulent flow. Key parameters, like active parameter, tumbling parameter and elastic constant, affect the characteristic scale of flow. Our findings show that the interaction of active stress and two-fluid hydrodynamics leads to complex non-equilibrium pattern formation. This offers insights into biological and synthetic active materials.

Figures (7)

• Figure 1: Snapshot of the concentration profile in the microphase-separated state, color bar denotes the concentration of active phase.
• Figure 2: Validation of our results with Thampi et al.Thampi-PTSAMPES-2014, for spatial correlation velocity.
• Figure 3: Root mean square of velocity difference ($\Delta u_{rms}$) and root mean square of vorticity difference ($\Delta \omega_{rms}$) for different values of active parameter $\zeta$ and $\phi$.
• Figure 4: Root mean square velocity and vorticity for different values of active parameter $\zeta$ (considering both extensile (solid lines) and contractile case (dish lines)) and $K$. (a)- root mean square of velocity difference ($\Delta u_{rms}$), (b)- root mean square of vorticity difference ($\Delta \omega_{rms}$), (c)- root mean square of velocity for active phase ($u_{1rms}$), (d)- root mean square of vorticity for active phase ($\omega_{1rms}$).
• Figure 5: Root mean square velocity and vorticity for different values of active parameter $\zeta$ (considering both extensile (solid lines) and contractile case (dish lines)) in both the flow-tumbling ($\lambda=1/2$) and shear-aligning ($\lambda=2$) regimes. (a)- root mean square of velocity difference ($\Delta u_{rms}$), (b)- root mean square of vorticity difference ($\Delta \omega_{rms}$).