Abstract
We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded in a viscous medium, in which stresses are induced through constant consumption of energy. The numerical method is based on Lagrangian particles and staggered Cartesian finite-difference meshes. We show that the method is second-order and first-order accurate with respect to grid and time-step sizes, respectively. Using the present method, we simulate the hydrodynamics in rectangular geometries, of a passive liquid crystal, of an active polar film and of active gels with topological defects in polarization. We show the emergence of spontaneous flow due to Fréedericksz transition, and transformation in the nature of topological defects by tuning the activity of the system.
Highlights
Dynamics of many processes is governed by the mechanics of active matter
We present a hybrid particle-mesh method [29,30,40,9,63,10] to simulate the macroscopic hydrodynamics of incompressible active polar viscous gels on rectangular geometries with arbitrary boundary conditions
+ λ μ p x − ν (u xx p x + u xy p y ) + ωxx p x + ωxy p y, We present a hybrid particle-mesh method to numerically solve the continuum hydrodynamic equations of incompressible active polar viscous gels in two-dimensional rectangular geometries with arbitrary boundary conditions
Summary
Dynamics of many processes is governed by the mechanics of active matter. Active matter is a system of interacting agents that exhibit coordinated motion mediated by active internal stresses induced by consumption of energy [41,58]. We present a hybrid particle-mesh method [29,30,40,9,63,10] to simulate the macroscopic hydrodynamics of incompressible active polar viscous gels on rectangular geometries with arbitrary boundary conditions. (1), (2), (8), (9), and (10), along with appropriate boundary conditions for velocity and polarization, govern the hydrodynamics of incompressible active polar viscous gels in two dimensions as a function of material constants, namely, η , ν , γ , ζ , λ, K s , and K b , and of the activity μ. We assume that the material constants are spatially homogeneous whereas μ ≡ μ(x, y , t ) is, in general, spatially and temporally variable across the two-dimensional domain
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