Custom flow in overdamped Brownian Dynamics

Abstract

When an external field drives a colloidal system out of equilibrium, the ensuing colloidal response can be very complex and obtaining a detailed physical understanding often requires case-by-case considerations. In order to facilitate systematic analysis, here we present a general iterative scheme for the determination of the unique external force field that yields a prescribed inhomogeneous stationary or time-dependent flow in an overdamped Brownian many-body system. The computer simulation method is based on the exact one-body force balance equation and allows to specifically tailor both gradient and rotational velocity contributions, as well as to freely control the one-body density distribution. Hence compressibility of the flow field can be fully adjusted. The practical convergence to a unique external force field demonstrates the existence of a functional map from both velocity and density to external force field, as predicted by the power functional variational framework. In equilibrium, the method allows to find the conservative force field that generates a prescribed target density profile, and hence implements the Mermin-Evans classical density functional map from density distribution to external potential. The conceptual tools developed here enable one to gain detailed physical insight into complex flow behaviour, as we demonstrate in prototypical situations.

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Cited by in corpus (18)

• Classical dynamical density functional theory: from fundamentals to applications
• Power functional theory for many-body dynamics
• Non-negative Interfacial Tension in Phase-Separated Active Brownian Particles
• Phase coexistence of active Brownian particles
• Perspective: How to overcome dynamical density functional theory
• Flow and structure in nonequilibrium Brownian many-body systems
• Dynamical density functional theory for the drying and stratification of binary colloidal dispersions
• Phase separation of active Brownian particles in two dimensions: Anything for a quiet life
• Active interface polarization is a state function
• Universality in Driven and Equilibrium Hard Sphere Liquid Dynamics
• Neural force functional for non-equilibrium many-body colloidal systems
• First-principles superadiabatic theory for the dynamics of inhomogeneous fluids
• Order-preserving dynamics in one dimension -- single-file diffusion and caging from the perspective of dynamical density functional theory
• Custom Flow in Molecular Dynamics
• Inhomogeneous steady shear dynamics of a three-body colloidal gel former
• Reduced-variance orientational distribution functions from torque sampling
• Shear and bulk acceleration viscosities in simple fluids
• Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids