Dynamical density functional theory analysis of the laning instability in sheared soft matter

Using dynamical density functional theory (DDFT) methods we investigate the laning instability of a sheared colloidal suspension. The nonequilibrium ordering at the laning transition is driven by non-affine particle motion arising from interparticle interactions. Starting from a DDFT which incorporates the non-affine motion, we perform a linear stability analysis that enables identification of the regions of parameter space where lanes form. We illustrate our general approach by applying it to a simple one-component fluid of soft penetrable particles

Flow induced crystallisation of penetrable particles

For a system of Brownian particles interacting via a soft exponential potential we investigate the interaction between equilibrium crystallisation and spatially varying shear flow. For thermodynamic state points within the liquid part of the phase diagram, but close to the crystallisation phase boundary, we observe that imposing a Poiseuille flow can induce nonequilibrium crystalline ordering in regions of low shear gradient. The physical mechanism responsible for this phenomenon is shear-induced particle migration, which causes particles to drift preferentially towards the center of the flow channel, thus increasing the local density in the channel center. The method employed is classical dynamical density functional theory

Power functional theory for the dynamic test particle limit

For classical Brownian systems both in and out of equilibrium we extend the power functional formalism of Schmidt and Brader (2013 J. Chem. Phys. 138 214101) to mixtures of different types of particles. We apply the framework to develop an exact dynamical test particle theory for the self and distinct parts of the van Hove function, which characterize tagged and collective particle motion. The memory functions that induce non-Markovian dynamics are related to functional derivatives of the excess (over ideal) free power dissipation functional. The method offers an alternative to the recently found nonequilibrium Ornstein–Zernike relation for dynamic pair correlation functions

Active Brownian particles at interfaces: An effective equilibrium approach

A simple theoretical approach is used to investigate active colloids at the free interface and near repulsive substrates. We employ dynamical density functional theory to determine the steady-state density profiles in an effective equilibrium system (Farage T. F. F. et al., Phys. Rev. E, 91 (2015) 042310). In addition to the known accumulation at surfaces, we predict wetting and drying transitions at a flat repulsive wall and capillary condensation and evaporation in a slit pore. These new phenomena are closely related to the motility-induced phase separation (MIPS) in the bulk

Free power dissipation from functional line integration

Power functional theory provides an exact generalisation of equilibrium density functional theory to non-equilibrium systems undergoing Brownian many-body dynamics. Practical implementation of this variational approach demands knowledge of an excess (over ideal gas) dissipation functional. Using functional line integration (i.e. the operation inverse to functional differentiation), we obtain an exact expression for the excess free power dissipation, which involves the pair interaction potential and the two-body, equal-time density correlator. This provides a basis for the development of approximation schemes

Local phase transitions in driven colloidal suspensions

Using dynamical density functional theory and Brownian dynamics simulations, we investigate the influence of a driven tracer particle on the density distribution of a colloidal suspension at a thermodynamic state point close to the liquid side of the binodal. In bulk systems, we find that a localised region of the colloid-poor phase, a ‘cavitation bubble’, forms behind the moving tracer. The extent of the cavitation bubble is investigated as a function of both the size and velocity of the tracer. The addition of a confining boundary enables us to investigate the interaction between the local phase instability at the substrate and that at the particle surface. When both the substrate and tracer interact repulsively with the colloids we observe the formation of a colloid-poor bridge between the substrate and the tracer. When a shear flow is applied parallel to the substrate the bridge becomes distorted and, at sufficiently high shear-rates, disconnects from the substrate to form a cavitation bubble

Phase separation on the sphere: Patchy particles and self-assembly

Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle surface lead to the formation of long-lived, metastable states for which the density is distributed in patches over the particle surface. We study the time evolution and stability of these states as a function of both the particle size and the thermodynamic parameters. Finally, by connecting our findings with studies of patchy particles, we consider the implications for self-assembly in many-particle systems

Shear-induced migration in colloidal suspensions

Using Brownian dynamics simulations, we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear-rates, considering both steady-states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems, size segregation is observed

Nonequilibrium phase behavior from minimization of free power dissipation

We develop a general theory for describing phase coexistence between nonequilibrium steady states in Brownian systems, based on power functional theory [M. Schmidt and J. M. Brader, J. Chem. Phys. 138, 214101 (2013)]. We apply the framework to the special case of fluid-fluid phase separation of active soft sphere swimmers. The central object of the theory, the dissipated free power, is calculated via computer simulations and compared to a simple analytical approximation. The theory describes well the simulation data and predicts motility-induced phase separation due to avoidance of dissipative clusters