Multiparticle collision dynamics for tensorial nematodynamics

Lock-key microfluidics: simulating nematic colloid advection along wavy-walled channels

Liquid crystalline media mediate interactions between suspended particles and confining geometries, which not only has potential to guide patterning and bottom-up colloidal assembly, but can also control colloidal migration in microfluidic devices. However, simulating such dynamics is challenging because nemato-elasticity, diffusivity and hydrodynamic interactions must all be accounted for within complex boundaries. We model the advection of colloids dispersed in flowing and fluctuating nematic fluids confined within 2D wavy channels. A lock-key mechanism between homeotropic colloids and troughs is found to be stronger for planar anchoring on the wavy walls compared to homeotropic anchoring on the wavy walls due to the relative location of the colloid-associated defects. Sufficiently large amplitudes result in stick-slip trajectories and even permanent locking of colloids in place. These results demonstrate that wavy walls not only have potential to direct colloids to specific docking sites but also to control site-specific resting duration and intermittent elution.

Particle-based and continuum models for confined nematics in two dimensions

We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.

Active nematic liquid crystals simulated by particle-based mesoscopic methods

Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.

Data-Driven Discovery of Active Nematic Hydrodynamics

Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.

Simulating the flow of interacting ferrofluids with multiparticle collision dynamics

Ferrofluid flow is fascinating since its fluid properties can conveniently be manipulated by external magnetic fields. Novel applications in micro- and nanofluidics as well as in biomedicine have renewed the interest in the flow of colloidal magnetic nanoparticles with a focus on small-scale behavior. Traditional flow simulations of ferrofluids, however, often use simplified constitutive models and do not include fluctuations that are relevant at small scales. Here we address these challenges by proposing a hybrid scheme that combines the multiparticle collision dynamics method for modeling hydrodynamics with Brownian dynamics simulations of a reliable kinetic model describing the microstructure, magnetization dynamics, and resulting stresses. Since both multiparticle collision dynamics and Brownian dynamics are mesoscopic methods that naturally include fluctuations, this hybrid scheme presents a promising alternative to more traditional approaches, also because of the flexibility to model different geometries and modifying the constitutive model. The scheme was tested in several ways. Poiseuille flow was simulated for various model parameters and effective viscosities were determined from the resulting flow profiles. The effective, field-dependent viscosities are found to be in very good agreement with theoretical predictions. We also study Stokes' second flow problem for ferrofluids. For weak amplitudes and low frequencies of the oscillating plate, we find that the velocity profiles are well described by the result for Newtonian fluids at the corresponding, field-dependent viscosity. Furthermore, the time-dependent profiles of the nonequilibrum magnetization component are well approximated by their steady-state values in stationary shear when evaluated with the instantaneous local shear rate. Finally, we also apply our scheme to simulate ferrofluid shear flow over a rough surface. We find characteristic differences in the nonequilibrium magnetization components when the external field is oriented in flow and in a gradient direction.

Mesoscopic simulations of active nematics

Coarse-grained, mesoscale simulations are invaluable for studying soft condensed matter because of their ability to model systems in which a background solvent plays a substantial role but is not the primary interest. Such methods generally model passive solvents; however, far-from-equilibrium systems may also be composed of complex solutes suspended in an active fluid. Yet, few coarse-grained simulation methods exist to model an active medium. We introduce an algorithm to simulate active nematics, which builds on multiparticle collision dynamics (MPCD) for passive fluctuating nematohydrodynamics by introducing dipolar activity in the local collision operator. Active nematic MPCD (AN-MPCD) simulations not only exhibit the key characteristics of active nematic turbulence but, as a particle-based algorithm, also reproduce crucial attributes of active particle models. Thus, mesoscopic AN-MPCD is an approach that bridges microscopic and continuum descriptions, allowing simulations of composite active-passive systems.

Multiparticle Collision Dynamics for Ferrofluids

Detailed studies of the intriguing field-dependent dynamics and transport properties of confined flowing ferrofluids require efficient mesoscopic simulation methods that account for fluctuating ferrohydrodynamics. Here, we propose such a new mesoscopic model for the dynamics and flow of ferrofluids, where we couple the multi-particle collision dynamics method as a solver for the fluctuating hydrodynamics equations to the stochastic magnetization dynamics of suspended magnetic nanoparticles. This hybrid model is validated by reproducing the magnetoviscous effect in Poiseuille flow, obtaining the rotational viscosity in quantitative agreement with theoretical predictions. We also illustrate the new method for the benchmark problem of flow around a square cylinder. Interestingly, we observe that the length of the recirculation region is increased whereas the drag coefficient is decreased in ferrofluids when an external magnetic field is applied, compared with the field-free case at the same effective Reynolds number. The presence of thermal fluctuations and the flexibility of this particle-based mesoscopic method provides a promising tool to investigate a broad range of flow phenomena of magnetic fluids and could also serve as an efficient way to simulate solvent effects when colloidal particles are immersed in ferrofluids.

Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets

Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.

Nonequilibrium Dynamics of a Magnetic Nanocapsule in a Nematic Liquid Crystal

Colloidal particles in nematic liquid crystals show a beautiful variety of complex phenomena with promising applications. Their dynamical behaviour is determined by topology and interactions with the liquid crystal and external fields. Here, a nematic magnetic nanocapsule reoriented periodically by time-varying magnetic fields is studied using numerical simulations. The approach combines Molecular Dynamics to resolve solute–solvent interactions and Nematic Multiparticle Collision Dynamics to incorporate nematohydrodynamic fields and fluctuations. A Saturn ring defect resulting from homeotropic anchoring conditions surrounds the capsule and rotates together with it. Magnetically induced rotations of the capsule can produce transformations of this topological defect, which changes from a disclination curve to a defect structure extending over the surface of the capsule. Transformations occur for large magnetic fields. At moderate fields, elastic torques prevent changes of the topological defect by tilting the capsule out from the rotation plane of the magnetic field.

Multiparticle collision dynamics simulations of a squirmer in a nematic fluid

We study the dynamics of a squirmer in a nematic liquid crystal using the multiparticle collision dynamics (MPCD) method. A recently developed nematic MPCD method [Phys. Rev. E 99, 063319 (2019)] which employs a tensor order parameter to describe the spatial and temporal variations of the nematic order is used to simulate the suspending anisotropic fluid. Considering both nematodynamic effects (anisotropic viscosity and elasticity) and thermal fluctuations, in the present study, we couple the nematic MPCD algorithm with a molecular dynamics (MD) scheme for the squirmer. A unique feature of the proposed method is that the nematic order, the fluid, and the squirmer are all represented in a particle-based framework. To test the applicability of this nematic MPCD-MD method, we simulate the dynamics of a spherical squirmer with homeotropic surface anchoring conditions in a bulk domain. The importance of anisotropic viscosity and elasticity on the squirmer's speed and orientation is studied for different values of self-propulsion strength and squirmer type (pusher, puller or neutral). In sharp contrast to Newtonian fluids, the speed of the squirmer in a nematic fluid depends on the squirmer type. Interestingly, the speed of a strong pusher is smaller in the nematic fluid than for the Newtonian case. The orientational dynamics of the squirmer in the nematic fluid also shows a non-trivial dependence on the squirmer type. Our results compare well with existing experimental and numerical data. The full particle-based framework could be easily extended to model the dynamics of multiple squirmers in anisotropic fluids.

Directing the far-from-equilibrium assembly of nanoparticles in confined liquid crystals by hydrodynamic fields

The assembly of nematic colloids relies on long-range elastic interactions that can be manipulated through external stimuli. Confinement and the presence of a hydrodynamic field alter the defect structures and the energetic interactions between the particles. In this work, the assembly landscape of nanoparticles embedded in a nematic liquid crystal confined in a nanochannel under a pressure-driven flow is determined. The dynamics of the liquid crystal tensor alignment field is determined through a Poisson-Bracket framework, namely the Stark-Lubensky equations, coupled with the zero-Reynolds momentum equations and the liquid crystal Landau-de Gennes free energy functional. A second order semi-implicit time integration and a three-dimensional Galerkin finite element method are used to resolve flow and nematic fields under several conditions. In general, the zero Reynolds flow displaces the defects around the particles in the upstream direction and renders the surface anchoring ineffective when the flow strength dominates over the nematic elasticity. More importantly, the potential of mean force for particle assembly is non-monotonic independent of surface anchoring. Our results show that the confinement length scale determines the repulsion/attraction transition between colloids, while the flow strength modifies the static defect structure surrounding the particles and determines the magnitude of the energetic barrier for successful assembly. In the attractive regime, the particles move at different rates through the nematic until one particle eventually catches up with the other. This process occurs against or along the direction of flow depending on the flow strength. Ultimately, these results provide a template for engineering and controlling the transport and assembly of nanoparticles under far-from equilibrium conditions in anisotropic media.

Dynamics of defects around anisotropic particles in nematic liquid crystals under shear

Nematic multiparticle collision dynamics is used to simulate disclination ring defects around spherocylinders suspended in a liquid crystal. A solvent-solute interaction potential is integrated over a short-time scale by an auxiliary molecular dynamics procedure that updates the translational and angular coordinates of the spherocylinders. For suspended particles with length in the range ∼(60,160)nm and a fixed aspect ratio, this method is able to simulate static defects reported previously in the literature. It also simulates orientation fluctuations of the elongated colloids that exhibit a broad distribution and a slow relaxation rate. Finally, a nematic host driven from equilibrium by shear flow is simulated, and the consequent dynamic behavior of the colloid-defect pair is studied. Defects under shear present significant structural transformations from chairlike disclination rings to extended defects that cover most of the cylindrical surface of the colloid. This effect results from the hydrodynamic torque on the nematic field caused by the distorted flow around the spherocylinder, and it is present for small Reynolds and Ericksen numbers of order unity.

Multi-particle collision dynamics with a non-ideal equation of state. I

The method of multi-particle collision dynamics (MPCD) and its different implementations are commonly used in the field of soft matter physics to simulate fluid flow at the micron scale. Typically, the coarse-grained fluid particles are described by the equation of state of an ideal gas, and the fluid is rather compressible. This is in contrast to conventional fluids, which are incompressible for velocities much below the speed of sound, and can cause inhomogeneities in density. We propose an algorithm for MPCD with a modified collision rule that results in a non-ideal equation of state and a significantly decreased compressibility. It allows simulations at less computational costs compared to conventional MPCD algorithms. We derive analytic expressions for the equation of state and the corresponding compressibility as well as shear viscosity. They show overall very good agreement with simulations, where we determine the pressure by simulating a quiet bulk fluid and the shear viscosity by simulating a linear shear flow and a Poiseuille flow.