Hydrodynamic segregation in a bidisperse colloidal suspension in microchannel flow: A theoretical study

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

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.

An SPH Approach for Non-Spherical Particles Immersed in Newtonian Fluids

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modeling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid–solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modeling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid and with other solid bodies by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortex formation in the fluid flow in between.

Label-free microfluidic sorting of microparticles

Massive growth of the microfluidics field has triggered numerous advances in focusing, separating, ordering, concentrating, and mixing of microparticles. Microfluidic systems capable of performing these functions are rapidly finding applications in industrial, environmental, and biomedical fields. Passive and label-free methods are one of the major categories of such systems that have received enormous attention owing to device operational simplicity and low costs. With new platforms continuously being proposed, our aim here is to provide an updated overview of the state of the art for passive label-free microparticle separation, with emphasis on performance and operational conditions. In addition to the now common separation approaches using Newtonian flows, such as deterministic lateral displacement, pinched flow fractionation, cross-flow filtration, hydrodynamic filtration, and inertial microfluidics, we also discuss separation approaches using non-Newtonian, viscoelastic flow. We then highlight the newly emerging approach based on shear-induced diffusion, which enables direct processing of complex samples such as untreated whole blood. Finally, we hope that an improved understanding of label-free passive sorting approaches can lead to sophisticated and useful platforms toward automation in industrial, environmental, and biomedical fields.

Collective dynamics in a monolayer of squirmers confined to a boundary by gravity

We present a hydrodynamic study of a monolayer of squirmer model microswimmers confined to a boundary by strong gravity using the simulation method of multi-particle collision dynamics. The squirmers interact with each other via their self-generated hydrodynamic flow fields and thereby form a variety of fascinating dynamic states when density and squirmer type are varied. Weak pushers, neutral squirmers, and pullers have an upright orientation. With their flow fields they push neighbors away and thereby form a hydrodynamic Wigner fluid at lower densities. Furthermore, states of fluctuating chains and trimers, of kissing, and at large densities a global cluster exist. Finally, pushers at all densities can tilt against the wall normal and their in-plane velocities align to show swarming. It turns into chaotic swarming for strong pushers at high densities. We characterize all these states quantitatively.

Dynamics and structure of colloidal aggregates under microchannel flow

The kinetics of colloidal gels under narrow confinement are of widespread practical relevance, with applications ranging from flow in biological systems to 3D printing. Although the properties of such gels under uniform shear have received considerable attention, the effects of strongly nonuniform shear are far less understood. Motivated by the possibilities offered by recent advances in nano- and microfluidics, we explore the generic phase behavior and dynamics of attractive colloids subject to microchannel flow, using mesoscale particle-based hydrodynamic simulations. Whereas moderate shear strengths result in shear-assisted crystallization, high shear strengths overwhelm the attractions and lead to melting of the clusters. Within the transition region between these two regimes, we discover remarkable dynamics of the colloidal aggregates. Shear-induced surface melting of the aggregates, in conjunction with the Plateau-Rayleigh instability and size-dependent cluster velocities, leads to a cyclic process in which elongated threads of colloidal aggregates break up and reform, resulting in large crystallites. These insights offer new possibilities for the control of colloidal dynamics and aggregation under confinement.

Collective sedimentation of squirmers under gravity

Active particles, which interact hydrodynamically, display a remarkable variety of emergent collective phenomena. We use squirmers to model spherical microswimmers and explore the collective behavior of thousands of them under the influence of strong gravity using the method of multi-particle collision dynamics for simulating fluid flow. The sedimentation profile depends on the ratio of swimming to sedimentation velocity as well as on the squirmer type. It shows closely packed squirmer layers at the bottom and a highly dynamic region with exponential density dependence towards the top. The mean vertical orientation of the squirmers strongly depends on height. For swimming velocities larger than the sedimentation velocity, squirmers show strong convection in the exponential region. We quantify the strength of convection and the extent of convection cells by the vertical current density and its current dipole, which are large for neutral squirmers as well as for weak pushers and pullers.

Self-Organized Velocity Pulses of Dense Colloidal Suspensions in Microchannel Flow

We present a numerical study of dense colloidal suspensions in a pressure-driven microchannel flow in two dimensions. The colloids are modeled as elastic and frictional spheres suspended in a Newtonian fluid, which we simulate using the method of multiparticle collision dynamics. The model reproduces periodic velocity and density pulse trains, traveling upstream in the microchannel, which are found in experiments conducted by Isa et al. [Phys. Rev. Lett. 102, 058302 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.058302]. We show that colloid-wall friction and the resultant force chains are crucial for the formation of these pulses. With an increasing colloid density, first solitary jams occur, which become periodic pulse trains at intermediate densities and unstable solitary pulses at high densities. We formulate a phenomenological continuum model and show how these spatiotemporal flow and density profiles can be understood as homoclinic and periodic orbits in traveling-wave equations.

Taylor line swimming in microchannels and cubic lattices of obstacles

Microorganisms naturally move in microstructured fluids. Using the simulation method of multi-particle collision dynamics, we study in two dimensions an undulatory Taylor line swimming in a microchannel and in a cubic lattice of obstacles, which represent simple forms of a microstructured environment. In the microchannel the Taylor line swims at an acute angle along a channel wall with a clearly enhanced swimming speed due to hydrodynamic interactions with the bounding wall. While in a dilute obstacle lattice swimming speed is also enhanced, a dense obstacle lattice gives rise to geometric swimming. This new type of swimming is characterized by a drastically increased swimming speed. Since the Taylor line has to fit into the free space of the obstacle lattice, the swimming speed is close to the phase velocity of the bending wave traveling along the Taylor line. While adjusting its swimming motion within the lattice, the Taylor line chooses a specific swimming direction, which we classify by a lattice vector. When plotting the swimming velocity versus the magnitude of the lattice vector, all our data collapse on a single master curve. Finally, we also report more complex trajectories within the obstacle lattice.