Mesoscale Hydrodynamic Simulations Research Articles

Hydrodynamic Anisotropy of Depletion in Nonequilibrium.

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

A Universal Chemotactic Targeted Delivery Strategy for Inflammatory Diseases.

Above 50% of deaths can be attributed to chronic inflammatory diseases; thus, the construction of drug delivery systems based on effective interaction of inflammatory factors with chemotactic nanoparticles is meaningful. Herein, a zwitterion-based artificial chemotactic nanomotor is proposed for universal precise targeting strategy in vivo, where the high level of reactive oxygen species (ROS) and inducible nitric oxide synthase (iNOS) in inflammatory sites are used as a chemoattractant. Multidimensional static models, dynamic models, and in vivo models are established to evaluate chemotactic performance. The results show that the upregulated ROS and iNOS can induce the chemotaxis of nanomotors to diseased tissues in inflammation-related disease models. Further, mesoscale hydrodynamics simulations are performed to explain the chemotactic behavior of the nanomotors. Such a chemotactic delivery strategy is expected to improve delivery efficiency and may be applicable to a variety of inflammatory diseases.

Alignment and propulsion of squirmer pusher-puller dumbbells.

The properties of microswimmer dumbbells composed of pusher-puller pairs are investigated by mesoscale hydrodynamic simulations employing the multiparticle collision dynamics approach for the fluid. An individual microswimmer is represented by a squirmer, and various active-stress combinations in a dumbbell are considered. The squirmers are connected by a bond, which does not impose any geometrical restriction on the individual rotational motion. Our simulations reveal a strong influence of the squirmers' flow fields on the orientation of their propulsion directions, their fluctuations, and the swimming behavior of a dumbbell. The properties of pusher-puller pairs with an equal magnitude of the active stresses depend only weakly on the stress magnitude. This is similar to dumbbells of microswimmers without hydrodynamic interactions. However, for non-equal stress magnitudes, the active stress implies strong orientational correlations of the swimmers' propulsion directions with respect to each other, as well as the bond vector. The orientational coupling is most pronounced for pairs with large differences in the active-stress magnitude. The alignment of the squirmers' propulsion directions with respect to each other is preferentially orthogonal in dumbbells with a strong pusher and weak puller, and antiparallel in the opposite case when the puller dominates. These strong correlations affect the active motion of dumbbells, which is faster for strong pushers and slower for strong pullers.

Multi-ciliated microswimmers\u2013metachronal coordination and helical swimming

The dynamics and motion of multi-ciliated microswimmers with a spherical body and a small number N (with 5< N < 60) of cilia with length comparable to the body radius, is investigated by mesoscale hydrodynamics simulations. A metachronal wave is imposed for the cilia beat, for which the wave vector has both a longitudinal and a latitudinal component. The dynamics and motion is characterized by the swimming velocity, its variation over the beat cycle, the spinning velocity around the main body axis, as well as the parameters of the helical trajectory. Our simulation results show that the microswimmer motion strongly depends on the latitudinal wave number and the longitudinal phase lag. The microswimmers are found to swim smoothly and usually spin around their own axis. Chirality of the metachronal beat pattern generically generates helical trajectories. In most cases, the helices are thin and stretched, i.e., the helix radius is about an order of magnitude smaller than the pitch. The rotational diffusion of the microswimmer is significantly smaller than the passive rotational diffusion of the body alone, which indicates that the extended cilia contribute strongly to the hydrodynamic radius. The swimming velocity is found to increase with the cilia number N with a slightly sublinear power law, consistent with the behavior expected from the dependence of the transport velocity of planar cilia arrays on the cilia separation.Graphic abstract

Flagellar arrangements in elongated peritrichous bacteria: bundle formation and swimming properties

The surface distribution of flagella in peritrichous bacterial cells has been traditionally assumed to be random. Recently, the presence of a regular grid-like pattern of basal bodies has been suggested. Experimentally, the manipulation of the anchoring points of flagella in the cell membrane is difficult, and thus, elucidation of the consequences of a particular pattern on bacterial locomotion is challenging. We analyze the bundle formation process and swimming properties of Bacillus subtilis-like cells considering random, helical, and ring-like arrangements of flagella by means of mesoscale hydrodynamics simulations. Helical and ring patterns preferentially yield configurations with a single bundle, whereas configurations with no clear bundles are most likely for random anchoring. For any type of pattern, there is an almost equally low probability to form V-shaped bundle configurations with at least two bundles. Variation of the flagellum length yields a clear preference for a single major bundle in helical and ring patterns as soon as the flagellum length exceeds the body length. The average swimming speed of cells with a single or two bundles is rather similar, and approximately 50% larger than that of cells of other types of flagellar organization. Considering the various anchoring patterns, rings yield the smallest average swimming speed independent of the type of bundle, followed by helical arrangements, and largest speeds are observed for random anchoring. Hence, a regular pattern provides no advantage in terms of swimming speed compared to random anchoring of flagella, but yields more likely single-bundle configurations.Graphic abstract

Flow driven transitions of polyelectrolytes

The nonequilibrium properties of uniformly charged linear polymers in the presence of explicit counterions under shear flow are studied by coarse-grained mesoscale hydrodynamics simulations. The conformational properties of the polyelectrolyte (PE) are quantified by the gyration tensor, the distribution of the end-to-end distance, and alignment with the flow, which display rather universal behavior for small and moderate electrostatic interaction strengths in the regime of condensed counterions. In the limit of strong counterion condensation, shear flow leads to a globule-coil transition and polymer stretching, associated with an increase of the effective PE charge. The polyelectrolytes exhibit a pronounced tumbling motion with cyclic stretched and collapsed conformations. The average tumbling-time period decreases with increasing shear rate by a power-law with the exponent −2/3 for PEs in the coiled state. The tumbling time exhibits a plateaulike regime over nearly a decade of shear rates for PEs in the globular state. In addition, we identify various characteristic PE structures under flow in the globule and coil limits determined by the condensed counterions.

Rheotaxis of spheroidal squirmers in microchannel flow: Interplay of shape, hydrodynamics, active stress, and thermal fluctuations

The authors perform mesoscale hydrodynamics simulations of spheroidal squirmers and show an enhanced wall and center depletion, and alignment of the propulsion direction parallel to the flow, which they interpret as a preferred downstream swimming for all active stresses,

Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures.

Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer–polymer () and oligomer–gel () systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel–oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz–Slyozov–Wagner (LSW) law . Our work allows for rational design of polymer/gel–oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.

Enhanced Rotational Motion of Spherical Squirmer in Polymer Solutions.

The rotational diffusive motion of a self-propelled, attractive spherical colloid immersed in a solution of self-avoiding polymers is studied by mesoscale hydrodynamic simulations. A drastic enhancement of the rotational diffusion by more than an order of magnitude in the presence of activity is obtained. The amplification is a consequence of two effects, a decrease of the amount of adsorbed polymers by active motion and an asymmetric encounter with polymers on the squirmer surface, which yields an additional torque and random noise for the rotational motion. Our simulations suggest a way to control the rotational dynamics of squirmer-type microswimmers by the degree of polymer adsorption and system heterogeneity.

Hydrodynamic interactions in squirmer dumbbells: active stress-induced alignment and locomotion.

Hydrodynamic interactions are fundamental for the dynamics of swimming self-propelled particles. Specifically, bonds between microswimmers enforce permanent spatial proximity and, thus, enhance emergent correlations by microswimmer-specific flow fields. We employ the squirmer model to study the swimming behavior of microswimmer dumbbells by mesoscale hydrodynamic simulations, where the squirmers' rotational motion is geometrically unrestricted. An important aspect of the applied particle-based simulation approach-the multiparticle collision dynamics method-is the intrinsic account for thermal fluctuations. We find a strong effect of active stress on the motility of dumbbells. In particular, pairs of strong pullers exhibit orders of magnitude smaller swimming efficiency than pairs of pushers. This is a consequence of the inherent thermal fluctuations in combination with the strong coupling of the squirmers' rotational motion, which implies non-exponentially decaying auto- and cross-correlation functions of the propulsion directions, and active stress-dependent characteristic decay times. As a consequence, specific stationary-state relative alignments of the squirmer propulsion directions emerge, where pullers are preferentially aligned in an antiparallel manner along the bond vector, whereas pushers are preferentially aligned normal to the bond vector with a relative angle of approximately 60° at weak active stress, and one of the propulsion directions is aligned with the bond at strong active stress. The distinct differences between dumbbells comprised of pusher or pullers suggest means to control microswimmer assemblies for future microbot applications.

Wall entrapment of peritrichous bacteria: a mesoscale hydrodynamics simulation study.

Microswimmers such as E. coli bacteria accumulate and exhibit an intriguing dynamics near walls, governed by hydrodynamic and steric interactions. Insight into the underlying mechanisms and predominant interactions demand a detailed characterization of the entrapment process. We employ a mesoscale hydrodynamics simulation approach to study entrapment of an E. coli-type cell at a no-slip wall. The cell is modeled by a spherocylindrical body with several explicit helical flagella. Three stages of the entrapment process can be distinguished: the approaching regime, where a cell swims toward a wall on a nearly straight trajectory; a scattering regime, where the cell touches the wall and reorients; and a surface-swimming regime. Our simulations show that steric interactions may dominate the entrapment process, yet, hydrodynamic interactions slow down the adsorption dynamics close to the boundary and imply a circular motion on the wall. The locomotion of the cell is characterized by a strong wobbling dynamics, with cells preferentially pointing toward the wall during surface swimming.

Role of Hydrodynamic Interactions in the Deformation of Star Polymers in Poiseuille Flow

Stretching polymer in fluid flow is a vital process for studying and utilizing the physical properties of these molecules, such as DNA linearization in nanofluidic channels. We studied the role of hydrodynamic interactions (HIs) in stretching a free star polymer in Poiseuille flow through a tube using mesoscale hydrodynamic simulations. As increasing the flow strength, star polymers migrate toward the centerline of tube due to HIs, whereas toward the tube wall in the absence of HIs. By analyzing the end monomer distribution and the perturbed flow around the star polymer, we found that the polymer acts like a shield against the flow, leading to additional hydrodynamic drag forces that compress the arm chains in the front of the star center toward the tube axis and lift the arm chains at the back toward the tube wall. The balanced hydrodynamic forces freeze the polymer into a trumpet structure, where the arm chains maintain a steady strongly stretched state at high flow strength. In contrast, the polymer displays remarkably large conformational change when switching off HIs. Our simulation results explained the coupling between HIs and the structure of star polymers in Poiseuille flow.

Microfluidic Pump Driven by Anisotropic Phoresis

Fluid flow along microchannels can be induced by keeping opposite walls at different temperatures, and placing elongated tilted pillars inside the channel. The driving force for this fluid motion arises from the anisotropic thermophoretic effect of the elongated pillars that generates a force parallel to the walls, and perpendicular to the temperature gradient. The force is not determined by the thermophilic or thermophobic character of the obstacle surface, but by the geometry and the thermophoretic anisotropy of the obstacle. Via mesoscale hydrodynamic simulations, we investigate the pumping properties of the device as a function of the channel geometry, and pillar surface properties. Applications as fluidic mixers, and fluid alternators are also outlined, together with the potential use of all these devices to harvest waste heat energy. Furthermore, similar devices can be also built employing diffusiophoresis or electrophoresis.

Sperm motility in modulated microchannels

Sperm cells swim through the fluid by a periodic wave-like beating of their flagellum. At low Reynolds numbers and in confinement, the directed motion of sperm and other microswimmers is strongly influenced by steric and hydrodynamic wall interactions. We model sperm motility in mesoscale hydrodynamics simulations by imposing a planar traveling bending wave along the flagellum. Sperm are simulated swimming in curved, straight, shallow and zigzag-shaped microchannels. Changes in the sidewall modulations and the imposed beat pattern allow the identification of a strong dependence of the surface attraction on the beat-shape envelope of the sperm cell. For swimming in zigzag microchannels, the deflection-angle distribution at sharp corners is calculated and found to be in good agreement with recent microfluidic experiments. The simulations reveal a strong dependence of the deflection angle on the orientation of the beat plane with respect to the channel sidewall, and thus deepen the understanding of sperm navigation under strong confinement. Detachment of sperm, while swimming along curved walls, is dominated by the change of beat-plane orientation. Therefore, either the emergence of a nonplanar component of the flagellar beat with increasing wavelength or the strong confinement in shallow channels drastically increases wall attraction. Our simulation results reveal a consistent picture of passive sperm guidance that is dominated by the steric interactions of the beat pattern with the nearby surfaces.

Individual circular polyelectrolytes under shear flow

Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics.

Multiscale modeling of shock wave localization in porous energetic material

Shock wave interactions with defects, such as pores, are known to play a key role in the chemical initiation of energetic materials. The shock response of hexanitrostilbene is studied through a combination of large-scale reactive molecular dynamics and mesoscale hydrodynamic simulations. In order to extend our simulation capability at the mesoscale to include weak shock conditions ($&lt;6$ GPa), atomistic simulations of pore collapse are used to define a strain-rate-dependent strength model. Comparing these simulation methods allows us to impose physically reasonable constraints on the mesoscale model parameters. In doing so, we have been able to study shock waves interacting with pores as a function of this viscoplastic material response. We find that the pore collapse behavior of weak shocks is characteristically different than that of strong shocks.

Shape and Diffusion of Circular Polyelectrolytes in Salt-Free Dilute Solutions and Comparison with Linear Polyelectrolytes

The shape and diffusion of circular polyelectrolytes in salt-free dilute solutions are investigated over a large range of the Bjerrum length lB by mesoscale hydrodynamic simulations, where lB characterizes the strength of electrostatic interactions (EIs). A comprehensive comparison of linear and circular polyelectrolytes is also made to gain a deep understanding of the effects of topological constraints on the conformational and dynamical properties. As lB increases, counterions become increasingly important due to their condensations on the polyelectrolyte backbone. The shape of a circular polyelectrolyte changes from a prolate coil to an oblate ring at small lB, then to a prolate coil at intermediate lB, and finally to a dense coil at large lB; in contrast, the shape of a linear polyelectrolyte changes from a prolate coil to a rod, then to a prolate coil, and finally to a dense coil. By switching on/off hydrodynamic interactions (HIs), the simulations clarify the complex coupling effects of hydrodynamic...

Solvent Induced Inversion of Core-Shell Microgels.

The morphology of core-shell microgels under different swelling conditions and as a function of the core-shell thickness ratio is systematically characterized by mesoscale hydrodynamic simulations. With increasing hydrophobic interaction of the shell polymers, we observe drastic morphological changes from a core-shell structure to an inverted microgel, where the core is turned to the outside, or a microgel with a patchy surface of core polymers directly exposed to the environment. We establish a phase diagram of the various morphologies. Moreover, we characterize the polymer and microgel conformations. For sufficiently thick shells, the changes of the shell size upon increasing hydrophobic interactions are well described by the Flory-Rehner theory. Additionally, this theory provides a critical line in the phase diagram separating core-shell structures from the distinct two other phases. The appearing new phases provide a novel route to nano- and microscale functionalized materials.

Anisotropic thermophoresis.

Colloidal migration in a temperature gradient is referred to as thermophoresis. In contrast to particles with a spherical shape, we show that elongated colloids may have a thermophoretic response that varies with the colloid orientation. Remarkably, this can translate into a non-vanishing thermophoretic force in the direction perpendicular to the temperature gradient. Opposite to the friction force, the thermophoretic force of a rod oriented with the temperature gradient can be larger or smaller than when oriented perpendicular to it. The precise anisotropic thermophoretic behavior clearly depends on the colloidal rod aspect ratio, and also on its surface details, which provides an interesting tunability to the devices constructed based on this principle. By means of mesoscale hydrodynamic simulations, we characterize this effect for different types of rod-like colloids.

Sorting cells by their dynamical properties.

Recent advances in cell sorting aim at the development of novel methods that are sensitive to various mechanical properties of cells. Microfluidic technologies have a great potential for cell sorting; however, the design of many micro-devices is based on theories developed for rigid spherical particles with size as a separation parameter. Clearly, most bioparticles are non-spherical and deformable and therefore exhibit a much more intricate behavior in fluid flow than rigid spheres. Here, we demonstrate the use of cells’ mechanical and dynamical properties as biomarkers for separation by employing a combination of mesoscale hydrodynamic simulations and microfluidic experiments. The dynamic behavior of red blood cells (RBCs) within deterministic lateral displacement (DLD) devices is investigated for different device geometries and viscosity contrasts between the intra-cellular fluid and suspending medium. We find that the viscosity contrast and associated cell dynamics clearly determine the RBC trajectory through a DLD device. Simulation results compare well to experiments and provide new insights into the physical mechanisms which govern the sorting of non-spherical and deformable cells in DLD devices. Finally, we discuss the implications of cell dynamics for sorting schemes based on properties other than cell size, such as mechanics and morphology.