Role Of Hydrodynamic Interactions Research Articles

Multiflagellate Swimming Controlled by Hydrodynamic Interactions.

Many eukaryotic microorganisms propelled by multiple flagella can swim very rapidly with distinct gaits. Here, we model a three-dimensional mutiflagellate swimmer, resembling the microalgae. When the flagella are actuated synchronously, the swimming efficiency can be enhanced or reduced by interflagella hydrodynamic interactions (HIs), determined by the intrinsic tilting angle of the flagella. The asynchronous gait with a phase difference between neighboring flagella can reduce oscillatory motion via the basal mechanical coupling. In the presence of a spherical body, simulations taking into account the flagella-body interactions reveal the advantage of anterior configuration compared with posterior configuration, where in the latter case an optimal flagella number arises. Apart from understanding the role of HIs in the multiflagellate microorganisms, this work could also guide laboratory fabrications of novel microswimmers.

Emergence of cooperative particle dynamics in quasi-two-dimensional glass-forming colloidal suspensions

As the concentration of particles in a glass-forming liquid increases, their dynamics slow down significantly, displaying solid-like behavior. This behavior is primarily attributed to cage formation, wherein particles are trapped by their neighbors. However, the particle dynamics near the onset of cage formation remain limitedly understood. In this study, we systematically investigated the dynamics of particles in a quasi-two-dimensional glass-forming colloidal suspension using a particle-level simulation. We utilized the “raspberry” model with a hybrid simulation approach. This approach combined lattice Boltzmann and molecular dynamics schemes for elucidating hydrodynamically interacting densely packed colloidal suspensions, with an area packing fraction of 0.45 ≤ ϕ ≤ 0.85. At a quiescent condition where particles underwent thermal motion, the string-like movements of particles became pronounced as ϕ increased. The hydrodynamic interactions between these particles were effective up to ϕ = 0.6, wherein the string-like motion first appeared, but were mostly screened at higher ϕ values. Furthermore, we extended our analysis by imposing a small probing force, locally applied to the suspensions. The most significant response occurred at ϕ = 0.6, where particles moved cooperatively during the cage formation process, similar to the experimental results of Li et al. [Nature 587, 225–229 (2020)]. By linking particle behaviors in two different scenarios, our study enhances our understanding of the emergence of highly cooperative particle movement and sheds light on the role of hydrodynamic interactions in glass-forming colloidal suspensions.

Impact of Inverse Squeezing Flow on the Self-Assembly of Oppositely Charged Colloidal Particles under Electric Field

Hydrodynamic interactions (HIs) play a critical role in the self-organization of colloidal suspensions and biological solutions. However, their roles have remained elusive particularly for charged soft matter systems. Here we consider the role of HIs in the self-assembly of oppositely charged colloidal particles, which is a promising candidate for electrical tunable soft materials. We employ the fluid particle dynamics method to consider many-body HIs and the coupling between the colloid, ion, and fluid motions. We find that, under a constant electric field, oppositely charged colloidal particles form clusters and percolate into a gel network, unlike bundlelike aggregates aligned in the field direction observed by Brownian dynamics simulations neglecting HIs. We reveal that the cluster-forming tendency originates from the incompressibility-induced "inverse squeezing flow" effect that dramatically slows down the disaggregation of attached colloids. Our findings indicate that the HI selects a unique kinetic pathway to the nonequilibrium colloidal self-assembly.

The role of hydrodynamic interactions on the aggregation kinetics of sedimenting colloidal particles.

The aggregation kinetics of sedimenting colloidal particles under fully destabilized conditions has been investigated over a wide range of particle volume fractions (Φ) and Péclet numbers (Pe) using the recent PSE algorithm implementing the Rotne-Prager-Yamakawa (RPY) approximation for long-range Hydrodynamic Interactions (HI). Fast Lubrication Dynamics (FLD) and simple Brownian Dynamics (BD) methods have also been employed to assess the importance of long range hydrodynamic interactions on the resulting dynamics. It has been observed that long-range hydrodynamic interactions are essential to capture the fast aggregation rates induced by the increase in sedimentation rate of clusters with increasing mass, which manifests with an explosive-like cluster growth after a given induction time. On the contrary, simulations employing only short-range hydrodynamic interactions (such as FLD) and BD (which neglects completely hydrodynamic interactions) are incapable of predicting this very rapid kinetics, because sedimentation simply leads to all particles and clusters moving vertically with identical velocity. It has been observed that at high volume fractions and low Pe values, a gel point can be formed and a phase diagram predicting when gelation is reached has been obtained. It was also observed that, as Pe increases, the anisotropy of the resulting clusters decreases, suggesting that denser clusters with spherical-like morphology are formed due to cluster breakage and restructuring. We can conclude that long-range hydrodynamic effects are of crucial importance in understanding the aggregation dynamics of settling clusters, revealing important features of the complex interplay between sedimentation, and colloidal interactions.

Long-time self-diffusion in quasi-two-dimensional colloidal fluids of paramagnetic particles.

The effect of hydrodynamic interactions (HI) on the long-time self-diffusion in quasi-two-dimensional fluids of paramagnetic colloidal particles is investigated using a combination of experiments and Brownian dynamics (BD) simulations. In the BD simulations, the direct interactions (DI) between the particles consist of a short-ranged repulsive part and a long-ranged part that is proportional to 1/r^{3}, with r the interparticle distance. By studying the equation of state, the simulations allow for the identification of the regime where the properties of the fluid are fully controlled by the long-ranged interactions, and the thermodynamic state solely depends on the dimensionless interaction strength Γ. In this regime, the radial distribution functions from the simulations are in quantitative agreement with those from the experiments for different fluid area fractions. This agreement confirms that the DI in the experiments and simulations are identical, which thus allows us to isolate the role of HI, as these are not taken into account in the BD simulations. Experiment and simulation fall onto a master curve with respect to the Γ dependence of D_{L}^{★}=D_{L}/(D_{0}Γ^{1/2}), with D_{0} the self-diffusion coefficient at infinite dilution and D_{L} the long-time self-diffusion coefficient. Our results thus show that, although HI affect the short-time self-diffusion, for a quasi-two-dimensional system with 1/r^{3} long-ranged DI, the reduced quantity D_{L}^{★} is effectively not affected by HI. Interestingly, this is in agreement with prior work on quasi-two-dimensional colloidal hard spheres.

Role of hydrodynamic interactions in chemotaxis of bacterial populations

How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this paper, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a hybrid computational model that incorporates hydrodynamic interactions and adding components from a classical velocity jump model. It is shown that by including hydrodynamic interactions, a suspension with a low initial volume fraction can exhibit locally high concentrations in bacterial aggregates. Also, it is shown that hydrodynamic interactions enhance the merging of the small aggregates into larger ones and lead to qualitatively different aggregate behavior than possible with pure chemotaxis models. Namely, differences in the shape, number, and dynamics of these emergent clusters.

Complex dynamical interplay between solid particles and flow in driven granular suspensions

Granular materials immersed in a fluid are ubiquitous in daily life, industry, and nature. They include food processing, pastes, cosmetics, paints, concretes, cements, muds, wet sands, snows, landslides, and lava flow. They are known to exhibit a rich variety of complex rheological behavior, but the role of a fluid component in such behavior has remained poorly understood due to the nonlocal and many-body nature of hydrodynamic interactions between solid particles mediated by the fluid. We address this fundamental problem by comparing the microrheological response of athermal granular suspensions with and without hydrodynamic interactions to an externally driven probe particle by numerical simulations. We find that the presence of the fluid drastically increases the drag coefficient of the probe particle by more than one order of magnitude near the jamming transition. We reveal that this is a consequence of the nontrivial long-range nature of hydrodynamic interactions, which originates from unlimited cumulative transmission of near-field hydrodynamic interactions due to the incompressibility of both fluid and solid particles. Force chain formation of solid particles is dynamically coupled with hydrodynamic flow, leading to strong spatiotemporal fluctuations of flow pattern and nonlinear rheological response. Our study reveals essential roles of hydrodynamic interactions in complex rheological behavior of dense granular suspensions under an external drive.

Active microswimmers in a finite two dimensional trap: The role of hydrodynamic interaction.

We investigate the dynamics of two identical artificial active particles suspended in a free-standing fluid film with a trap of finite radius in an acoustic tweezer. In the two dimensional Oseen approximation, their hydrodynamic coupling is long ranged, which naturally raises the question as under what conditions they can simultaneously reside in the trap. We determine a critical value of the hydrodynamic coupling below which that happens and study the ensuing active pair dynamics inside the trap. For larger couplings, only one particle sits in the trap, while the other diffuses freely until it eventually replaces the particle in the trap. Such a mechanism repeats itself with a characteristic noise-dependent mean residence-retrapping time.

On the role of hydrodynamic interactions in the engineered-assembly of droplet ensembles

Droplets, as they flow inside a microchannel, interact hydrodynamically to result in spatio-temporal patterns. The nature of the interaction decides the type of collective behaviour observed. In this context, we study the application of droplet microfluidics in the area of complex-shape particle synthesis. We show how the dynamics of droplet motion, the steady-state characteristics, the short and long-range hydrodynamics, the dependence on inlet conditions etc. are all related to the features that characterize a device like the functionality (producing many shapes) and robustness (insensitivity to fluctuations). Two primary operating regimes are identified, one where long-range interactions are dominant and the other where they are short-range. In the former, the shapes formed by droplets are steady-state solutions to the governing equations, while in the latter they are a function of how the droplets enter the channel (frequency of entry). We show that identifying the inlet conditions for producing a particle of the desired shape requires the use of a systematic approach to design which involves solving an optimization problem (using genetic algorithms) to identify the optimal operating strategy. With the knowledge of the hydrodynamics between the droplets, we demonstrate how one can reduce the complexity of the design process. We also discuss the control strategies required if one were to realize the identified operating strategy experimentally.

The medium amplitude oscillatory shear of semidilute colloidal dispersions. Part II: Third harmonic stress contribution

In Paper I [J. W. Swan et al., J. Rheol. 58, 307–338 (2014)], we derived an exact theoretical description of medium amplitude oscillatory shear for a semidilute colloidal dispersion. Through solution of the Smoluchowski equation governing the spatial distribution of suspended particles in the semidilute limit, we calculated the stresses that arise from an oscillatory linear flow as an expansion in powers of the rate of deformation. Here, this is extended to calculation of the first departures from linearity in the first and third harmonics of the suspension stress driven by oscillatory deformation. The role of hydrodynamic interactions is investigated via the excluded-annulus model in which particles are given an impenetrable core with a radius larger than their hydrodynamic radius. The ratio of these length scales controls the strength of hydrodynamic interactions. The third harmonic of the suspension stress is predicted to be dominated by hydrodynamic stresses at high frequency, a result that is shown to be valid experimentally for the oscillatory shear response of concentrated near hard-sphere dispersions. The calculations anticipate recent experimental observations on model near hard-sphere colloidal dispersions, and quantitative agreement is demonstrated when the predictions are scaled appropriately to account for volume fraction effects. The first departures from linearity in harmonics of the suspension stress are separated into several material functions that are independent of the flow geometry. These functions are generated from detailed numerical solutions, while asymptotic analysis is shown to predict the values of these functions at high frequency. These exact calculations provide a basis for understanding the onset of nonlinear rheological behavior of colloidal suspensions under dynamic oscillatory flow.

The Role of Hydrodynamic Interactions in the Rate of Protein Folding

Hydrodynamic interactions (HI) affect the diffusivity of protein dynamics. However, a computationally quantitative assessment of its role in protein folding has been an under explored research field. A lack of HI in molecular dynamics simulations fails to capture the experimentally measured translational and rotational diffusion coefficients when HI is no longer negligible, such as inside a crowded cell. In our study, we incorporated hydrodynamic interactions into the equations of motion from the Brownian dynamics by computing the diffusion correlation matrices between each residue. We used a, structure-based model to investigate the folding of two well studied proteins: chymo-trypsin inhibitor 2 (CI2) and the Src Homology 3 (SH3) domain of alpha-spectrin.For both proteins, we observed that HI increases the folding rate varying from 50% to 5% depending on the free energy barrier height. Furthermore, we measured the diffusion throughout the stages of folding to relate HI effect to the structural differences of these two proteins. Lastly, we compared our simulation results with the folding rates predicted by the Free Energy Landscape Theory. Our theoretical calculations will allow us better develop a computational framework for protein folding in crowded cells.

Rectified motion in an asymmetric channel: the role of hydrodynamic interactions with walls.

Dynamics of a Brownian particle in an asymmetric microchannel that is subjected to an external oscillating force is numerically analyzed. In addition to the elastic collisions with the walls that are kind of short range interactions, the long range hydrodynamic influences of the walls have been considered in an approximate way. We demonstrate how the geometrical parameters of the channel change the rectified current of the particle. As a result of numerical calculations, we show that long range hydrodynamic interactions with walls decrease the efficiency of the Brownian ratchet.

The hydrodynamics of colloidal gelation.

Colloidal gels are formed during arrested phase separation. Sub-micron, mutually attractive particles aggregate to form a system spanning network with high interfacial area, far from equilibrium. Models for microstructural evolution during colloidal gelation have often struggled to match experimental results with long standing questions regarding the role of hydrodynamic interactions. In nearly all models, these interactions are neglected entirely. In the present work, we report simulations of gelation with and without hydrodynamic interactions between the suspended particles executed in HOOMD-blue. The disparities between these simulations are striking and mirror the experimental-theoretical mismatch in the literature. The hydrodynamic simulations agree with experimental observations, however. We explore a simple model of the competing transport processes in gelation that anticipates these disparities, and conclude that hydrodynamic forces are essential. Near the gel boundary, there exists a competition between compaction of individual aggregates which suppresses gelation and coagulation of aggregates which enhances it. The time scale for compaction is mildly slowed by hydrodynamic interactions, while the time scale for coagulation is greatly accelerated. This enhancement to coagulation leads to a shift in the gel boundary to lower strengths of attraction and lower particle concentrations when compared to models that neglect hydrodynamic interactions. Away from the gel boundary, differences in the nearest neighbor distribution and fractal dimension persist within gels produced by both simulation methods. This result necessitates a fundamental rethinking of how dynamic, discrete element models for gelation kinetics are developed as well as how collective hydrodynamic interactions influence the arrest of attractive colloidal dispersions.

良溶剂中环形高分子单链的结构与动力学性质的模拟研究

The conformational and dynamical properties of individual linear and ring polymers in good solution were studied by mesoscale simulations which combining multi-particle collision dynamics and molecular dynamics simulations. The excluded volume interactions play a more significant role for ring polymers than for linear polymers because of the smaller average distance among monomers of rings without ends. The ratio of mean-square radius of gyration between the linear and ring polymer with a same molecular weight in the presence of excluded volume interactions is 1.77, which is slightly smaller than the theoretical estimation (2) in theta solvents, indicating that ring polymers swell more in good solvents than their linear counterparts. Correspondingly, the ratio of diffusion coefficients between the ring and linear polymer was estimated as 1.10. The diffusion properties are dominated by the interplay between excluded volume interactions and hydrodynamic interactions. Furthermore, in order to elucidate the role of hydrodynamic interactions, we also compared these results with those without hydrodynamic interactions. The results showed that the diffusion coefficients with hydrodynamic interactions are larger than those without hydrodynamic interactions.

Motion transition of active filaments: rotation without hydrodynamic interactions.

We investigate the dynamics of an active semiflexible filament in a bead–rod model involving dynamically the hydrodynamic interaction (HI), active force, filament flexibility and viscous drag. We find that the filament can show three distinct types of motion, namely, translation, snaking and rotation, with the variation of the rigidity or active force. The transition from translation to snaking is continuous and mainly due to transverse instability, while the snaking–rotation transition is first-order like and shown to result from a type of symmetry breaking associated with the shape kinematics. Of particular interest, we find that HI is not necessary for the rotation or snaking motion, but can enlarge remarkably the parameter regions in which they can occur. Combining with local collisions, we show that, for the parameter region where HI is essential for the maintenance of rotation curvature of a single filament, HI is also essential for the emergence of collective vortexes. Thus, our findings provide new insights into the subtle role of HI in the formation of collective structures in active systems

Nonequilibrium Work Relations for Polymer Dynamics in Dilute Solutions

Equilibrium and nonequilibrium free energies of complex fluids are fundamental quantities that can be used to determine a wide array of system properties. Recently, we demonstrated the direct determination of the equilibrium free energy landscape and corresponding elasticity of polymer chains from work calculations in highly nonequilibrium fluid flows.1 In the present study, we further demonstrate the generality of this formalism by applying this method to polymeric systems driven by fluid flows with vorticity and for molecules with dominant intramolecular hydrodynamic interactions (HI). We employ Brownian dynamics simulations of double stranded DNA with fluctuating HI, and we analyze polymer dynamics and the resultant free energy calculations in the context of the nonequilibrium work relations. Furthermore, we investigate the role of HI on the work and housekeeping power required to maintain a polymer chain at a nonequilibrium steady-state in flow, and we consider the relationship between housekeeping po...

Single-file diffusion in periodic energy landscapes: The role of hydrodynamic interactions

We report on the dynamical properties of interacting colloids confined to one dimension and subjected to external periodic energy landscapes. We particularly focus on the influence of hydrodynamic interactions on the mean-square displacement. Using Brownian dynamics simulations, we study colloidal systems with two types of repulsive interparticle interactions, namely, Yukawa and superparamagnetic potentials. We find that in the homogeneous case, hydrodynamic interactions lead to an enhancement of the particle mobility and the mean-square displacement at long times scales as t(α), with α=1/2+ε and ε being a small correction. This correction, however, becomes much more important in the presence of an external field, which breaks the homogeneity of the particle distribution along the line and, therefore, promotes a richer dynamical scenario due to the hydrodynamical coupling among particles. We provide here the complete dynamical scenario in terms of the external potential parameters: amplitude and commensurability.

Effect of repulsive interactions on structure and rheology of sheared colloidal dispersions

A previously developed Smoluchowski theory for concentrated hard-sphere suspensions in shear flow is extended to study structure and rheology of colloidal suspensions with soft repulsive interactions. Accelerated Stokesian Dynamics simulations are carried out to provide insight and to enable direct comparison with theoretical predictions. The effect of extended range repulsive interactions is studied by considering repulsive interactions with different steepness, using identical potentials in simulation and theory, for varying shear rates characterized in dimensionless form as 0.1 ≤ Pe ≤ 100; here, Pe = 6πηa3/kbT is the ratio of hydrodynamic to Brownian forces and η is the fluid viscosity, is the shear rate, a is the particle radius and kbT is the thermal energy. Examples of predicted microstructures and the equivalent simulated results for hard-sphere suspensions at ϕ = 0.40 are also presented for comparison. The predicted pair distribution function is in good agreement with simulations before the onset of a shear-induced ordering transition in simulations of the soft colloids. The calculations of shear viscosity based on the predicted microstructure were also in general agreement with simulation results. The role of hydrodynamic interactions on flow-induced structures is discussed in the context of the proposed theory.

The Role of Hydrodynamic Interactions in Self-Organization of Biological Molecules

Self-organization is one of the most fundamental phenomena in biology. Elucidating the mechanisms of the self-assembly of biological molecules, such as protein folding/binding and formation of lipid bilayer membranes, have been a fascinating topic over decades in biological field. Hydrodynamic interactions (HIs) give rise to collective motions between molecules. Therefore, they may play an important role on dynamics of self-assembly. Although there are significant advances in theoretical and computational studies on thermodynamics and kinetics of self-assembling systems recent years, analysis on effects of HIs to the reactions are limited due to their high complexity. Here, by using a Brownian dynamics (BD) simulation technique, we evaluate the importance of HIs on kinetic of self-assembly in a set of examples, formation of lipid membrane and actin polymerization reaction. We first built coarse-grained models of lipid and actin monomer. A cluster of lipid molecules was represented by two particles, one is hydrophilic head group and the other is hydrophobic tail group, and attractive interaction between tail groups was applied. For actin polymerization system, each monomer was represented by two particles and an angle-dependent attractive interaction was applied to form long filaments. In BD simulations, the Rotne-Prager-Yamakawa tensor was used to account for HIs between particles. In the early stage of self-assembly, HIs between inter-monomer particles decelerated the association rate of monomers to form oligomers compared with that in the simulations without inter-monomer HIs in both systems. On the other hand, the HIs accelerate the reaction of oligomers to form a fully-assembled state or much longer polymers. This phenomenon could be explained by the Kirkwood-Riseman theory. Those results clearly suggest that HIs greatly affect kinetics of self-assembly reactions and considering the interactions is crucial for studying dynamics of biological systems.

Generic Conditions for Hydrodynamic Synchronization

Synchronization of actively oscillating organelles such as cilia and flagella facilitates self-propulsion of cells and pumping fluid in low Reynolds number environments. To understand the key mechanism behind synchronization induced by hydrodynamic interaction, we study a model of rigid-body rotors making fixed trajectories of arbitrary shape under driving forces that are arbitrary functions of the phase. For a wide class of geometries, we obtain the necessary and sufficient conditions for synchronization of a pair of rotors. We also find a novel synchronized pattern with an oscillating phase shift. Our results shed light on the role of hydrodynamic interactions in biological systems, and could help in developing efficient mixing and transport strategies in microfluidic devices.