Hydrodynamic Interactions Research Articles

Group cohesion and passive dynamics of a pair of inertial swimmers with three-dimensional hydrodynamic interactions.

When swimming animals form cohesive groups, they can reap several benefits. Our understanding of collective animal motion has traditionally been driven by models based on phenomenological behavioral rules, but more recent work has highlighted the critical importance of hydrodynamic interactions among a group of inertial swimmers. To study how hydrodynamic interactions affect group cohesion, we develop a three-dimensional, inviscid, far-field model of a swimmer. In a group of two model swimmers, we observe several dynamical phases, including following, divergence, collision, and cohesion. Our results illustrate when cohesive groups can passively form through hydrodynamic interactions alone, and when other action is needed to maintain cohesion. We find that misalignment between swimmers makes passive cohesion less likely; nevertheless, it is possible for a cohesive group to form through passive hydrodynamic interactions alone. We also find that the geometry of swimmers critically affects the group dynamics due to its role in how swimmers sample the velocity gradient of the flow.

Analysis of Macromolecular Size Distributions in Concentrated Solutions

AbstractThe solution state of macromolecules in concentrated solutions impacts fields ranging from cell biology, to colloid chemistry and engineering of protein pharmaceuticals. Dependent on the interplay between repulsive and weakly attractive forces, proteins may exhibit oligomerization, aggregation, crystallization, liquid‐liquid phase separation, or the formation of multiprotein complexes. The particle size‐distribution is a key characteristic, but difficult to determine when interparticle distances are on the order of their size and macromolecular motion is coupled through hydrodynamic interactions. Here we extend sedimentation velocity analytical ultracentrifugation to measure macromolecular size distributions under these conditions: We apply results from statistical fluid mechanics for the concentration‐dependence of hindered settling and diffusion, embedded in a mean‐field approximation that can resolve coupled sedimentation and diffusion processes of different sized species given experimental sedimentation data. This is combined with a description of transient optical aberrations from lensing in the refractive index gradients associated with sedimentation boundaries (Wiener skewing). We demonstrate this approach in the application to protein solutions with macromolecular volume fractions up to ≈10 %, for example, resolving monomers and dimers of albumin at 140 mg/ml. This enables size‐distribution analysis of proteins at concentrations of therapeutic antibody formations and close to physiological concentration in serum and cells.

Run-and-tumble motion of ellipsoidal microswimmers

A hallmark of bacteria is their so-called “run-and-tumble” motion and its variants, consisting of a sequence of linear directed “runs” and distinct rotation events that constantly alternate due to biochemical feedback. It plays a crucial role in the ability of bacteria to move through chemical gradients and has inspired a fundamental active particle model. Nevertheless, synthetic active particles generally do not exhibit run-and-tumble motion but rather active Brownian motion. We show in experiments that ellipsoidal thermophoretic Janus particles, propelling along their short axis, can yield run-and-reverse motion, i.e., where rotation events flip the direction of motion, even without feedback. Their hydrodynamic wall interactions under strong confinement give rise to an effective double-well potential for the declination of the short axis. The geometry-induced timescale separation of the in-plane rotational dynamics and noise-induced transitions in the potential then yield run-and-reverse motion. Published by the American Physical Society 2024

Physical mechanism reveals bacterial slowdown above a critical number of flagella.

Numerous studies have explored the link between bacterial swimming and the number of flagella, a distinguishing feature of motile multi-flagellated bacteria. We revisit this open question using augmented slender-body theory simulations, in which we resolve the full hydrodynamic interactions within a bundle of helical filaments rotating and translating in synchrony. Unlike previous studies, our model considers the full torque-speed relationship of the bacterial flagellar motor, revealing its significant impact on multi-flagellated swimming. Because the viscous load per motor decreases with the flagellar number, the bacterial flagellar motor transitions from the high-load to the low-load regime at a critical number of filaments, leading to bacterial slowdown as further flagella are added to the bundle. We explain the physical mechanism behind the observed slowdown as an interplay between the load-dependent generation of torque by the motor, and the load-reducing cooperativity between flagella, which consists of both hydrodynamic and non-hydrodynamic components. The theoretically predicted critical number of flagella is remarkably close to the values reported for the model organism Escherichia coli. Our model further predicts that the critical number of flagella increases with viscosity, suggesting that bacteria can enhance their swimming capacity by growing more flagella in more viscous environments, consistent with empirical observations.

Particulate fouling simulation in unit micropore using a hydrodynamically coupled Lagrangian framework

Predicting and mitigating pore clogging is challenging for the sustainable operation of water treatment systems. During transport and filtration through membrane micropores, buoyant contaminants in water gradually deposit on the surface, reducing the membrane's lifespan and performance, and sometimes completely blocking the pores. To alleviate the negative effects of fouling and to ensure sustainable operation, it is necessary to understand the fundamental mechanisms of fouling and to predict the probability of fouling formation under specific geometrical and material conditions. In this study, multiscale simulations are conducted to understand the fundamental mechanisms of particulate fouling at a microscopic level based on a Lagrangian framework incorporating inter-particle hydrodynamic interactions. We investigate both dead-end and cross-flow filtration, considering the direction of the feed stream relative to the unit micropore. The results elucidate the quantitative background of fouling history, which agrees with experimental findings. Depending on the level of hydrodynamic stress specific to the clog location and the nature of inter-particle interactions, deformation or resuspension of the clog is observed, competing with deposition, which leads to a two-way fouling history. Dominant deposition leads to micropore clogging, and to the best of the authors' knowledge, this is the first study to observe complete blockage and subsequent reopening. With this approach, the microscopic backgrounds between permanent and temporary pore blocking are distinguished. This study is expected to provide useful insights for controlling operational conditions to optimize anti-fouling performance in the transport and filtration through micropores.

Relative size matters: Spawning substrate roughness size and spacing affect egg dislodgement and retention in the benthos

AbstractThe consequences of hydrodynamic effects on survival of embryonic benthic organisms remain unknown. This is because the interaction of hydrodynamics and substrate roughness is complex, but it can be conceptualized in two dimensions by roughness flow regimes (isolated, wake interference, and skimming flow) or roughness types (k‐ and d‐type). We examined the effect of different roughness flow regimes/roughness types and roughness heights (k) on the dislodgement of walleye (Sander vitreus) eggs (2 mm diameter, ⌀) using a wall jet apparatus. We expected that lower wall shear stress (τw) would be required for dislodgement in more‐exposed/less‐sheltered roughness type/flow regimes (i.e., k‐type/isolated roughness flow) and when k ≤ ⌀. Surprisingly, the opposite was found, indicating that other mechanism(s) are also responsible for egg dislodgement on these rough surfaces. Hydrodynamic sheltering occurred when flow was directed over exposed eggs (k ≤ ⌀) adjacent to roughness elements effectively increasing their width, and thus requiring higher τw for rolling and then ejection. When k > ⌀, eggs dislodgement likely occurred via the lower pressure in the eddies recirculating in the groove width between roughness elements, rather than due to τw. These results indicate the relevance of heterogeneous sorting and sizing of substrate elements to provide suitable spawning habitats in benthic environments.

Dispersion and particle pressure in sedimenting suspensions with hydrodynamic interactions and particle inertia

Particle inertia is a feature of suspension dynamics that is often neglected. However, its neglect changes the order of the governing equations of particle motion. In this work, we examine the impact of the inertia of particles over their velocity fluctuations and the resulting stresses. In order to observe effects of particle inertia, we consider dusty-gas suspensions of spherical weakly Brownian microparticles sedimenting in a Newtonian fluid at low Reynolds numbers. We first investigate the motion of a single spherical particle. The simulations for this simple case allow us to define the appropriate physical parameters of the flow and to validate the numerical calculation of velocity statistics over a range of Péclet and Stokes numbers. Next, we perform Langevin dynamics simulations with periodic boundary conditions to integrate the equations governing the translational and rotational motions of N hydrodynamically interacting particles suspended in the viscous fluid. The first aim of this paper is to examine the behavior of the velocity variance of inertial particles, with small fluctuations produced by Brownian motion at the moderate Péclet numbers. The interplay between mild Brownian forces and hydrodynamic interactions decreases the anisotropy of velocity fluctuations observed in non-Brownian suspensions (Pe≫1) of sedimenting particles. The simulation results suggest that particle inertia attenuates the magnitude of velocity fluctuations produced by both Brownian motion and viscous hydrodynamic interactions. Additionally, we study the long-time behavior of the velocity fluctuations by calculating their autocorrelation functions and the particle diffusivities. The numerical simulations show clear evidence of particle pressure arising from the flow disturbance produced by hydrodynamic interactions in a suspension. From the particle velocity variance obtained in the present numerical simulations, we propose a simple model for particle-phase pressure as a linear function of the particle volume fraction ϕ⩽5%, which is usually a closure quantity required in models of more complex particulate systems such as fluidized beds.

Generalized Langevin dynamics for single beads in linear elastic networks

We derive generalized Langevin equations (GLEs) for single beads in linear elastic networks. In particular, the derivations of the GLEs are conducted without employing normal modes, resulting in two distinct representations in terms of resistance and mobility kernels. The fluctuation-dissipation relations are also confirmed for both GLEs. Subsequently, we demonstrate that these two representations are interconnected via Laplace transforms. Furthermore, another GLE is derived by utilizing a projection operator method, and it is shown that the equation obtained through the projection scheme is consistent with the GLE with the resistance kernel. As simple examples, the general theory is applied to the Rouse model and the ring polymer, where the GLEs with the resistance and mobility kernels are explicitly derived for arbitrary positions of the tagged bead in these models. Finally, the GLE with the mobility kernel is also derived for the elastic network with hydrodynamic interactions under the pre-averaging approximation. ©2024 American Physical Society 2024 American Physical Society

Collective swimming pattern and synchronization of fish pairs (Gobiocypris rarus) in response to flow with different velocities.

Collective behaviors in moving fish originate from social interactions, which are thought to be driven by beneficial factors, such as predator avoidance and reduced energy expenditure. Despite numerical simulations and physical experiments aiming at the hydrodynamic mechanisms and interaction rules, how shoaling is influenced by flow velocity and group size is still only partially understood. In this study, spatial distributions, kinematics, and synchronization states between pairs (smallest subsystem of a shoal) of Gobiocypris rarus were investigated in a recirculating swim tunnel with increasing flow velocities from 0.1 to 0.5 m/s (Ucrit = 0.6 m/s). Tests of single fish were also conducted as the control group. The results of spatial distributions showed that fish pairs preferred to swim in the side-by-side configuration under high flows, while under low flows the neighboring fish's positions were more uniformly distributed around the focal fish in the transverse direction. Kinematic analysis revealed that fish pairs adopted similar tail beats (i.e., frequency and Strouhal number) as single fish in low flows, while in high flows both the frequency and Strouhal number of fish pairs were slightly lower. Moreover, the synchronization rates of fish pairs were found to increase with flow velocities, suggesting that synchronized swimming may be beneficial, especially in high flows.

Numerical investigation of the effects of short-crested irregular waves on the performance of a floating power capture platform

This paper presents a novel power capture platform concept consisting of a semi-submersible platform and multiple point-absorber wave energy converters (WECs). The primary objective of the current study is to investigate the dynamic behavior of the power capture platform under short-crested irregular wave conditions. A spreading function is used to modify the JONSWAP spectrum into a wave spectrum that accounts for both frequency and direction. To ensure the reliability of the numerical analysis, three-dimensional potential flow theory and boundary element method (BEM) are utilized to perform mesh convergence analysis and hydrodynamic validation of the platform and WEC models. Time-domain simulations are conducted to evaluate the effects of wave directionality on the platform motion, mooring line tension, and power absorption of the WEC array. In addition, three models, “single WEC”, “WEC array” and “fixed power capture platform” are defined. The influence of hydrodynamic interactions and platform motion are predicted by comparing the power absorption of individual WEC, WEC row, and WEC array among these models. The results show that the effects of wave directionality on the performance of the floating power capture platform cannot be ignored. The findings of this study may provide some insights into the design of power capture platforms. Meanwhile, it is recommended to determine the wave characteristics of the target operational area in advance, in order to find out the optimal design for system stability and power absorption.

The Countoscope: Measuring Self and Collective Dynamics without Trajectories

Driven by physical questions pertaining to quantifying particle dynamics, microscopy can now resolve complex systems at the single-particle level, from cellular organisms to individual ions. Yet, available analysis techniques face challenges reconstructing trajectories in dense and heterogeneous systems where accurately labeling particles is difficult. Furthermore, the inescapable finite field of view of experiments hinders the measurement of collective effects. Inspired by Smoluchowski, we introduce a broadly applicable analysis technique that probes dynamics of interacting particle suspensions based on a remarkably simple principle: counting particles in finite observation boxes. Using colloidal experiments, advanced simulations, and theory, we first demonstrate that statistical properties of fluctuating counts can be used to determine self-diffusion coefficients, so alleviating the hurdles associated with trajectory reconstruction. We also provide a recipe for practically extracting the diffusion coefficient from experimental data at variable particle densities, which is sensitive to steric and hydrodynamic interactions. Remarkably, by increasing the observation box size, counting naturally enables the study of collective dynamics in dense suspensions. Using our novel analysis of particle counts, we uncover a surprising enhancement of collective behavior due to hydrodynamics as well as a new length scale which can be connected with hyperuniform structure. Our counting framework, the “countoscope,” thus enables efficient measurements of self and collective dynamics in dense suspensions and opens the way to quantifying dynamics and identifying novel physical mechanisms in diverse complex systems where single particles can be resolved. Published by the American Physical Society 2024

Fluid mediated communication among flexible micro-posts in chemically reactive solutions.

Communication in biological systems typically involves enzymatic reactions that occur within fluids confined between the soft, elastic walls of bio-channels and chambers. Through the inherent transformation of chemical to mechanical energy, the fluids can be driven to flow within the confined domains. Through fluid-structure interactions, the confining walls in turn are deformed by and affect this fluid flow. Imbuing synthetic materials with analogous feedback among chemo-mechanical, hydrodynamic and fluid-structure interactions could enable materials to perform self-driven communication and self-regulation. Herein, we develop computational models to determine how chemo-hydro-mechanical feedback affects interactions in biomimetic arrays of chemically active and passive micro-posts anchored in fluid-filled chambers. Once activated, the enzymatic reactions trigger the latter feedback, which generates a surprising variety of long-range, cooperative motion, including self-oscillations and non-reciprocal interactions, which are vital for propagating coherent, directional signals over net distances in fluids. In particular, the array propagates a distinct message; each post interprets the message; and the system responds with a specific mode of organized, collective behavior. This level of autonomous remote control is relatively rare in synthetic systems, particularly as this system operates without external electronics or power sources and only requires the addition of chemical reactants to function.

Wave-to-wire modelling and hydraulic PTO optimization of a dense point absorber WEC array

We investigate the hydrodynamic interactions and power extraction efficiency of a dense array of Point Absorber (PA) Wave Energy Converters (WECs) clustered around the fixed pillar of a wind turbine –the Ocean Grazer device– with a standard hydraulic Power Take-Off (PTO) system. Using potential flow theory, a detailed wave-to-wire model is developed in WEC-Sim with four distinct hydraulic PTO designs: i) Multi PTO-with individual hydraulic PTO systems for each buoy, ii) Shared PTO V1-with a unified PTO system for the entire array, iii) Shared PTO V2-with the accumulator volume split into two segments, and iv) Shared PTO V3-with four strategically distributed segments. Key parameters such as the diameter of the hydraulic pistons, volume and pre-charged pressure of the high-pressure accumulators, hydraulic motor displacement and the speed of the electric generator are optimized with a genetic algorithm and a parametric analysis across various sea states. The results highlight that strategically allocating the accumulators across the floaters of a dense WEC array can yield significantly higher power production and should be considered at the early design stages.

Enhanced Diffusion and Non-Gaussian Displacements of Colloids in Quasi-2D Suspensions of Motile Bacteria

In the real world, active agents interact with surrounding passive objects, thus introducing additional degrees of complexity. The relative contributions of far-field hydrodynamic and near-field contact interactions to the anomalous diffusion of passive particles in suspensions of active swimmers remain a subject of ongoing debate. We constructed a quasi-two-dimensional microswimmer–colloid mixed system by taking advantage of Serratia marcescens’ tendency to become trapped at the air–water interface to investigate the origins of the enhanced diffusion and non-Gaussianity of the displacement distributions of passive colloidal tracers. Our findings reveal that the diffusion behavior of colloidal particles exhibits a strong dependence on bacterial density. At moderate densities, the collective dynamics of bacteria dominate the diffusion of tracer particles. In dilute bacterial suspensions, although there are multiple dynamic types present, near-field contact interactions such as collisions play a major role in the enhancement of colloidal transport and the emergence of non-Gaussian displacement distributions characterized by heavy exponential tails in short times. Despite the distinct types of microorganisms and their diverse self-propulsion mechanisms, a generality in the diffusion behavior of passive colloids and their underlying dynamics is observed.

The method of fundamental solutions for multi-particle Stokes flows: Application to a ring-like array of spheres

A method is presented for calculating Stokes flow around multiple particles of arbitrary shape. It uses the Method of Fundamental Solutions (MFS) applied to single particles, combined with an iterative scheme to resolve the many particle-particle hydrodynamic interactions; an approach that is reminiscent of the Method of Reflections. The attractive features of the proposed method are inherited from the MFS — simplicity and accuracy — while providing orders of magnitude computational speed-up for large particle systems. The method is verified through a series of test cases, including those involving strong lubrication forces and non-spherical particles. Unlike applications of the Method of Reflections reported in the literature, the iterative scheme we propose (a block Gauss-Seidel approach to solving a particle-particle interaction matrix) converges for all the cases we consider, for both resistance and mobility problems. The scheme is applied to the study of Stokes flow around ring-like arrays of spheres. We show that the relationship between globally applied velocity or force to the response of individual spheres can be described by just 5 coefficients (or 9 in total) for any given configuration. The results indicate that for 7–10 spheres in sedimentation, there exists a certain spacing that produces steady-state translation of the ring, independent of its orientation. For large numbers of spheres, slender-body theory can be applied to the problem, providing remarkably close agreement to the numerical results over a wide range of parameters.

Electrotaxis of Self-Propelling Artificial Swimmers in Microchannels.

Biological microswimmers alter their swimming trajectories to follow the direction of an applied electric field, exhibiting electrotaxis. We show that synthetic active droplet microswimmers also autonomously change swimming trajectories in microchannels, even undergoing "U-turns," in response to an electric field, mimicking electrotaxis. We exploit such electrotaxis, in the presence of an external flow, to robustly tune the swimming trajectory of active droplets between wall-adjacent, oscillatory, and channel centerline swimming. A general hydrodynamic model demonstrates that the electrotactic dynamics is governed by the electrical effects due to the swimmer's inherent surface charge, besides its motility, hydrodynamic wall interactions, and relative orientations of the electric field and imposed flow. Our study demonstrates a simple method for controlling active agents in complex geometries for microrobotic applications, like autonomous cargo delivery.

Robust Edge Flows in Swarming Bacterial Colonies

Understanding if and how the chirality of biomolecules is transferred across scales into larger components and active processes remains elusive. For instance, flagellated bacteria swim in helical trajectories but chirality seems absent from the active turbulence dynamics they display in dense suspensions. We address this question by examining multiscale dynamics in colonies. We find active turbulence without manifest chirality in the bulk, but wide, clockwise (viewed from the air side) circulation all along the tortuous centimeter-scale external boundary, while similar but counterclockwise flows follow internal boundaries. We trace the origin of these robust edge flows to an unexpected asymmetry at the individual level that is amplified by local interactions. We rationalize our findings with a model of noisy self-propelled particles immersed in a Stokes fluid that accounts faithfully for our observations. Our modeling and experimental efforts reveal that local nematic alignment and hydrodynamic interactions amplify the weak chiral bias in individual motion, promoting the formation of strong edge flows. The likely topological protection of these flows provides robust transport mechanism over large scales. Such robust boundary phenomena in weakly chiral active fluids may inspire new control strategies for active and biological matter. Published by the American Physical Society 2024

Experimental and numerical study on dynamic responses of a TLP-type modular floating structure system

This paper explores a proposed TLP-type modular floating structure system, incorporating both central TLP modules and peripheral floating artificial reef modules. The outermost floating artificial reef module can function as a floating breakwater, and also serving as a habitat for surrounding marine organisms. To assess the system's multi-body coupling dynamics under various wave conditions, both scale model tests (1:80) and time-domain numerical simulations were performed. The simulations accounted for hydrodynamic interactions among the bodies and the mechanical coupling effects. During the scale model test, a survival strategy has been proposed to prevent collision risks between reef modules and adjacent TLP modules, which involving a hinge connector with additional linear spring. A preliminary stiffness recommendation was suggested by a trade-off between the pitch of the reef module and the spring force. Numerical and experimental results have been widely compared and discussed, including the multi-body motion responses and the tension leg loads. A good agreement has been achieved, although responses are slightly overestimated by numerical simulation due to the neglect of the viscous damping effect. In addition, the responses of the proposed system, connected with and without the outermost floating artificial reef module, have been compared and analyzed. The results suggest that the connection of the reef module can significantly reduce the system's surge response and enhance its survivability under severe sea conditions. The validated numerical model can serve as a valuable reference for subsequent system optimization and further engineering applications.

A scaling relationship between thermodynamic and hydrodynamic interactions in protein solutions

Weak protein interactions are associated with a broad array of biological functions and are often implicated in molecular dysfunction accompanying human disease. In addition, these interactions are a critical determinant in the effective manufacturing, stability, and administration of biotherapeutic proteins. Despite their prominence, much remains unknown about how molecular attributes influence the hydrodynamic and thermodynamic contributions to the overall interaction mechanism. To systematically probe these contributions, we have evaluated self-interaction in a diverse set of proteins that demonstrate a broad range of behaviors from attractive to repulsive. Analysis of the composite trending in the data provides a convenient interconversion among interaction parameters measured from the concentration dependence of the molecular weight, diffusion coefficient, and sedimentation coefficient, as well as insight into the relationship between thermodynamic and hydrodynamic interactions. We find relatively good agreement between our data and a model for interacting hard spheres in the range of weak self-association. In addition, we propose an empirically derived, general scaling relationship applicable across a broad range of self-association and repulsive behaviors.

Two-dimensional one-way coupled modelling for fluid-structure-seabed interactions around a semicircular breakwater using OpenFOAM

Semicircular breakwaters, preferred for their lighter weight, wider base and superior resistance to overturning and sliding, have seen focused research on wave forces and hydrodynamic performance. Despite documented failures due to seabed instability, numerical examinations of the seabed response and stability around these structures are lacking in the literature. This study establishes an OpenFOAM model to numerically investigate hydrodynamic interactions, structural dynamics, seabed consolidation and liquefaction potential near a semicircular breakwater in two-dimensional, addressing complex fluid–structure-seabed interactions in a one-way coupling manner. A novel method for determining the compressibility of the pore fluid has been implemented, which integrates geostatic stress, atmospheric pressure and wave-induced excessive pore pressure within the seabed. The numerical results indicate that seabed responses are sensitive to the bulk modulus of pore air in partially saturated cases, where a decrease in pore pressure, an increase in the vertical effective stress and a decrease in the horizontal effective stress are observed. Further numerical analysis reveals that the most vulnerable part of the breakwater appears on the wave-facing side of the caisson, where reinforcement measurements are recommended during construction. A pronounced liquefaction zone is observed ahead of the breakwater, corresponding to the area with upward seepage, which is attributed to the combined effect of hydrodynamic interactions and direct stress action transferred from the semicircular breakwater.