Hydrodynamic Interactions Research Articles

Coupled response analysis of dual lifting vessels during collaborative lifting topside module

Offshore assembly and disassembly operations represent a multi-billion-dollar market potential. Collaborative lifting by multiple vessels has emerged as a new operating paradigm for integrated offshore facilities assembly and disassembly. Hence, this paper investigates the hydro-dynamic interaction of dual lifting vessels in collaborative lifting operations. The coupled motions during multi-body operations are simulated using the commercial software SESAM. The feasibility of the numerical model for coupled motions in collaborative lifting is verified by comparing the numerical results of topside motions, vessel motions, and vertical lifting arm loads against experimental measurements. The effects of wave heading and period on the hydrodynamic responses of the topside module, dual lifting vessels, and lifting arms during collaborative operations are studied. Their influence patterns and mechanisms are analysed in detail. The results show that transverse waves and head wave induce significant heave and pitch motions of the topside module and vessels, but the maximum vertical loads on the lifting arms occur in oblique waves. The motion responses of the topside module and vessels increase with longer wave periods under the oblique sea condition, and roll motions are more sensitive to large periods compared to the gradual rise in heave and pitch.

Theoretical analysis of linear oscillations of bubbles in a polydisperse cluster

The dynamics of a single air bubble in an unbounded liquid are significantly different from the dynamics of an individual bubble in clusters due to the hydrodynamic interaction between the bubbles. Studying the mechanism of this interaction is one of the important aspects in the study of the fundamental nature of acoustic and hydrodynamic cavitation. In this work, to analyze small oscillations of bubbles in a spherical cluster near a stable equilibrium position, the mathematical theory of a linear conservative system with several degrees of freedom is applied to explain the mechanism of interaction between bubbles of different sizes. Using this theory, in the general case, it has been proven that the number of resonance frequencies in a polydisperse cluster coincides with the number of fractions. It is shown that in the regions of the main resonance (at low frequencies) bubbles of different fractions oscillate in phase, and in the regions of secondary resonances (at high frequencies) the phases successively change to the opposite, starting with the fraction containing bubbles of the largest radius, and further changing in order of decreasing. Using the example of a two-fraction cluster, it was found that there is an inertial connection between the bubbles, but there is no force connection; when the number of bubbles of one of the fractions is small, the connection between them and the bubbles of the other fraction is weak, while the interaction between them can be strong. An analysis of the energy transfer between bubbles of different fractions showed that the change in the nature of bubbles oscillations in the fraction with a small radius, while the nature of vibration of bubbles in the other fraction does not change, is the result of dynamic damping.

Multiple moonpools within a vessel free to heave and pitch: An experimental study

Moonpools in marine vessels and offshore platforms are vertical openings through the structure used to support underwater operations. Experimental investigations of multiple moonpool resonant responses coupled with vessel heave and pitch motions are presented in this study. For three moonpools at forward, central, and aft locations of a rectangular vessel, the simultaneous location-dependent free surface response amplitudes and oscillation phases are compared for a range of incident wave frequencies in the piston mode range. For the vessel free to heave and pitch, the central moonpool has the highest response amplitude; whereas, a previous study with fixed vessel (Garad et al. 2023) showed that the largest free surface responses are observed in the forward moonpool. Due to coupled hydrodynamic interactions between the moonpool oscillations and the vessel motions, the moonpool resonance frequency is linked with the vessel heave response. Multiple response amplitudes peaks are observed in the forward and aft moonpools due to body motions. The non-dimensional response amplitude increases nonlinearly with decreasing wave steepness close to the resonance frequency. The multiple moonpool oscillations show distinct phase differences from one another and with the outer wave, the individual values depending on the incident wave frequency. Considering the vessel motions, comparison with experiments without moonpools shows that the pitch response is increased due to multiple moonpool oscillations. The hydrodynamic interactions between multiple moonpools and a floating vessel have prospective applications in the case of marine platforms, where the resonant motions can be used for wave energy conversion through oscillating water column devices.

Characterizing the Janus colloidal particles in AC electric field and a step towards label-free cargo manipulation

In recent years, researchers have been exploring Janus particles, a unique type of colloidal system, which has gained enormous attention across diverse fields, from soft matter physics to biology. These particles, possessing an asymmetric surface, can be manipulated in the fluid using external energy sources. This versatility makes them suitable for mimicking biological systems and applications like cargo transportation, drug delivery, biosensing, and environmental cleanup. The study focuses on the response of metal-dielectric (Ti-PMMA) Janus spheres in the AC field, created through the Physical Vapor Deposition (PVD) technique. When subjected to a uniform AC electric field, these particles exhibit different dynamic behaviors at various frequency ranges. The particles show diverse responses from induced-charge electrophoresis (ICEP: 500 Hz-80 kHz) to reversed motion (r: ICEP:100 kHz-1 MHz) and linear chain formation (1 MHz). Additionally, they randomly cluster near the lower characteristic frequency (800 Hz) of the ICEP, whereas they exhibit the 3D motion at frequencies (100 Hz) below this lower characteristic value. The mechanisms behind these dynamic phenomena could be explained by considering the concept of electric double layer (EDL), self-dielectrophoresis (sDEP), dipolar interactions, hydrodynamic interactions, and electrothermal effects. These active Janus Colloids are further leveraged to manipulate 1 µm diameter PMMA passive microparticles and E. coli bacteria at 1 kHz, showcasing their potential applications in cargo delivery under various microfluidic research areas. The manipulation of payloads could be explained based on dielectrophoretic trapping due to locally generated field gradients around the surface of the Janus sphere. Therefore, the present work offers an unprecedented opportunity to study such out-of-equilibrium complex active matter systems and create novel functional materials. Moreover, it could also be extended as a fuel-free microrobotics system for various biomedical applications such as sensing and on-demand drug or cargo delivery inside the microfluidics chamber.

Floating bridge global responses to slowly varying wave loads

The global responses of a 5530-m-long floating bridge under linear and slowly varying wave loads were studied. The bridge has modes from seconds to around 2 min. A comparative study was carried out applying full Quadratic Transfer Functions (QTFs) or Newman's approximation (Newman, 1974) for slowly varying loads. Four groups of QTFs were computed: one fixed pontoon, one pontoon with specified stiffnesses, three fixed pontoons, and three pontoons with stiffnesses for the mid-pontoon. The importance of damping to the global response was demonstrated by a sensitivity check on the viscous damping. The study showed the importance of hydrodynamic interaction in both first and second order wave loads and responses. Hydrodynamic interaction led to more ‘distributed’ QTF peak values away from the diagonal, which may reduce the correctness of Newman's approximation. Parametric study showed that the floating bridge responses were sensitive to wave direction, wave height and period. This study suggested that full QTFs based on three fixed pontoons provided the most conservative results for the base case. Newman's approximation provided reasonable levels of overall responses but underpredicted specific responses in this study. Though the full QTFs method is preferred in a detailed analysis, the efficient Newman's approximation is considered as a valuable tool for large-scale screening analysis during the early design phase of practical engineering.

Impact of Hydrodynamic Interactions on the Kinetic Pathway of Protein Folding.

Protein folding is a fundamental process critical to cellular function and human health, but it remains a grand challenge in biophysics. Hydrodynamic interaction (HI) plays a vital role in the self-organization of soft and biological materials, yet its role in protein folding is not fully understood despite folding occurring in a fluid environment. Here, we use the fluid particle dynamics method to investigate many-body hydrodynamic couplings between amino acid residues and fluid motion in the folding kinetics of a coarse-grained four-α-helices bundle protein. Our results reveal that HI helps select fast folding pathways to the native state without being kinetically trapped, significantly speeding up the folding kinetics compared to its absence. First, the directional flow along the protein backbone expedites protein collapse. Then, the incompressibility-induced squeezing flow effects retard the accumulation of non-native hydrophobic contacts, thus preventing the protein from being trapped in local energy minima during the conformational search of the native structure. We also find that the significance of HI in folding kinetics depends on temperature, with a pronounced effect under biologically relevant conditions. Our findings suggest that HI, particularly the short-range squeezing effect, may be crucial in avoiding protein misfolding.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments.

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Pair Interactions of Self-Propelled SiO2-Pt Janus Colloids: Chemically Mediated Encounters.

Driven by the necessity to achieve a thorough comprehension of the bottom-up fabrication process of functional materials, this experimental study investigates the pairwise interactions or collisions between chemically active SiO2-Pt Janus colloids. These collisions are categorized based on the Janus colloids' orientations before and after they make physical contact. In addition to the hydrodynamic interactions, the Janus colloids are also known to affect each other's chemical field, resulting in chemophoretic interactions, which depend on the degree of surface anisotropy in reactivity of Janus colloid and the solute-surface interaction at play. Our study reveals that these interactions lead to a noticeable decrease in particle speed and changes in orientation that correlate with the contact duration and yield different collision types. Distinct configurations of contact during collisions were found, whose mechanisms and likelihood are found to be dependent primarily on the chemical interactions. Such estimates of collision and their characterization in dilute suspensions shall have a key impact in determining the arrangement and time scales of dynamical structures and assemblies of denser suspensions and potentially the functional materials of the future.

Dynamics of a bubble-pair between two parallel rigid walls

The dynamics of two gas bubbles placed side-by-side in liquid between parallel rigid plates is studied numerically using the multiphase volume of fluid (VOF) model in OpenFOAM. This model solves a single set of Navier–Stokes equations for both the gas in the bubbles and the surrounding liquid. Being initially stationary, the bubbles first expand to their maximum volume due to the high gas pressure inside them and then collapse. Both phases are treated as viscous and immiscible without any phase change. The model is validated against available experimental data of a single bubble oscillation between parallel plates and a bubble-pair oscillation near a single rigid wall. Parametric studies are then performed, with the main variables being the initial sizes of the bubbles and their standoff distances from the rigid plates. The bubbles exhibit symmetric or asymmetric behavior depending on these two variables. Three distinct scenarios are identified in the symmetric case based on the relative influence of bubble-bubble and bubble-wall interactions. The jet strength and direction, bubble oscillation period, coalescence, and early asymmetric bubble collapse are characterized by initial distances and radii. This study provides valuable insights into intricate hydrodynamic interactions and behaviors of bubble pairs bounded by rigid surfaces.

Stochastic kinetic theory applied to coarse-grained polymer model.

A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison with explicit Langevin equation simulations under conditions with analytical solutions. The polymers are modeled as Hookean dumbbells in one dimension, without including hydrodynamic interactions and polymer-polymer interactions. Stochastic moment equations are derived from full field theory. The accuracy of the field theory and moment equations is quantified using autocorrelation functions. The full field theory is only accurate for a large number of polymers due to keeping track of rare occurrences of polymers with a large stretch. The moment equations do not have this error because they do not explicitly track these configurations. The accuracy of both methods depends on the spatial degree of discretization. The timescale of decorrelation over length scales bigger than the spatial discretization is accurate, while there is an error over the scale of single mesh points.

Collective motion in a sheet of microswimmers

Self-propelled particles such as bacteria or algae swimming through a fluid are non-equilibrium systems where particle motility breaks microscopic detailed balance, often resulting in large-scale collective motion. Previous theoretical work has identified long-ranged hydrodynamic interactions as the driver of collective motion in unbounded suspensions of rear-actuated (“pusher”) microswimmers. In contrast, most experimental studies of collective motion in microswimmer suspensions have been carried out in restricted geometries where both the swimmers’ motion and their long-range flow fields become altered due to the proximity of a boundary. Here, we study numerically a minimal model of microswimmers in such a restricted geometry, where the particles move in the midplane between two no-slip walls. For pushers, we demonstrate collective motion with short-ranged order, in contrast with the long-ranged flows observed in unbounded systems. For front-actuated (“puller”) microswimmers, we discover a long-wavelength density instability resulting in the formation of dense microswimmer clusters. Both types of collective motion are fundamentally different from their previously studied counterparts in unbounded domains. Our results show that this difference is dictated by the geometrical restriction of the swimmers’ motion, while hydrodynamic screening due to the presence of a wall is subdominant in determining the suspension’s collective state.

Diffusing Wave Spectroscopy Measurements of Colloidal Suspension Dynamics.

Diffusing wave spectroscopy (DWS) is used to measure the dynamics of charged silica particles between the volume fractions 0.065 ≤ ϕ ≤ 0.352 (weight percentages from 12.7 to 55.8 wt %). The short-time diffusivity averaged over the scattering vectors sampled by DWS (ϕ) decreases with an increasing concentration. An effective hard-sphere model that accounts for hydrodynamic interactions and a double-layer repulsion fits the values up to an effective volume fraction , where is the excluded shell radius normalized by the particle radius = b/a = 1.3. While DWS measurements of diffusivity are sensitive to repulsive interactions, we show that they are relatively insensitive to attraction, such as those due to secondary minima in the interaction potential or weak depletion interaction.

Hydrodynamic interactions between rough surfaces

Hydrodynamic interactions between rough surfaces

Numerical study of the effects of hydrodynamic interactions among cells for microfluidic holographic cyto-tomography

When cells in a suspension flow through a microfluidic channel and rotate within the field of view (FOV) of a holographic microscope, they become accessible to a light beam from various angles. This allows the retrieval of a three-dimensional refractive index map for each flowing cell, essentially a 3D phase-contrast tomogram. Understanding the effects of hydrodynamic interactions among cells on their rotational behaviour during flow is crucial for designing microfluidic devices for holographic imaging. In this study, we employ direct numerical simulations to investigate the dynamics of cell clusters suspended in a Newtonian liquid under pressure-driven flow within a microfluidic channel, with the aim of clarifying the influence of hydrodynamic interactions on cell rotation.

Detailed characterization of extreme clustering at near-contact scales in isotropic turbulence

Recent measurements of inertial particles in isotropic turbulence (Hammond & Meng, J. Fluid Mech., vol. 921, 2021, A16) revealed surprising extreme clustering of particles at near-contact separations $(r)$ , whereby the radial distribution function, $g(r)$ , grows from $O(10)$ to $O(10^3)$ with a $(r/a)^{-6}$ scaling (where $a$ is the particle radius), and a surprising upturn of the mean inward particle-pair relative velocity (MIRV). Hydrodynamic interactions (HIs) were proposed to explain the extreme clustering, but despite predicting the correct scaling $(r/a)^{-6}$ , the HI theory underpredicted $g(r)$ by at least two orders of magnitude (Bragg et al., J. Fluid Mech., vol. 933, 2022, A31). To further understand the extreme clustering phenomenon and the relevance of HI, we characterize $g(r)$ and particle-pair kinematics for Stokes numbers $0.07 \leq St \leq 3.68$ in a homogeneous isotropic turbulence chamber using three-dimensional (3-D) particle tracking resolved to near–contact. A drift–diffusion equation governing $g(r)$ is presented to investigate the kinematic mechanisms of particle pairs. Measurements in all 24 conditions show that when $r/a\lessapprox 20$ , extreme clustering consistently occurs, scaling as $g(r) \sim (r/a)^{-k}$ with $4.5 \leq k \leq 7.6$ , which increases with $St$ . Here $g(r)$ varies with $St$ , particle size, density and polydispersity in ways that HI cannot explain. The extreme clustering region features an inward drift contributed by particle-pair turbophoresis and an inward radial relative acceleration. The latter indicates an interparticle attractive force at these separations that HI also cannot explain. The MIRV turns upward when approaching the extreme clustering region, opposite to direct numerical simulation predictions. These observations further support our previous assessment that extreme clustering arises from particle–particle interactions, but HI is not the main mechanism.

Effects of chain resolution on the configurational and rheological predictions of dilute polymer solutions in flow fields with hydrodynamic interactions

In a recent study, the resolution of a polymer chain model was shown to significantly affect rheological predictions from Brownian dynamics (BD) simulations [Kumar and Dalal, “Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow,” J. Non-Newtonian Fluid Mech. 315, 105017 (2023)], even in the absence of hydrodynamic interactions (HI) and excluded volume. In this study, we investigate the effects of chain resolution in the presence of HI. Toward this, we perform BD simulations of a long polymer chain, with the discretization level varying from a single Kuhn step (bead–rod model) to several tens of Kuhn-steps (bead–spring model). The chain models were subjected to flow fields of uniaxial extension (purely stretching) and steady shear (equal rates of stretching and rotation). Broadly, our results indicate an amplification of the differences observed between the differently resolved bead–rod and bead–spring models, in the presence of HI. Interestingly, all rheological predictions qualitatively fall in two groups for extensional flow, with the predictions from the bead–spring model with HI being close to those of the bead–rod model without HI. This indicates significantly reduced sensitivity of coarser bead–spring models to HI, relative to the one resolved to a single Kuhn step. However, in shear flow, the bead–spring rheological predictions fall between those of the bead–rod model with and without HI, forming a third group. This is linked to the presence of stretched and coiled states in the ensemble for shear flow. HI effects are large for the coiled states and weak for the stretched states, thereby yielding predictions that are intermediate between those for no HI and dominant HI. Thus, quite surprisingly, the quality of predictions of the bead–spring models is strongly affected by the physics of the flow field, irrespective of the parameterization.

Three-Dimensional Numerical Study of Hydrodynamic Interactions between Pectoral Fins and the Body of Aquatic Organisms.

Fish swimming has attracted attention as a locomotion system with excellent propulsive efficiency. They swim by moving their body, fins, and other organs simultaneously, which developed during evolution. Among their many organs, the pectoral fin plays a crucial role in swimming, such as forward-backward movement and change of direction. In order to investigate the hydrodynamic interaction between pectoral fins and fish bodies, we examined the asymmetric flapping motion of the pectoral fin concerning the body axis and investigated the effect of the pectoral fin on the propulsive performance of the body of a small swimming object by numerical simulation. In this study, the amplitude ratio, frequency ratio, and phase of the body and pectoral fin varied. Therefore, although propulsive performance increased in tandem with the frequency ratio, the amplitude ratio change had negatively affected the propulsive performance. The results revealed that the propulsive performance of the fish was high even in low-frequency ratios when the phase difference was varied. The highest propulsion efficiency increased by a factor of about 3.7 compared to the phase difference condition of 0.

Analysis and estimation of time step sizes and stiffness parameters for efficient simulations of macromolecules with hydrodynamic interactions

Recent studies have shown the importance of using highly resolved models for Brownian Dynamics (BD) simulations of long macromolecules. For computational efficiency, such models use stiff springs to mimic a single Kuhn step and use a single-step semi-implicit (SS) scheme. Somewhat unexpectedly, time step sizes for such a single-step method need to be reduced with increasing chain size and level of hydrodynamic interactions (HIs), for good convergence. The conventional predictor–corrector (PC) method works reasonably well but remains computationally slow, owing to multiple iterations per time step to convergence. In this study, we reveal how the time step size for the much faster SS method is tied to the physics of the problem. Using simple physical principles, we derive an analytical estimate of the upper limit on the time step size for given levels of HI, chain size, and stiffness of connecting springs. Detailed BD simulations at equilibrium and in flow fields highlight the success of our analytical estimate. We also provide a lower limit on spring stiffness parameter such that it remains effectively rigid and successfully mimics a Kuhn step. Our investigations show that the resulting BD simulations using our estimated time step size in the SS scheme are significantly faster than the conventional PC technique. The analysis presented here is expected to be useful in general for any type of simulations of macromolecules, with or without flow fields, owing to deep connections with the underlying physics.

Numerical simulations of the sedimentation of soft particles in confined Newtonian liquids

The gravitational sedimentation of solid particles in liquids is important in several applications, many of which involve soft particles (e.g., microplastics, microgels, and biological cells). However, there is still little knowledge on the sedimentation of deformable beads. In this work, we employ fully three-dimensional finite-element numerical simulations to investigate the sedimentation of an initially spherical elastic bead in a Newtonian liquid contained inside a square-cross section vessel. In particular, we carry out a wide parametric analysis to understand the effects of inertia, particle deformability, and geometrical confinement on the particle sedimentation dynamics and settling velocity. In addition, the sedimentation of a particle in a Newtonian liquid close to a vertical wall is studied. When the particle sediments at the center of the vessel, the settling velocity increases at increasing inertia and decreases at increasing confinement and deformability. However, at intermediate inertia, the settling velocity passes through a minimum and then rises as the particle gets softer. Correspondingly, the equilibrium deformed shape of the particle shows the appearance of a concavity at the rear. When the sedimentation occurs close to a vertical wall, the closer the particle to the solid surface, the slower its sedimentation. On the other hand, the hydrodynamic interaction between the particle and the wall makes the particle move away from the wall.

Effects of body shape on hydrodynamic interactions in a dense diamond fish school

To examine the effect that body shape plays in the interactions between fish in a dense fish school, fish-like undulating foils are numerically studied in a high-density diamond school. Shape parameters of leading edge radius, boattail angle, and maximum thickness location along the body are independently varied to control the body shape. A traveling wave is prescribed to the body, and the flow around the school is solved using an immersed boundary method-based incompressible Navier–Stokes flow solver. Our findings indicate that body shape does play a significant role in the performance of the school and varies school efficiency and thrust productions by as much as 7% and 40%, respectively, and changes the efficiency in individual swimmers within the school by up to 25%. The leading edge radius drives the scale of the anterior body suction experienced throughout the school. A rounder leading edge generates more suction but consequently consumes more power. Changes to the location of the maximum thickness along the foil significantly impact the wall effect in the school by changing the shape of the “wall.” A maximum thickness that occurs at or in front of the closest point of interaction between the body and tail is favored. Finally, changes to the boattail angle manipulate the shape of the active channels in the school altering vortex–body interactions and the wall effect. A large boattail angle leads to a pinching that prohibits significant flow in the channels, reducing performance.