Hydrodynamic Interactions Research Articles

Hydrodynamic Radii of Intrinsically Disordered Proteins: Fast Prediction by Minimum Dissipation Approximation and Experimental Validation.

The diffusion coefficients of globular and fully unfolded proteins can be predicted with high accuracy solely from their mass or chain length. However, this approach fails for intrinsically disordered proteins (IDPs) containing structural domains. We propose a rapid predictive methodology for estimating the diffusion coefficients of IDPs. The methodology uses accelerated conformational sampling based on self-avoiding random walks and includes hydrodynamic interactions between coarse-grained protein subunits, modeled using the generalized Rotne-Prager-Yamakawa approximation. To estimate the hydrodynamic radius, we rely on the minimum dissipation approximation recently introduced by Cichocki et al. Using a large set of experimentally measured hydrodynamic radii of IDPs over a wide range of chain lengths and domain contributions, we demonstrate that our predictions are more accurate than the Kirkwood approximation and phenomenological approaches. Our technique may prove to be valuable in predicting the hydrodynamic properties of both fully unstructured and multidomain disordered proteins.

Accelerating the force-coupling method for hydrodynamic interactions in periodic domains

The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions between the structures. One approach for periodic domains involves utilising a compact or exponentially decaying kernel function to spread the force on the structure to a regular grid where the resulting flow and interactions can be computed efficiently using an FFT-based solver. A limitation to this approach is that the grid spacing must be chosen to resolve the kernel and thus, these methods can become inefficient when the separation between the structures is large compared to the kernel width. In this paper, we address this issue for the force-coupling method (FCM) by introducing a modified kernel that can be resolved on a much coarser grid, and subsequently correcting the resulting interactions in a pairwise fashion. The modified kernel is constructed to ensure rapid convergence to the exact hydrodynamic interactions and a positive-splitting of the associated mobility matrix. We provide a detailed computational study of the methodology and establish the optimal choice of the modified kernel width, which we show plays a similar role to the splitting parameter in Ewald summation. Finally, we perform example simulations of rod sedimentation and active filament coordination to demonstrate the performance of fast FCM in application.

Hydrodynamic performance analysis of formations of dual three-dimensional undulating fins

The work seeks to understand the hydrodynamic performance and interaction mechanisms of double-fin formations. A high-resolution numerical technique based on the constraint immersed boundary method is used for simulating the 3D double-fin system. Comprehensive analysis is carried out, focusing on the hydrodynamic performance of formations with various arrangements, phase differences, and spatial distances. The result shows that the side-by-side formation can suppress the thrust of the fins while reducing energy consumption. The tandem formation notably enhances the thrust for the fin positioned at the rear, albeit at the cost of increased energy consumption. In the tandem formation with a small spacing, the following fin can obtain a thrust increase of 28% and an efficiency increase of 10%, independent of the phase difference. The thrust enhancement in the tandem formation is related to the suction-based propulsion mechanism induced by hydrodynamic interactions. However, the interaction mechanism between the two side-by-side fins resembles the so-called channelling effect. The unilateral channel flow perturbs the pressure equilibrium on either side of the fin, potentially imposing additional resistance on the undulating fin, with effects depending on the phase difference. The study offers new insights into understanding the collective behaviours of undulating fins.

Hydrodynamic Interactions and Enhanced Energy Harnessing amongst Many WEC Units in Large-Size Wave Parks

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects.

Dynamics of seaweed-inspired piezoelectric plates for energy harvesting from oscillatory cross flow.

Inspired by the vibrations of aquatic plants such as seaweed in the unsteady flow fields generated by free-surface waves, we investigate a novel device based on piezoelectric plates to harvest energy from oscillatory cross flows. Towards this end, numerical studies are conducted using a flow-structure-electric interaction model to understand the underlying physical mechanisms involved in the dynamics and energy harvesting performance of one or a pair of piezoelectric plates in an oscillatory cross flow. In a single-plate configuration, both periodic and irregular responses have been observed depending on parameters such as normalized plate stiffness and Keulegan-Carpenter number. Large power harvesting is achieved with the excitation of natural modes. Besides, when the time scale of the motion and the intrinsic time scale of the circuit are close to each other the power extraction is enhanced. In a two-plate configuration with tandem
formation, the hydrodynamic interaction between the two plates can induce irregularity in the response. In terms of energy harvesting, two counteracting mechanisms have been identified, shielding and energy recovery. The shielding effect reduces plate motion and energy harvesting, whereas with the energy recovery effect one plate is able to recovery energy from the wake of another for performance enhancement. The competition between these mechanisms leads to constructive or destructive interactions between the two plates. These results suggest that for better performance the system should be excited at its natural period, which should be close to the intrinsic time scale of the circuit. Moreover, using a pair of plates in a tandem formation can further improve the energy harvesting capacity when conditions for constructive interaction are satisfied.

Collapse and expansion kinetics of a single polyelectrolyte chain with hydrodynamic interactions.

We investigate the collapse and expansion dynamics of a linear polyelectrolyte (PE) with hydrodynamic interactions. Using dissipative particle dynamics with a bead-spring PE model, long-range electrostatics, and explicit ions, we examine how the timescales of collapse tcol and expansion texp depend on the chain length N and obtain scaling relationships tcol ∼ Nα and texp ∼ Nβ. For neutral polymers, we derive values of α = 0.94 ± 0.01 and β = 1.97 ± 0.10. Interestingly, the introduction of electrostatic interaction markedly shifts α to α ≈ 1.4 ± 0.1 for salt concentrations within c = 10-4 to 10-2M. A reduction in the ion-to-monomer size ratio noticeably reduces α. On the other hand, the expansion scaling remains approximately constant, β ≈ 2, regardless of the salt concentration or ion size considered. We find β > α for all conditions considered, implying that expansion is always slower than collapse in the limit of long polymers. This asymmetry is explained by distinct kinetic pathways of collapse and expansion processes.

Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences

In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-of-unity (POU) based representation of the surface that enables asymptotically faster computations compared to spherical-harmonics based representations. We use a boundary integral equation formulation to represent and discretize hydrodynamic interactions. The boundary integrals are weakly singular. We use the quadrature scheme based on the regularized Stokes kernels by Tlupova and Beale 2019 (given in [34]). We also use partition-of unity based finite differences that are required for the computation of interfacial forces. Given an N-point surface discretization, our numerical scheme has fourth-order accuracy and O(N) asymptotic complexity, which is an improvement over the O(N2log⁡N) complexity of a spherical harmonics based spectral scheme that uses product-rule quadratures by Veerapaneni et al. 2011 [36]. We use GPU acceleration and demonstrate the ability of our code to simulate the complex shapes with high resolution. We study capsules that resist shear and tension and their dynamics in shear and Poiseuille flows. We demonstrate the convergence of the scheme and compare with the state of the art.

Shape deformation, disintegration, and coalescence of suspension drops: Efficient simulation enabled by graph neural networks

Understanding the behaviors of suspension drops (particle swarms) as they settle in a viscous fluid holds significant importance across various applications. Due to hydrodynamic interactions (HIs), suspension drops would undergo a series of intricate behaviors, including shape deformation, disintegration, and coalescence. This work presents the hydrodynamic interaction graph neural network (HIGNN), developed in our prior work (Ma et al., 2022), as an efficient and accurate modeling framework for simulating the dynamics of suspension drops and investigating the various behaviors they exhibit. The HIGNN effectively incorporates the many-body nature of HIs, a feature lacking in most previous simulations that employ the Stokeslet assumption. In the meanwhile, the HIGNN achieves superior computational efficiency compared to traditional, high-fidelity numerical tools such as Stokesian dynamics and PDE solvers. Moreover, the HIGNN, once trained, is applicable to predicting suspension drops across a range of particle concentrations and under diverse forces (such as gravity and Coulombic interactions). Training the HIGNN only requires the data containing a small number of particles, leading to low training cost. Our results demonstrate that the HIGNN can effectively reproduce the various behaviors of suspension drops that were previously reported in literature. More specifically, a single, initially spherical drop slowly evolves into a torus-shaped drop, as particles escape from its rear and form a tail along the sedimenting direction. Subsequently, the torus breaks into secondary droplets, each undergoing a similar transition (deformation into a torus followed by disintegration), thereby leading to a repeating cascade. Further, we quantitatively analyze the correlation between the drop’s sedimentation velocity and volume fraction. We also propose new scaling laws for evaluating both the leakage rate of particles and the expansion rate of the horizontal radius of a suspension drop. For single suspension drops, we also systematically investigate how their dynamics is affected by their initial shapes and the formed tori’s aspect ratios, as well as with or without Coulombic interactions between particles. For a pair of suspension drops, we study the process of coalescence of two vertically aligned particles and examine the effect of introducing a horizontal offset on the subsequent breakup of the coalesced drop. All simulations were executed on a single GPU, with the computation of velocities for several thousand particles requiring less than five seconds per time step. This computational efficiency enables fast and resource-saving simulations of large suspension drops over extended time scales.

Data-based modelling of arrays of wave energy systems: Experimental tests, models, and validation

One of the key steps towards economic feasibility of wave energy conversion technology concerns scaling up to farms of multiple devices, in the attempt to reduce installation costs by sharing infrastructure, and a consequent drop in levelised cost of energy. Moreover, whenever wave energy systems are deployed in proximity (in so-called arrays), the exploitation of the hydrodynamic interactions between single devices is fully enabled, potentially increasing the final energy outcome. To achieve this in real (operational) time, the employed energy-maximising control strategies require control-oriented array models, able to efficiently describe the dynamics of these interconnected systems in a representative fashion. This can be, nonetheless, a difficult task when considering first principles alone, under small motion assumptions, for modelling purposes. Recognising the uncertainty associated to array numerical models obtained from the linearisation of simplified system equations around their equilibria, this paper presents models of several array configurations identified following a frequency domain approach on the basis of experimental data. Tailored tests on laboratory-scale devices have been designed and conducted in the Aalborg University (Denmark) wave tank facility, with the purpose of performing representative system identification of the wave energy systems arrays. The obtained models are validated on different representative sea states configurations, in controlled and uncontrolled motion operational conditions. The validation results are fully discussed and analysed in terms of standard error measures and time lag, while the obtained models are made freely accessible via a linked repository (named OCEAN), in the attempt to openly provide validated models for different array configurations.

Effect of Graphene Oxide Localization on Morphology Development and Rheological and Mechanical Properties of Poly(lactic acid)/ethylene vinyl Alcohol Copolymer Blend Composites: A Comprehensive Study.

This study investigates the rheological, morphological, and mechanical properties of melt-processed polylactide/ethylene vinyl alcohol (70PLA/30EVOH) blend composites containing 0.25, 0.5, and 1 wt.% of graphene oxide (GO) nanoplates. Thermodynamic-based suggested the localization of nanoparticles in EVOH, SEM studies showed that the introduction of GO to the blend increased dispersed droplet size, which was attributed to the localization of GO within EVOH, as confirmed by TEM. The rheology results indicated a decrease in the elasticity for the composite containing 0.25 wt.% of GO compared to the neat blend, which was attributed to the sliding effect of the added GO nanoplatelets. However, samples containing higher amounts of GO nanoplatelets exhibited more excellent elasticity than the neat blend. The increased elasticity was suggestively attributed to the dominance of hydrodynamic interactions, the physical network of added nanoplatelets, and polymer/GO interactions over the sliding role of the GO nanoplatelets at higher loadings. In addition, the effect of the order of mixing was investigated, and the premixing of PLA and GO exhibited a decrease in the droplet radius compared to the neat blend. It was ascribed to the localization of GO nanosheets in the PLA and interface, which was confirmed by rheological results and mechanical assessments.

Dynamics of meniscus-bound particle clusters in extensional flow

Capillary suspensions are three-phase mixtures containing a solid particulate phase, a continuous liquid phase, and a second immiscible liquid forming capillary bridges between particles. Capillary suspensions are encountered in a wide array of applications including 3D printing, porous materials, and food formulations, but despite recent progress, the micromechanics of particle clusters in flow is not fully understood. In this work, we study the dynamics of meniscus-bound particle clusters in planar extensional flow using a Stokes trap, which is an automated flow control technique that allows for precise manipulation of freely suspended particles or particle clusters in flow. Focusing on the case of a two-particle doublet, we use a combination of experiments and analytical modeling to understand how particle clusters rearrange, deform, and ultimately break up in extensional flow. The time required for cluster breakup is quantified as a function of capillary number Ca and meniscus volume V. Importantly, a critical capillary number Cacrit for cluster breakup is determined using a combination of experiments and modeling. Cluster relaxation experiments are also performed by deforming particle clusters in flow, followed by flow cessation prior to breakup and observing cluster relaxation dynamics under zero-flow conditions. In all cases, experiments are complemented by an analytical model that accounts for capillary forces, lubrication forces, hydrodynamic drag forces, and hydrodynamic interactions acting on the particles. Results from the analytical models are found to be in good agreement with experiments. Overall, this work provides a new quantitative understanding of the deformation dynamics of capillary clusters in extensional flow.

Modeling and simulation of anisotropic cross-linked cellulose fiber networks with an out-of-plane topography

Non-woven cellulose fiber networks of low areal density are widely used in many industrial applications and consumer products. A discrete element method (DEM) modeling framework is advanced to simulate the formation of strongly anisotropic cellulose fiber network sheets in the dilute limit with simplified hydrodynamic and hydroelastic interactions. Our modeling accounts for in-plane fiber orientation and viscous drag indirectly by using theories developed by Niskanen (2018 Fundamentals of Papermaking, Trans. 9th Pulp and Paper Fundamental Research Symp. Cambridge, 1989 (FRC) pp 275–308) and Cox (1970 J. Fluid Mech. 44 791–810) respectively. Networks formed on a patterned and flat substrate are simulated for different fiber types, and their tensile response is used to assess the influence of the out-of-plane topographical pattern, specifically, on their stiffness and strength. Sheets with the same grammage and thickness, but composed with a higher fraction of softwood fiber (longer fibers with large diameter), have higher strength and higher strain to failure compared to sheets made from hardwood fibers (short fibers with small diameter). However, varying the fiber fraction produces only an insignificant variation in the initial sheet stiffness. The above simulation predictions are confirmed experimentally for sheets comprised of fibers with different ratios of Eucalyptus kraft and Northern Bleached Softwood Kraft fibers. Sheets with out-of-plane topography show an unsymmetric mass distribution, lower tensile stiffness, and lower tensile strength compared to those formed on a flat substrate. The additional fiber deformation modes activated by the out-of-plane topography, such as bending and twisting, explain these differences in the sheet mechanical characteristics.

Hydrodynamic performance of vertical cylindrical wave energy absorbers in front of a vertical wall

This paper studies the hydrodynamic performance of vertical cylindrical absorbers in front of a vertical wall. All the absorbers are independent of each other and restricted to only the heave motion. Based on a linear potential flow theory, an analytical solution is developed for the problems of wave diffraction and radiation by absorbers. In the solving procedure, the hydrodynamic problem is first transformed into an equivalent problem in an open water domain using the image principle. The number of absorbers in the equivalent problem is twice that in the real problem, and the plane layout is symmetric about the original vertical wall. The velocity potential of the fluid domain is obtained using the method of variable separation, and the unknown expansion coefficients in the velocity potential are determined by the matched boundary conditions. The heave excitation force, added mass, radiation damping, motion response, and energy capture width of the absorbers are calculated. Case studies are presented to show the effects of the wall reflection and hydrodynamic interaction on the energy extraction performance of the wave energy converter (WEC) system. Subsequently, the WEC performance under the action of irregular waves is analyzed by considering an incident wave spectrum, and the mean annual absorbed power of the device is estimated by considering the wave data statistics at the actual sites. The results indicate that when the wave motion resonates with the absorber motion, the energy extraction performance of the absorbers is significantly improved. The performance of the absorbers can be effectively improved when the structures are close to the antinodes of a standing wave field. By designing a reasonable plane layout, the hydrodynamic interaction can play a constructive role in the performance of the WEC system.

Flow-induced Vibrations of Dual-cylinders in Axial Flow via LES Simulations

The axial-flow-induced vibration (AFIV) of fuel rods in the nuclear power plant is closely related to nuclear safety. In this article, a numerical study is performed on vibration of two elastic cylinders arranged side-by-side in axial flow. Large eddy simulation (LES) is employed to predict the turbulent flow. The numerical method has been verified using the experimental root-mean-square vibration amplitude of a single cylinder. A wide range of inflow velocities u*, incident turbulence intensity Tu and space ratio P/D have been examined, where D and P are the diameter and centre-to-centre distance of the cylinders, respectively. The results show that the vibration amplitudes increase with an increasing u*, comparable to the case of a single cylinder in axial flow. However, the two cylinders could bend outwards during a relatively high u* and low Tu. Although Tu significantly affects the amplitudes of the cylinders, it does not change the vibration frequency and the critical velocity at which buckling instability occurs. As the gap between the two cylinders is sufficiently small, the vibration amplitude enhances significantly due to the pronounced hydrodynamic interaction between the two elastic cylinders and surrounding fluid. The direction of buckling is no longer random but fixed.

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.