Presence Of Hydrodynamic Interactions Research Articles

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.

Supercoiled ring polymers under shear flow.

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.

Brownian dynamics simulations of shear-induced aggregation of charged colloidal particles in the presence of hydrodynamic interactions

HypothesisIn spite of the abundant literature on Brownian simulations of the aggregation behavior of colloidal suspensions both under quiescent conditions and in the presence of shear, few works performed simulations including the effect of hydrodynamic interactions. Even fewer works have investigated the effects of shear on the aggregation of electrostatically-stabilized colloidal suspensions. SimulationsIn this work, we employed Brownian dynamics simulations implementing the Rotne-Prager-Yamakawa approximation to account for hydrodynamic interactions and investigated the aggregation kinetics of electrostatically-stabilized colloidal suspensions exposed to simple shear, for various Péclet number values, particle volume fractions and surface potential values. ResultsThe increase in Péclet number (i.e., in the shear rate), leads to an overall increase in the aggregation rate and the formation of large aggregates that, for sufficiently high volume fractions, rapidly grow, leading to either breakup and restructuring phenomena or percolation of the system. In some cases, a bimodal distribution of the cluster population was observed. Our simulations further indicate that at the highest Péclet, the aggregation dynamics is independent of the energy barrier and entirely controlled by shear. A comparison with a simple BD method reveals that neglecting long-range hydrodynamic interactions leads to a substantial underestimation of the aggregation rate.

Nanoparticle dispersion in porous media: Effects of hydrodynamic interactions and dimensionality

AbstractWe investigate the effect of steric and hydrodynamic interactions (HI) on quiescent diffusion and flow‐driven transport of finite‐sized nanoparticles through periodic 2D (two‐dimensional) and 3D (three‐dimensional) nanopost arrays using Stokesian dynamics simulations. We find that steric and HI hinder particle diffusivity under quiescent conditions and enhance longitudinal dispersion under flow. Moreover, the presence of HI leads to a power‐law increase in the longitudinal dispersion coefficient with Pe due to spatial variations in the fluid velocity. Lastly, our simulations reveal that longitudinal particle dispersion coefficients behave similarly in 2D and 3D when HI are included.

Hydrodynamics of polymers in an active bath.

The conformational and dynamical properties of active polymers in solution are determined by the nature of the activity. Here, the behavior of polymers with self-propelled, active Brownian particle-type monomers differs qualitatively from that of polymers with monomers driven externally by colored-noise forces. We present simulation and theoretical results for polymers in solution in the presence of external active noise. In simulations, a semiflexible bead-spring chain is considered, in analytical calculations, a continuous linear wormlike chain. Activity is taken into account by independent monomer or site velocities, with orientations changing in a diffusive manner. In simulations, hydrodynamic interactions (HIs) are taken into account by the Rotne-Prager-Yamakawa tensor or by an implementation of the active polymer in the multiparticle-collision-dynamics approach for fluids. To arrive at an analytical solution, the preaveraged Oseen tensor is employed. The active process implies a dependence of the stationary-state properties on HIs via the polymer relaxation times. With increasing activity, HIs lead to an enhanced swelling of flexible polymers, and the conformational properties differ substantially from those of polymers with self-propelled monomers in the presence of HIs, or free-draining polymers. The polymer mean-square displacement is enhanced by HIs. Over a wide range of timescales, hydrodynamics leads to a subdiffusive regime of the site mean-square displacement for flexible active polymers, with an exponent of 5/7, larger than that of the Rouse (1/2) and Zimm (2/3) models of passive polymers.

The combined hydrodynamic and thermodynamic effects of immobilized proteins on the diffusion of mobile transmembrane proteins

The plasma membranes of cells are thin viscous sheets in which some transmembrane proteins have two-dimensional mobility and some are immobilized. Previous studies have shown that immobile proteins retard the short-time diffusivity of mobile particles through hydrodynamic interactions and that steric effects of immobile proteins reduce the long-time diffusivity in a model that neglects hydrodynamic interactions. We present a rigorous derivation of the long-time diffusivity of a single mobile protein interacting hydrodynamically and thermodynamically with an array of immobile proteins subject to periodic boundary conditions. This method is based on a finite element method (FEM) solution of the probability density of the mobile protein diffusing with a position-dependent mobility determined through a multipole solution of Stokes equations. The simulated long-time diffusivity in square arrays decreases as the spacing in the array approaches the particle size in a manner consistent with a lubrication analysis. In random arrays, steric effects lead to a percolation threshold volume fraction above which long-time diffusion is arrested. The FEM/multipole approach is used to compute the long-time diffusivity far away from this threshold. An approximate analysis of mobile protein diffusion through a network of pores connected by bonds with resistances determined by the FEM/multipole calculations is then used to explore higher immobile area fractions and to evaluate the finite simulation cell size scaling behaviour of diffusion near the percolation threshold. Surprisingly, the ratio of the long-time diffusivity to the spatially averaged short-time diffusivity in these two-dimensional fixed arrays is higher in the presence of hydrodynamic interactions than in their absence. Finally, the implications of this work are discussed, including the possibility of using the methods developed here to investigate more complex diffusive phenomena observed in cell membranes.

Active Brownian filaments with hydrodynamic interactions: conformations and dynamics.

The conformational and dynamical properties of active self-propelled filaments/polymers are investigated in the presence of hydrodynamic interactions by both, Brownian dynamics simulations and analytical theory. Numerically, a discrete linear chain composed of active Brownian particles is considered, analytically, a continuous linear semiflexible polymer with active velocities changing diffusively. The force-free nature of active monomers is accounted for-no Stokeslet fluid flow induced by active forces-and higher order hydrodynamic multipole moments are neglected. Hence, fluid-mediated interactions are assumed to arise solely due to intramolecular forces. The hydrodynamic interactions (HI) are taken into account analytically by the preaveraged Oseen tensor, and numerically by the Rotne-Prager-Yamakawa tensor. The nonequilibrium character of the active process implies a dependence of the stationary-state properties on HI via the polymer relaxation times. In particular, at moderate activities, HI lead to a substantial shrinkage of flexible and semiflexible polymers to an extent far beyond shrinkage of comparable free-draining polymers; even flexible HI-polymers shrink, while active free-draining polymers swell monotonically. Large activities imply a reswelling, however, to a less extent than for non-HI polymers, caused by the shorter polymer relaxation times due to hydrodynamic interactions. The polymer mean square displacement is enhanced, and an activity-determined ballistic regime appears. Over a wide range of time scales, flexible active polymers exhibit a hydrodynamically governed subdiffusive regime, with an exponent significantly smaller than that of the Rouse and Zimm models of passive polymers. Compared to simulations, the analytical approach predicts a weaker hydrodynamic effect. Overall, hydrodynamic interactions modify the conformational and dynamical properties of active polymers substantially.

Impact of hydrodynamic interactions on protein folding rates depends on temperature.

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue α/β chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue β-barrel α-spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a "crossover" behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

Dynamical density functional theory for circle swimmers

The majority of studies on self-propelled particles and microswimmers concentrates on objects that do not feature a deterministic bending of their trajectory. However, perfect axial symmetry is hardly found in reality, and shape-asymmetric active microswimmers tend to show a persistent curvature of their trajectories. Consequently, we here present a particle-scale statistical approach to circle-swimmer suspensions in terms of a dynamical density functional theory. It is based on a minimal microswimmer model and, particularly, includes hydrodynamic interactions between the swimmers. After deriving the theory, we numerically investigate a planar example situation of confining the swimmers in a circularly symmetric potential trap. There, we find that increasing curvature of the swimming trajectories can reverse the qualitative effect of active drive. More precisely, with increasing curvature, the swimmers less effectively push outwards against the confinement, but instead form high-density patches in the center of the trap. We conclude that the circular motion of the individual swimmers has a localizing effect, also in the presence of hydrodynamic interactions. Parts of our results could be confirmed experimentally, for instance, using suspensions of L-shaped circle swimmers of different aspect ratio.

Local NMR Relaxation of Dendrimers in the Presence of Hydrodynamic Interactions

We study the role of hydrodynamic interactions for the relaxation of segments' orientations in dendrimers. The dynamics is considered in the Zimm framework. It is shown that inclusion of correlations between segments' orientations plays a major role for the segments' mobility, that reveals itself in the NMR relaxation functions. The enhancement of the reorientation dynamics of segments due to the hydrodynamic interactions is more significant for the inner segments. This effect is clearly pronounced in the reduced spectral density $\omega J(\omega)$, whose maximum shifts to higher frequencies when the hydrodynamic interactions are taken into account.

Self-Assembly of Polymeric Particles in Poiseuille Flow: A Hybrid Lattice Boltzmann/External Potential Dynamics Simulation Study

We present a hybrid simulation method which allows one to study the dynamical evolution of self-assembling (co)polymer solutions in the presence of hydrodynamic interactions. The method combines an established dynamic density functional theory for polymers that accounts for the nonlocal character of chain dynamics at the level of the Rouse model, the external potential dynamics (EPD) model, with an established Navier–Stokes solver, the Lattice Boltzmann (LB) method. We apply the method to study the self-assembly of nanoparticles and vesicles in two-dimensional copolymer solutions in a typical microchannel Poiseuille flow profile. The simulations start from fully mixed systems which are suddenly quenched below the spinodal line. In order to isolate effects caused by walls, we use a reverse Poiseuille flow geometry with periodic boundary conditions. We identify three stages of self-assembly, i.e., initial spinodal decomposition, particle nucleation, and particle growth (ripening). We find that (i) in the presence of shear the nucleation of droplets is delayed by an amount roughly proportional to the shear rate, (ii) shear flow greatly increases the rates of particle fusions, and (iii) in later stages of self-assembly stronger shear flows may induce irreversible shape transformation via finger formation, in particular in vesicle systems. The combination of these effects leads to an accumulation of particles close to the center of the Poiseuille flow profile, and the polymeric matter has a double peak distribution centered around the flow maximum.

Dynamics of Branched Polymers in Random Layered Flows with Intramolecular Hydrodynamic Coupling: Star and Dendrimer

The authors develop a theoretical formalism to incorporate the effect of intramolecular hydrodynamic interactions (HIs) on the dynamics of flexible branched polymer in the presence of random layered flows. The influence of HIs on the anomalous diffusive behavior of branched polymers is illustrated through the preaveraged Oseen tensor approach. Although the formalism is valid for polymer structures with arbitrary topology, particular attention is paid here to the study of stars and dendrimers. The macromolecular property that is evaluated is the average square displacement (ASD) of drift center of the polymer. Qualitatively, our analysis highlights two anomalous power‐law regimes, viz. subdiffusive (intermediate‐time polymer stretching and flow induced diffusion) and superdiffusive (long‐time flow induced diffusion). The time dependence of the ASD in the presence of HIs within the preaveraging approximation reveals the anomalous long‐time dynamics which is governed by scaling behavior, t2 − α/2. The introduction of HIs in random flows speeds up the dynamics resulting in the shorter crossover time (from subdiffusive to superdiffusive regime) with enhanced magnitude of ASD compared to the free‐draining limit. image

Learning to school in the presence of hydrodynamic interactions

Schooling, an archetype of collective behaviour, emerges from the interactions of fish responding to sensory information mediated by their aqueous environment. A fundamental and largely unexplored question in fish schooling concerns the role of hydrodynamics. Here, we investigate this question by modelling swimmers as vortex dipoles whose interactions are governed by the Biot–Savart law. When we enhance these dipoles with behavioural rules from classical agent-based models, we find that they do not lead robustly to schooling because of flow-mediated interactions. We therefore propose to use swimmers equipped with adaptive decision-making that adjust their gaits through a reinforcement learning algorithm in response to nonlinearly varying hydrodynamic loads. We demonstrate that these swimmers can maintain their relative position within a formation by adapting their strength and school in a variety of prescribed geometrical arrangements. Furthermore, we identify schooling patterns that minimize the individual and collective swimming effort, through an evolutionary optimization. The present work suggests that the adaptive response of individual swimmers to flow-mediated interactions is critical in fish schooling.

How colloid–colloid interactions and hydrodynamic effects influence the percolation threshold: A simulation study in alumina suspensions

The percolation behavior of alumina suspensions is studied by computer simulations. The percolation threshold ϕc is calculated, determining the key factors that affect its magnitude: the strength of colloid–colloid attraction and the presence of hydrodynamic interactions (HIs). To isolate the effects of HIs, we compare the results of Brownian Dynamics, which do not include hydrodynamics, with those of Stochastic Rotation Dynamics–Molecular Dynamics, which include hydrodynamics. Our results show that ϕc decreases with the increase of the attraction between the colloids. The inclusion of HIs always leads to more elongated structures during the aggregation process, producing a sizable decrease of ϕc when the colloid–colloid attraction is not too strong. On the other hand, the effects of HIs on ϕc tend to become negligible with increasing attraction strength. Our ϕc values are in good agreement with those estimated by the yield stress model by Flatt and Bowen.

Significance of thermal fluctuations and hydrodynamic interactions in receptor-ligand-mediated adhesive dynamics of a spherical particle in wall-bound shear flow.

The dynamics of adhesion of a spherical microparticle to a ligand-coated wall, in shear flow, is studied using a Langevin equation that accounts for thermal fluctuations, hydrodynamic interactions, and adhesive interactions. Contrary to the conventional assumption that thermal fluctuations play a negligible role at high Péclet numbers, we find that for particles with low surface densities of receptors, rotational diffusion caused by fluctuations about the flow and gradient directions aids in bond formation, leading to significantly greater adhesion on average, compared to simulations where thermal fluctuations are completely ignored. The role of wall hydrodynamic interactions on the steady-state motion of a particle, when the particle is close to the wall, has also been explored. At high Péclet numbers, the shear induced force that arises due to the stresslet part of the Stokes dipole plays a dominant role, reducing the particle velocity significantly and affecting the states of motion of the particle. The coupling between the translational and rotational degrees of freedom of the particle, brought about by the presence of hydrodynamic interactions, is found to have no influence on the binding dynamics. On the other hand, the drag coefficient, which depends on the distance of the particle from the wall, plays a crucial role at low rates of bond formation. A significant difference in the effect of both the shear force and the position-dependent drag force on the states of motion of the particle is observed when the Péclet number is small.

Hydrodynamic interactions of deformable polymeric nanocarriers and the effect of crosslinking.

We report theoretical as well as numerical investigations of deformable nanocarriers (NCs) under physiologically relevant flow conditions. Specifically, to model the deformable lysozyme-core/dextran-shell crosslinked polymer based NC with internal nanostructure and subject it to external hydrodynamic shear, we have introduced a coarse-grained model for the NC and have adopted a Brownian dynamics framework, which incorporates hydrodynamic interactions, in order to describe the static and dynamic properties of the NC. In order to represent the fluidity of the polymer network in the dextran brush-like corona, we coarse-grain the structure of the NC based on the hypothesis that Brownian motion, polymer melt reptations, and crosslinking density dominate their structure and dynamics. In our model, we specify a crosslinking density and employ the simulated annealing protocol to mimic the experimental synthesis steps in order to obtain the appropriate internal structure of the core-shell polymer. We then compute the equilibrium as well as steady shear rheological properties as functions of the Péclet number and the crosslinking density, in the presence of hydrodynamic interactions. We find that with increasing crosslinking, the stiffness of the nanocarrier increases, the radius of gyration decreases, and as a consequence the self-diffusivity increases. The nanocarrier under shear deforms and orients along the direction of the applied shear and we find that the orientation and deformation under shear are dependent on the shear rate and the crosslinking density. We compare various dynamic properties of the NC as a function of the shear force, such as orientation, deformation, intrinsic stresses etc., with previously reported computational and experimental results of other model systems. The computational approach described here serves as a powerful tool for the rational design of NCs by taking both the physiological as well as the hydrodynamic environments into consideration. Development of such models is essential in order to gain useful insights that may be translated into the optimal design of NCs for diagnostic as well as targeted drug delivery applications.

Viscosity Radius of Polymers in Dilute Solutions: Universal Behavior from DNA Rheology and Brownian Dynamics Simulations

The swelling of the viscosity radius, αη, and the universal viscosity ratio, UηR, have been determined experimentally for linear DNA molecules in dilute solutions with excess salt, and numerically by Brownian dynamics simulations, as a function of the solvent quality. In the latter instance, asymptotic parameter free predictions have been obtained by extrapolating simulation data for finite chains to the long chain limit. Experiments and simulations show a universal crossover for αη and UηR from θ to good solvents in line with earlier observations on synthetic polymer–solvent systems. The significant difference between the swelling of the dynamic viscosity radius from the observed swelling of the static radius of gyration is shown to arise from the presence of hydrodynamic interactions in the nondraining limit. Simulated values of αη and UηR are in good agreement with experimental measurements in synthetic polymer solutions reported previously and with the measurements in linear DNA solutions reported here.

Effects of excluded volume and hydrodynamic interactions on the behavior of isolated bead‐rod polymer chains in shearing flow

A detailed study of the effects of hydrodynamic interaction (HI) and excluded volume (EV), on isolated bead‐rod chains in shear flows, where the “rods” are mimicked by stiff Fraenkel springs is presented. It is observed that the deformation behavior at weak and intermediate shear rates is qualitatively similar to that observed for polymer chains in the absence of EV and HI, while that at high‐shear rates is sensitive to modeling details and chain resolution. Our simulations with varying degrees of resolution reveal universality in chain behavior in the presence of EV (without HI), while the onset of the transition to a compressed chain in the presence of HI (without EV) shifts to higher shear rates with increasing chain resolution. The results also highlight the success of the bead‐spring models in predicting the chain behavior in shear flows in the presence of HI, when the HI parameter is appropriately chosen. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1400–1412, 2014

Rheology of a vesicle suspension with finite concentration: A numerical study

Vesicles, closed membranes made of a bilayer of phospholipids, are considered as a biomimetic system for the mechanics of red blood cells. The understanding of their dynamics under flow and their rheology is expected to help the understanding of the behavior of blood flow. We conduct numerical simulations of a suspension of vesicles in two dimensions at a finite concentration in a shear flow imposed by countertranslating rigid bounding walls by using an appropriate Green's function. We study the dynamics of vesicles, their spatial configurations, and their rheology, namely, the effective viscosity η(eff). A key parameter is the viscosity contrast λ (the ratio between the viscosity of the encapsulated fluid over that of the suspending fluid). For small enough λ, vesicles are known to exhibit tank treading (TT), while at higher λ they exhibit tumbling (TB). We find that η(eff) decreases in the TT regime, passes a minimum at a critical λ=λ(c), and increases in the TB regime. This result confirms previous theoretical and numerical works performed in the extremely dilute regime, pointing to the robustness of the picture even in the presence of hydrodynamic interactions. Our results agree also with very recent numerical simulations performed in three dimensions both in the dilute and more concentrated regime. This points to the fact that dimensionality does not alter the qualitative features of η(eff). However, they disagree with recent simulations in two dimensions. We provide arguments about the possible sources of this disagreement.

Dynamics of end-to-end loop formation: A flexible chain in the presence of hydrodynamic interaction

Based on the Wilemski–Fixman approach [G. Wilemski, M. Fixman, J. Chem. Phys. 60 (1974) 866], we show that, for a flexible chain in θ solvent, hydrodynamic interaction treated with a pre-averaging approximation makes ring closing faster if the chain is not very short. We also show that the ring closing time for a long chain with hydrodynamic interaction in θ solvent scales with the chain length (N) as N1.5, in agreement with the previous renormalization group calculation based prediction by Freidman and O’Shaughnessy [B. Friedman, B. O’Shaughnessy, Phys. Rev. A 40 (1989) 5950].