Rotating colloids in rotating magnetic fields: Dipolar relaxation and hydrodynamic coupling.

Absolute Protein-Protein Association Rate Constants from Flexible, Coarse-Grained Brownian Dynamics Simulations: The Role of Intermolecular Hydrodynamic Interactions in Barnase-Barstar Association

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

The long time self-diffusion of highly charged colloidal particles consisting of polybutylacrylate was studied employing pulsed field gradient NMR (PFGNMR) and Brownian dynamics (BD) simulations. The potential parameters for the Yukawa interaction potential used in the BD simulations were derived from the static structure factor measured by means of light scattering. The long time self-diffusion coefficients resulting from NMR and BD were compared for different ionic strengths, which cause a screening of the interaction potential due to stray ions. Increasing the ionic strength of the colloidal suspensions, we observed a phase transition from a crystalline to a liquidlike structure. Whereas at high salt concentrations both long time diffusion coefficients agree within a few percent, at intermediate ionic strengths the values measured via PFGNMR are by a factor of 2 higher than those predicted by the BD simulation. This deviation is explained by hydrodynamic interactions which are expected to enhance long time self-diffusion and which are not taken into account in our BD algorithm.

Weakly conducting dielectric particles suspended in a dielectric liquid of higher conductivity can undergo a transition to spontaneous sustained rotation when placed in a sufficiently strong dc electric field. This phenomenon of Quincke rotation has interesting implications for the rheology of these suspensions, whose effective viscosity can be controlled and reduced by application of an external field. While previous models based on the rotation of isolated particles have provided accurate estimates for this viscosity reduction in dilute suspensions, discrepancies have been reported in more concentrated systems where particle-particle interactions are likely significant. Motivated by this observation, we extend the classic description of Quincke rotation based on the Taylor-Melcher leaky dielectric model to account for pair electrohydrodynamic interactions between two identical spheres using the method of reflections. A coupled system of evolution equations for the dipole moments and angular velocities of the spheres is derived that accounts for electric dipole-dipole interactions and hydrodynamic rotlet interactions up to order O(R(-5)), where R is the separation distance between the spheres. A linear stability analysis of this system shows that interactions modify the value of the critical electric field for the onset of Quincke rotation: both electric and hydrodynamic interactions can either stabilize or destabilize the system depending on the orientation of the spheres, but the leading effect of interactions on the onset of rotation is hydrodynamic. We also analyze the dynamics in the nonlinear regime by performing numerical simulations of the governing equations. In the case of a pair of spheres that are fixed in space, we find that particle rotations always synchronize in magnitude at long times, though the directions of rotation of the spheres need not be the same. The steady-state angular velocity magnitude depends on the configuration of the spheres and electric field strength and agrees very well with an asymptotic estimate derived for corotating spheres. In the case of freely-suspended spheres, dipolar interactions are observed to lead to a number of distinct behaviors depending on the initial relative configuration of the spheres and on any infinitesimal initial perturbation introduced in the system: in some cases the spheres slowly separate in space while steadily rotating, while in other cases they pair up and either corotate or counterrotate depending on their orientation relative to the field.

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.

We use lattice Boltzmann simulations, in conjunction with Ewald summation methods, to investigate the role of hydrodynamic interactions in colloidal suspensions of dipolar particles, such as ferrofluids. Our work addresses volume fractions phi of up to 0.20 and dimensionless dipolar interaction parameters lambda of up to 8. We compare quantitatively with Brownian dynamics simulations, in which many-body hydrodynamic interactions are absent. Monte Carlo data are also used to check the accuracy of static properties measured with the lattice Boltzmann technique. At equilibrium, hydrodynamic interactions slow down both the long-time and the short-time decays of the intermediate scattering function S(q, t), for wavevectors close to the peak of the static structure factor S(q), by a factor of roughly two. The long-time slowing is diminished at high interaction strengths, whereas the short-time slowing (quantified via the hydrodynamic factor H(q)) is less affected by the dipolar interactions, despite their strong effect on the pair distribution function arising from cluster formation. Cluster formation is also studied in transient data following a quench from lambda = 0; hydrodynamic interactions slow the formation rate, again by a factor of roughly two.

To begin to elucidate the principles of intermolecular dynamics in the crowded environment of cells, employing brownian dynamics (BD) simulations, we examined possible mechanism(s) responsible for the great reduction in diffusion constants of macromolecules in vivo from that at infinite dilution. In an Escherichia coli cytoplasm model comprised of 15 different macromolecule types at physiological concentrations, BD simulations of molecular-shaped and equivalent sphere representations were performed with a soft repulsive potential. At cellular concentrations, the calculated diffusion constant of GFP is much larger than experiment, with no significant shape dependence. Next, using the equivalent sphere system, hydrodynamic interactions (HI) were considered. Without adjustable parameters, the in vivo experimental GFP diffusion constant was reproduced. Finally, the effects of nonspecific attractive interactions were examined. The reduction in diffusivity is very sensitive to macromolecular radius with the motion of the largest macromolecules dramatically slowed down; this is not seen if HI dominate. In addition, long-lived clusters involving the largest macromolecules form if attractions dominate, whereas HI give rise to significant, size independent intermolecular dynamic correlations. These qualitative differences provide a testable means of differentiating the importance of HI vs. nonspecific attractive interactions on macromolecular motion in cells.

The importance of wave-current interaction effects on the determination of mean drift forces on floating offshore structures is well documented. Wave-current interaction effects will also influence the first-order motions and loads as well as the diffracted and radiated waves around the structure. One of the significant contributions to the influence of wave-current interaction effects on the motion responses is the additional coupling between motion modes due to the current. These effects are well known from seakeeping calculations of ships with forward speed. A structure with fore-aft symmetry will have no hydrodynamic coupling between heave and pitch in regular waves only. Due to the presence of a current, the symmetry of the flow around the body is lost, resulting in hydrodynamic coupling between the modes. This will also occur for a moored structure with slowly varying motions in the horizontal plane. The most important couplings are from the heave motion into pitch and surge and from heave to roll and sway. These couplings are otherwise present only for asymmetric structures. Due to the presence of the heave resonance and cancellation periods, the motion responses in roll and pitch for a semi-submersible will be influenced by the wave-current interaction effects. Due to the differences in phase between the different motion modes, the hydrodynamic coupling may have significant influence on the rotational motions roll and pitch and thus significant influence on the prediction of airgap. This coupling between the heave and roll/pitch modes due to the current adds complexity to the numerical simulations since the structure responses are more sensitive to the actual orientation of the structure, mooring configuration etc. A three-dimensional linear potential flow code, MULDIF, has been developed by SINTEF Ocean. This code accounts for hydrodynamic interaction between waves and current from arbitrary directions. The code can be applied to single or multiple bodies in infinite or finite water depth. Verification studies have previously shown good agreement with other numerical codes, Hermundstad et.al. [1], Zhiyuan et.al [2]. Validation studies with emphasis on airgap and comparison with experimental results are presented and numerical results for airgap and upwell are visualized and discussed. It is demonstrated how MULDIF can be used in airgap studies.

We have measured the mean square displacement of a particle (MSD) and mean product of displacement of a particle and that of another particle (x-MSD) in two-dimensional (2d) and three-dimensional (3d) colloidal crystals for the first time using digital video microscopy. These (x-)MSDs have been compared to an overdamped bead-spring lattice model with effective viscous drag γeff (the OBS-γeff model). The observed 3d system contained ordered structures created by sedimentation equilibrium adjacent to the internal cell wall and was regarded as the (1 1 1) surface of a face-centered cubic lattice. The observed 2d system was a single layer of hexagonal-like ordered structures which were generated in a certain region of the space between the flat surface of the internal cell wall and a convex lens. In the observed time region, the MSDs for 2d system and 3d system were in good agreement with the theoretical MSDs for 2d system and 3d system, which were predicted to logarithmically diverge and to converge, respectively. The observed x-MSDs for the 2d system were in disagreement with theoretical ones in short time behavior. For the 3d system, the disagreement between the theory and the experimental results were found in the amplitudes as well as in the short time behavior. It was assumed that these differences were caused by the hydrodynamic coupling which was not fully incorporated in the OBS-γeff, and an improved treatment, the OBS-cutoff model was introduced. The OBS-γeff elongates the relaxation time of each mode with the constant ratio of γeff/γ, while the OBS-cutoff assumes the relaxation time of the modes to be infinity if the wave number of a mode is larger than a certain cutoff wave number. For the 3d system, the MSD and x-MSD for nearest neighbors obtained from the OBS-cutoff were in excellent agreement with the observed ones. In addition, it was found that the hydrodynamic interaction was the dominant factor on the short time behavior of (x-)MSD.

Cilia and flagella often exhibit synchronized behavior; this includes phase locking, as seen in Chlamydomonas, and metachronal wave formation in the respiratory cilia of higher organisms. Since the observations by Gray and Rothschild of phase synchrony of nearby swimming spermatozoa, it has been a working hypothesis that synchrony arises from hydrodynamic interactions between beating filaments. Recent work on the dynamics of physically separated pairs of flagella isolated from the multicellular alga Volvox has shown that hydrodynamic coupling alone is sufficient to produce synchrony. However, the situation is more complex in unicellular organisms bearing few flagella. We show that flagella of Chlamydomonas mutants deficient in filamentary connections between basal bodies display markedly different synchronization from the wild type. We perform micromanipulation on configurations of flagella and conclude that a mechanism, internal to the cell, must provide an additional flagellar coupling. In naturally occurring species with 4, 8, or even 16 flagella, we find diverse symmetries of basal body positioning and of the flagellar apparatus that are coincident with specific gaits of flagellar actuation, suggesting that it is a competition between intracellular coupling and hydrodynamic interactions that ultimately determines the precise form of flagellar coordination in unicellular algae.

We review some results concerning the dynamics of ionic solutions that we have recently obtained by Brownian dynamics simulations; we also present new results concerning the dynamical behavior of asymmetrical electrolytes (1–10 and 2–20 electrolytes). The Brownian dynamics treats the solution in the framework of the continuous solvent model, with a ‘soft-core’ version of the primitive model. Both direct interactions and hydrodynamic interactions between solutes are taken into account in the calculations. The method allows one to obtain the self-diffusion coefficient of each ion and the electrical conductivity of the solution. The computed transport coefficients are in good agreement with experimental determinations in various cases (in aqueous solutions of 1–1 electrolytes as well as in aqueous solutions of micelles). We show that hydrodynamic interactions must be taken into account to obtain electrical conductivities in agreement with experiments. The effect of hydrodynamic interactions on the self-diffusion is also striking, especially in solutions of asymmetrical electrolytes. If this effect remains weak in simple electrolyte solutions and for small ions in 1–20 and 2–20 electrolyte solutions, it is great for macroions in latter solutions (increase of about 15 to 40%).

Brownian Dynamics Simulations of Aldolase Binding Glyceraldehyde 3-Phosphate Dehydrogenase and the Possibility of Substrate Channeling

Based on Brownian Dynamics (BD) simulations, we study the dynamical self-assembly of active Brownian particles with dipole-dipole interactions, stemming from a permanent point dipole at the particle center. The propulsion direction of each particle is chosen to be parallel to its dipole moment. We explore a wide range of motilities and dipolar coupling strengths and characterize the corresponding behavior based on several order parameters. At low densities and low motilities, the most important structural phenomenon is the aggregation of the dipolar particles into chains. Upon increasing the particle motility, these chain-like structures break, and the system transforms into a weakly correlated isotropic fluid. At high densities, we observe that the motility-induced phase separation is strongly suppressed by the dipolar coupling. Once the dipolar coupling dominates the thermal energy, the phase separation disappears, and the system rather displays a flocking state, where particles form giant clusters and move collective along one direction. We provide arguments for the emergence of the flocking behavior, which is absent in the passive dipolar system.

We have elucidated the feasibility of trapping magnetic rod-like particles that flow in a cylindrical pipe in terms of a non-uniform magnetic field. We have performed Brownian dynamics (BD) simulations in order to clarify the influence that various factors have on the attachment or trapping characteristics of magnetic rod-like particles to the poles. The employment of a local linearisation approximation enables us to apply the BD method that was fully-developed for a simple shear flow to the present Hagen-Poiseuille flow. In the case of a sufficiently small magnetic interaction between the particles, numerous rod-like particles may attach to the magnetic poles if the influence of a non-uniform magnetic field is sufficiently more dominant than that of the flow field, otherwise, the particles flow away along the centreline of the cylindrical pipe. If the magnetic interactions are sufficiently more dominant than both the flow field and the non-uniform magnetic field, the particles aggregate to form densely-packed clusters that flow away along the centreline area of the pipe without being trapped at the poles. In the situation of insufficient magnetic interactions, thin chain-like clusters may be formed from several anchored particles trapped to the poles and incline in the downstream direction.

Larmor frequency dependent NMR studies of dipolar order relaxation in liquid crystals have seldom been tried in the past. Using conventional static magnetic field techniques, the experiment cannot be extended to the low Larmor frequency (νL) regime due to limitations in the signal-to-noise ratio of the dipolar echo. In this work, we present an experimental study of the dipolar relaxation time in the frequency range 103–7×107 Hz in nematic thermotropic liquid crystals. To extend the study to such low frequencies, we used the Jeener–Broekaert pulse sequence combined with fast field-cycling NMR technique. For frequencies higher than 105 Hz, the dipolar relaxation time T1D(νL) follows the νL1/2-law that is characteristic of order fluctuations of the director (OFD) in nematics. In contrast, the Zeeman relaxation is driven by faster and less correlated motions, specially in the MHz frequency range. The relaxation of dipolar energy was measured to be remarkably faster than the one predicted by the usual semiclassical model of isolated spin pairs. Conceivably, the failure of the usual two-spin model should be sought in the absence of multispin interactions and multispin correlations. We propose that the OFD are the dominant relaxation mechanism for the dipolar order, even in the MHz regime. This result turns T1D(νL) experiment in a useful NMR technique for the study of slow molecular dynamics in mesophases.