Range Hydrodynamic Interactions Research Articles

The role of hydrodynamic interactions on the aggregation kinetics of sedimenting colloidal particles.

The aggregation kinetics of sedimenting colloidal particles under fully destabilized conditions has been investigated over a wide range of particle volume fractions (Φ) and Péclet numbers (Pe) using the recent PSE algorithm implementing the Rotne-Prager-Yamakawa (RPY) approximation for long-range Hydrodynamic Interactions (HI). Fast Lubrication Dynamics (FLD) and simple Brownian Dynamics (BD) methods have also been employed to assess the importance of long range hydrodynamic interactions on the resulting dynamics. It has been observed that long-range hydrodynamic interactions are essential to capture the fast aggregation rates induced by the increase in sedimentation rate of clusters with increasing mass, which manifests with an explosive-like cluster growth after a given induction time. On the contrary, simulations employing only short-range hydrodynamic interactions (such as FLD) and BD (which neglects completely hydrodynamic interactions) are incapable of predicting this very rapid kinetics, because sedimentation simply leads to all particles and clusters moving vertically with identical velocity. It has been observed that at high volume fractions and low Pe values, a gel point can be formed and a phase diagram predicting when gelation is reached has been obtained. It was also observed that, as Pe increases, the anisotropy of the resulting clusters decreases, suggesting that denser clusters with spherical-like morphology are formed due to cluster breakage and restructuring. We can conclude that long-range hydrodynamic effects are of crucial importance in understanding the aggregation dynamics of settling clusters, revealing important features of the complex interplay between sedimentation, and colloidal interactions.

Clogging transition induced by self filtration in a slit pore.

Particles that flow through porous environments like soils, inside a filter or within our arteries, often lead to pore clogging. Even though tremendous efforts have been made in analysing this to circumvent this issue, the clog formation and its dynamics remain poorly understood. Coupling two experimental techniques, we elucidate the clogging mechanism at the particle scale of a slit pore with its height slightly larger than the particle diameter. We identify all the particle deposition modes during the clog formation and accurately predict the corresponding deposition rate. We show how the geometrical features of the pores and the competition between deposition modes can profoundly change the clog morphology. We find that the direct capture of particles by the pore wall is rather limited. The clog formation is more closely related to the short range hydrodynamic interaction between flowing particles and those which are already immobilized within the pore. Finally we demonstrate that all the clogging regimes can be gathered on a single phase diagram based on the flow conditions and the filter design.

Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear

We present a 3D numerical investigation of the viscometric functions for suspensions in viscoelastic fluids under steady shear including comparisons with theoretical predictions in the dilute regime and experimental results for non-colloidal suspensions in a Boger fluid. The comparison with dilute suspension theoretical predictions resolves a discrepancy in the literature regarding the second normal stress difference calculated using the Landau–Lifshitz averaging procedure versus using the ensemble averaging procedure. We also determine that the particle contribution to the stress in a dilute suspension in viscoelastic fluids shear-thickens in all viscometric material properties and we present the scaling of the viscometric functions with the Weissenberg number (Wi). This shear-thickening behavior is fundamentally different from that shown in 2D numerical simulations which are attributed to elongation flow effects between particles. Comparisons with experimental results at volume fraction ϕ=0.05, which is the lowest volume fraction available in existing experimental measurements of bulk viscometric functions, highlight the important role of long range hydrodynamic interactions between particles to fully describe the suspension rheology even at low volume fractions. We investigate the effect of hydrodynamic interactions in the flow, vorticity, and gradient directions and show that these interactions can greatly enhance or decrease the viscometric functions as well as change the shear rate dependent behavior of the suspension.

Numerical simulations of the rheology of suspensions of rigid spheres at low volume fraction in a viscoelastic fluid under shear

We present a 3D numerical investigation of the viscometric functions for suspensions in viscoelastic fluids under steady shear including comparisons with theoretical predictions in the dilute regime and experimental results for non-colloidal suspensions in a Boger fluid. The comparison with dilute suspension theoretical predictions resolves a discrepancy in the literature regarding the second normal stress difference calculated using the Landau–Lifshitz averaging procedure versus using the ensemble averaging procedure. We also determine that the particle contribution to the stress in a dilute suspension in viscoelastic fluids shear-thickens in all viscometric material properties and we present the scaling of the viscometric functions with Weissenberg number (Wi). This shear-thickening behavior is fundamentally different from that shown in 2D numerical simulations which are attributed to elongation flow effects between particles. Comparisons with experimental results at volume fraction ϕ=0.05, which is the lowest volume fraction available in existing experimental measurements of bulk viscometric functions, highlight the important role of long range hydrodynamic interactions between particles to fully describe the suspension rheology even at low volume fractions. We investigate the effect of hydrodynamic interactions in the flow, vorticity, and gradient directions and show that these interactions can greatly enhance or decrease the viscometric functions as well as change the shear rate dependent behavior of the suspension.

Dynamics of two interacting active Janus particles.

Starting from a microscopic model for a spherically symmetric active Janus particle, we study the interactions between two such active motors. The ambient fluid mediates a long range hydrodynamic interaction between two motors. This interaction has both direct and indirect hydrodynamic contributions. The direct contribution is due to the propagation of fluid flow that originated from a moving motor and affects the motion of the other motor. The indirect contribution emerges from the re-distribution of the ionic concentrations in the presence of both motors. Electric force exerted on the fluid from this ionic solution enhances the flow pattern and subsequently changes the motion of both motors. By formulating a perturbation method for very far separated motors, we derive analytic results for the translation and rotational dynamics of the motors. We show that the overall interaction at the leading order modifies the translational and rotational speeds of motors which scale as O[1/D](3) and O[1/D](4) with their separation, respectively. Our findings open up the way for studying the collective dynamics of synthetic micro-motors.

Modeling Paramecium swimming in a capillary tube

In certain types of biomimetic surgery systems, micro robots inspired by Paramecium are designed to swim in a capillary tube for gaining access to internal organs with minimal invasion. Gaining insights into the mechanics of Paramecium swimming in a capillary tube is vital for optimizing the design of such systems. There are two approaches to modeling the physics of micro swimming. In the envelope approach which is widely accepted by researchers, Paramecium is approximated as a sphere self-propelled by tangential and normal surface distortions. Not only this approach is incapable of considering the specific geometry of Paramecium, but also it neglects short range hydrodynamic interactions due to beating cilia. Thus it leads to dissimilarity between experimental data and simulation results. In this study, it is aimed to present a sub layer approach to modeling Paramecium locomotion which is capable of directly applying the hydrodynamic interactions due to beating cilia on Paramecium boundary. In this approach, Paramecium’s boundary is discretized to hydrodynamically independent elements; in each time step of swimming, a specific function is fit to Paramecium boundary. Then, element coordinates are extracted and fluid dynamic equations are solved to model the physics of micro swimming.

Can we reduce debris flow to an equivalent one-phase flow?

A recent extension of the discrete element method is reported for the simulation of dense mixtures of non-colloidal particles and viscous fluids in the non-inertial regime. As an application, we examine the interplay between rate dependent dilatancy and hydro-mechanical coupling which can be expected in debris flow. The numerical model includes sphere-sphere contacts using a soft contact approach [2], short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique [3]. The bulk shear stress is decomposed into contact stress and hydrodynamic stress. Both contributions are shown to be increasing functions of a dimensionless shear rate Iv, in agreement with experimental results [4]. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared satured granular media in which pore pressure feedback plays a key role. We argue that it can be the case for debris fow, especially during the triggering phase, when run-out include transitional phases, and when the flow is stopped. It is then concluded that debris cannot be computed by assuming solely the rheological properties of an equivalent mixture.

Microscopic origins of shear stress in dense fluid–grain mixtures

A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere–sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant expressions of forces and torques in the lubrication approximation, and drag forces resulting from the poromechanical coupling computed with the DEM-PFV technique. Series of simulations in which some of the coupling terms are neglected highlight the role of the poromechanical coupling in the transient regimes. They also reveal that the shear component of the lubrication forces, though frequently neglected in the literature, has a dominant effect in the volume changes. On the other hand, the effects of lubrication torques are much less significant. The bulk shear stress is decomposed into contact stress and hydrodynamic stress terms whose dependency on a dimensionless shear rate—the so called viscous number \(I_v\)—are examined. Both contributions are increasing functions of \(I_v\), contacts contribution dominates at low viscous number (\(I_v<0.15\)) whereas lubrication contributions are dominant for \(I_v> 0.15\), consistently with a phenomenological law infered by other authors. Statistics of microstructural variables highlight a complex interplay between solid contacts and hydrodynamic interactions. In contrast with a popular idea, the results suggest that lubrication may not necessarily reduce the contribution of contact forces to the bulk shear stress. The proposed model is general and applies directly to sheared immersed granular media in which pore pressure feedback plays a key role (triggering of avalanches, liquefaction).

Rectified motion in an asymmetric channel: the role of hydrodynamic interactions with walls.

Dynamics of a Brownian particle in an asymmetric microchannel that is subjected to an external oscillating force is numerically analyzed. In addition to the elastic collisions with the walls that are kind of short range interactions, the long range hydrodynamic influences of the walls have been considered in an approximate way. We demonstrate how the geometrical parameters of the channel change the rectified current of the particle. As a result of numerical calculations, we show that long range hydrodynamic interactions with walls decrease the efficiency of the Brownian ratchet.

Hydrodynamic simulations of self-phoretic microswimmers

A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines stick boundary conditions with colloid-solvent potential interactions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus particles. A comparative study of Janus and microdimer phoretic swimmers is performed in terms of their swimming velocities and induced flow behavior. Self-phoretic microdimers display long range hydrodynamic interactions with a decay of 1/r(2), which is similar to the decay of gradient fields generated by self-phoretic particle, and can be characterized as pullers or pushers. In contrast, Janus particles are characterized by short range hydrodynamic interactions with a decay of 1/r(3) and behave as neutral swimmers.

Hydrodynamic interaction induced spontaneous rotation of coupled active filaments.

We investigate the coupled dynamics of active filaments with long range hydrodynamic interactions (HI). Remarkably, we find that filaments can rotate spontaneously under the same conditions in which a single filament alone can only move in translation. Detailed analysis reveals that the emergence of coupled rotation originates from an asymmetric flow field associated with HI which breaks the symmetry of translational motion when filaments approach. The breaking is then further stabilized by HI to form self-sustained coupled rotation. Intensive simulations show that coupled rotation forms easily when one filament tends to collide with the front-half of the other. For head-to-tail approaching, we observe another interesting HI-induced coupled motion, where filaments move together in the form of one following the other. Moreover, the radius of coupled rotation increases exponentially as the rigidity of the filament increases, which suggests that HI are also important for the alignment of rigid-rod-like filaments which has been assumed to be solely a consequence of direct collisions.

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: Algorithm and limitations

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N(3)) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions.

Chain deformation in translocation phenomena

Deformation of single stranded DNA in a translocation process before reaching the pore is investigated. By solving the Laplace equation in a suitable coordinate system and with appropriate boundary conditions, an approximate solution for the electric field inside and outside a narrow pore is obtained. With an analysis based on the “electrohydrodynamic equivalence” we determine the possibility of the extension of a charged polymer due to the presence of an electric field gradient in the vicinity of the pore entrance. With a multi-scale hybrid simulation (LB-MD), it is shown that an effective deformation before reaching the pore occurs, which facilitates the process of finding the entrance for the end monomers. We also highlight the role of long range hydrodynamic interactions via comparison of the LB-MD results with those obtained using a Langevin thermostat instead of the LB solver.

Unusual response to a localized perturbation in a generalized elastic model

The generalized elastic model encompasses several physical systems such as polymers, membranes, single-file systems, fluctuating surfaces, and rough interfaces. We consider the case of an applied localized potential, namely, an external force acting only on a single (tagged) probe, leaving the rest of the system unaffected. We derive the fractional Langevin equation for the tagged probe, as well as for a generic (untagged) probe, where the force is not directly applied. Within the framework of the fluctuation-dissipation relations, we discuss the unexpected physical scenarios arising when the force is constant and time periodic, whether or not the hydrodynamic interactions are included in the model. For short times, in the case of the constant force, we show that the average drift is linear in time for long-range hydrodynamic interactions and behaves ballistically or exponentially for local hydrodynamic interactions. Moreover, it can be opposite to the direction of the external disturbance for some values of the model's parameters. When the force is time periodic, the effects are macroscopic: the system splits into two distinct spatial regions whose size is proportional to the value of the applied frequency. These two regions are characterized by different amplitudes and phase shifts in the response dynamics.

Traffic Jams and Intermittent Flows in Microfluidic Networks

We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a nonlinear process: the particle current does not scale with the particle density even in the dilute limit where no particle collision occurs. We demonstrate that this nonlinear behavior stems from long-range hydrodynamic interactions. Importantly, we also establish that there exists a maximal current above which no stationary particle flow can be sustained. For higher current values, intermittent traffic jams form, thereby inducing the ejection of the particles from the initial path and the subsequent invasion of the network. Eventually, we put our findings in the broader context of the transport processes of driven particles in low dimension.

Viscosity of Dilute Model Bead Arrays at Low Shear: Inclusion of Short Range Solute−Solvent Interactions

The intrinsic viscosity, [eta], of certain polymer-solvent systems, such as alkanes in benzene, are "anomalous" in the sense that [eta] for low molecular weight fractions are low and in certain cases negative (Dewan, K. K.; Bloomfield, V. A.; Berget, P. G.; J. Phys. Chem. 1974, 75, 3120). In this work, the theory of the viscosity of a dilute suspension of macromolecules at low shear is formulated that accounts for possible solute-solvent interactions. In doing so, we show that negative intrinsic viscosities are possible and are able to reproduce quite well the known length dependence of [eta] for alkanes in benzene. The coarse grained, solvent continuum, bead model developed here is an extension of previous work (Allison, S. A.; Pei, H. J. Phys. Chem. B 2009, 113, 8056). Following Fixman (Fixman, M. J. Chem. Phys. 1990, 92, 6858), we assume that solute-solvent interactions are short-range in character and can be separated from long-range hydrodynamic interactions between different beads. These interactions are accounted for by introducing three adjustable parameters specific to the transport of small "monomeric" solutes in the solvent of interest. Long range hydrodynamic interactions are accounted for to order a(J)(2)/r(IJ)(3) (a(J) is a bead radius and r(IJ) is an interbead distance). In modeling a macromolecule as an arbitrary array of N beads, the transport of the array is examined numerically in 5 different elementary shear fields. The most computationally demanding component of the procedure involves the inversion of a 12N by 12N matrix. In the present work, we restrict ourselves to systems with a maximum N of about 100. Our procedure is first applied to short rods and rings of from 2 to 10 beads which can be compared with independent results from the literature. Agreement is found to be better than 5%. Modeling macromolecules as wormlike chains, the procedure is then applied first to duplex DNA and then to alkanes in benzene. In both cases, it is possible to obtain excellent agreement between modeling and experiment.

Dynamic simulation of arbitrarily shaped particles in shear flow

A new simulation framework was created for modeling the dynamics of arbitrarily shaped particles dispersed in Newtonian fluid. Theoretical complexity usually restricts suspension simulations to those for spheroids. This new simulation is loosely based on the Stokesian Dynamics method including long range hydrodynamic interaction and uses spheres as building components for greater particulates of arbitrary shape. This approach is capable of accurately reproducing the dynamics of an isolated arbitrarily shaped particle. As verification, the simulated results are compared against known results for a rod-like particle. An elongated rod-shaped structure made from linked spheres is shown to reproduce the well-known elongated ellipsoidal particle dynamics described by [Jeffrey Proc R Soc Lond A 102:161–179, 1923]. The predicted orbital period and spin rates for a fiber in shear are reproduced and compare well with theoretical prediction over a wide aspect ratio range. Predicted particle dynamics for other shaped particles are then demonstrated.

Self-diffusion coefficient in dense hard sphere colloids

By means of hard sphere Brownian dynamics simulation technique, it was confirmed that the ratio of short- and long-self diffusion coefficient is not affected whether the solvent-mediated long range hydrodynamic interaction exists or not, and that the density dependence of diffusion coefficient is well represented by the theory of Tokuyama and Oppenheim.

Stability analysis and scattering properties of charged crosslinked blends in solution

AbstractThe phase behavior and scattering properties of crosslinked charged polymer blends in solution are examined. De Gennes' analogy between the effects of crosslinks in a network and electrostatic charges in a dielectric medium on the scattering properties and the phase behavior of crosslinked polymer blends is used. This analogy is extended to include the effects of screening in order to improve its agreement with the experimental data in the small q range. The excluded volume interactions are explicitely introduced through the blob model. The enhancement of compatibility of the mixture and the increase of its rigidity constant are evaluated in certain cases. The limit of neutral polymers is discussed because it corresponds to the case of charged mixtures in the presence of excess salt. The kinetics of the microphase separation transition is briefly discussed. A dynamical model including the long range hydrodynamic interaction is presented. The relaxation frequency of the stable modes and the growth rate of unstable ones are also considered.

Analysis of particle trajectories of small particles in flotation when the particles and bubbles are both charged

AbstractThe trajectory of a small particle moving to a bubble surface was analyzed by taking into account the effects of surface charges of the bubble and particle and the short range hydrodynamic interaction near the bubble surface, in a flotation process. The particle trajectories obtained theoretically were in good agreement with those obtained by direct observation. Even if the signs of the surface charges of the bubble and particle were the same, the particle adhered to the bubble surface when the net surface force, that is, the sum of the electrostatic force and the van der Waals force, was attractive. Particle capture efficiency, ηS, per bubble was estimated by trajectory analysis and the flotation efficiency, ηT, was calculated. The values of ηT calculated by the particle trajectory analysis were in reasonable agreement with those obtained experimentally. The dependence of particle diameter on ηT was also examined by the particle trajectory analysis.