Full Hydrodynamic Interactions Research Articles

Active Stokesian dynamics

Since its development, Stokesian dynamics has been a leading approach for the dynamic simulation of suspensions of particles at arbitrary concentrations with full hydrodynamic interactions. Although developed originally for the simulation of passive particle suspensions, the Stokesian dynamics framework is equally well suited to the analysis and dynamic simulation of suspensions of active particles, as we elucidate here. We show how the reciprocal theorem can be used to formulate the exact dynamics for a suspension of arbitrary active particles, and then show how the Stokesian dynamics method provides a rigorous way to approximate and compute the dynamics of dense active suspensions where many-body hydrodynamic interactions are important.

Collision efficiency of non-Brownian spheres in a simple shear flow – the role of non-continuum hydrodynamic interactions

We study the collisions in a gaseous medium of a dilute bidisperse suspension of non-Brownian spherical particles sedimenting along the flow axis of a simple shear flow. Continuum lubrication forces prevent particles from coming into contact in a finite time, thus collisions can occur only due to attractive interactions such as the van der Waals force. However, in a low-pressure medium, the lubrication forces are weaker than their continuum counterparts and allow particle pairs to collide, even without any attractive forces. The Knudsen number, defined as the ratio of the mean free path of the medium to the mean radius of the interacting spheres, captures the significance of non-continuum interactions. We use uniformly valid hydrodynamic mobility functions, reflecting non-continuum lubrication at small separations and full continuum hydrodynamic interactions at moderate to larger separations. Due to the nature of the pair trajectory topology, the collision efficiency vanishes at a critical Knudsen number when simple shear flow alone drives the dynamics. Thus we perform collision calculations where particles experience the combined effects of van der Waals attraction and non-continuum hydrodynamics; van der Waals interactions enable collisions below the critical Knudsen number. Next, we calculate the collision efficiency for coupled differential sedimentation and simple shear driven motion in the presence of van der Waals interaction and non-continuum hydrodynamics. Finally, we explore the role of small particle inertia on relative trajectories and collision efficiencies in a non-continuum gas subject to a simple shear flow, ignoring the van der Waals force and gravity.

Collision rate of bidisperse, hydrodynamically interacting spheres settling in a turbulent flow

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Exact axisymmetric interaction of phoretically active Janus particles

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Nonaffinity and Fluid-Coupled Viscoelastic Plateau for Immersed Fiber Networks.

We employ a matrix-based solver for the linear rheology of fluid-immersed disordered spring networks to reveal four distinct dynamic response regimes. One regime-completely absent in the known vacuum response-exhibits coupled fluid flow and network deformation, with both components responding nonaffinely. This regime contains an additional plateau (peak) in the frequency-dependent storage (loss) modulus-features that vanish without full hydrodynamic interactions. The mechanical response of immersed networks such as biopolymers and hydrogels is thus richer than previously established and offers additional modalities for design and control through fluid interactions.

Rheology of polymers in many-body dissipative particle dynamics simulations: Schmidt number effect

The Schmidt number effect on the rheology of finitely extensible nonlinear elastic chains (FENE) in many-body dissipative particle dynamics (MDPD) is investigated in this work. We find that the Schmidt number, ranging from (101) to (103), has limited influence on the polymer properties, such as its radius of gyration (Rg), diffusion coefficient (D) and relaxation time (τ). The simulation results follow Zimm model's predictions well. The hydrodynamic interaction strength parameter h* demonstrates that the full hydrodynamic interaction can be simulated for Schmidt number from (100-106) in MDPD. Next, the rheology of FENE polymers is studied using Lees-Edward boundary condition in shear flow. The shear-thinning and normal stress difference are measured and analysed with MDPD; meanwhile, the volume fraction, solvent quality and chain length are varied to explore their effects on the extent of the Newtonian region. Finally, the non-Newtonian droplet is firstly simulated in MDPD. Its maximum spreading diameter is measured for both Newtonian and non-Newtonian droplet with Weber number (We) ranging from 4.37 to 109.2 on hydrophilic, moderate and hydrophobic surfaces, respectively. The fluid shear-thinning property increases at high shear rate and is further enhanced on more hydrophobic surface, from the maximum spreading diameter results. The non-Newtonian (FENE) droplet can be now well simulated in MDPD and this provides additional insight to further research concerning polymer-solvent-surface interactions, which is crucial in various applications.

Bistability in the synchronization of actuated microfilaments

Cilia and flagella are essential building blocks for biological fluid transport and locomotion at the micrometre scale. They often beat in synchrony and may transition between different synchronization modes in the same cell type. Here, we investigate the behaviour of elastic microfilaments, protruding from a surface and driven at their base by a configuration-dependent torque. We consider full hydrodynamic interactions among and within filaments and no slip at the surface. Isolated filaments exhibit periodic deformations, with increasing waviness and frequency as the magnitude of the driving torque increases. Two nearby but independently driven filaments synchronize their beating in-phase or anti-phase. This synchrony arises autonomously via the interplay between hydrodynamic coupling and filament elasticity. Importantly, in-phase and anti-phase synchronization modes are bistable and coexist for a range of driving torques and separation distances. These findings are consistent with experimental observations of in-phase and anti-phase synchronization in pairs of cilia and flagella and could have important implications on understanding the biophysical mechanisms underlying transitions between multiple synchronization modes.

Chemotactic and hydrodynamic effects on collective dynamics of self-diffusiophoretic Janus motors

Collective motion in nonequilibrium steady state suspensions of self-propelled Janus motors driven by chemical reactions can arise due to interactions coming from direct intermolecular forces, hydrodynamic flow effects, or chemotactic effects mediated by chemical gradients. The relative importance of these interactions depends on the reactive characteristics of the motors, the way in which the system is maintained in a steady state, and properties of the suspension, such as the volume fraction. From simulations of a microscopic hard collision model for the interaction of fluid particles with the Janus motor we show that dynamic cluster states exist and determine the interaction mechanisms that are responsible for their formation. The relative importance of chemotactic and hydrodynamic effects is identified by considering a microscopic model in which chemotactic effects are turned off while the full hydrodynamic interactions are retained. The system is maintained in a steady state by means of a bulk reaction in which product particles are reconverted into fuel particles. The influence of the bulk reaction rate on the collective dynamics is also studied.

Rational design and dynamics of self-propelled colloidal bead chains: from rotators to flagella

The quest for designing new self-propelled colloids is fuelled by the demand for simple experimental models to study the collective behaviour of their more complex natural counterparts. Most synthetic self-propelled particles move by converting the input energy into translational motion. In this work we address the question if simple self-propelled spheres can assemble into more complex structures that exhibit rotational motion, possibly coupled with translational motion as in flagella. We exploit a combination of induced dipolar interactions and a bonding step to create permanent linear bead chains, composed of self-propelled Janus spheres, with a well-controlled internal structure. Next, we study how flexibility between individual swimmers in a chain can affect its swimming behaviour. Permanent rigid chains showed only active rotational or spinning motion, whereas longer semi-flexible chains showed both translational and rotational motion resembling flagella like-motion, in the presence of the fuel. Moreover, we are able to reproduce our experimental results using numerical calculations with a minimal model, which includes full hydrodynamic interactions with the fluid. Our method is general and opens a new way to design novel self-propelled colloids with complex swimming behaviours, using different complex starting building blocks in combination with the flexibility between them.

An iterative method for hydrodynamic interactions in Brownian dynamics simulations of polymer dynamics

Brownian Dynamics (BD) simulations are a standard tool for understanding the dynamics of polymers in and out of equilibrium. Quantitative comparison can be made to rheological measurements of dilute polymer solutions, as well as direct visual observations of fluorescently labeled DNA. The primary computational challenge with BD is the expensive calculation of hydrodynamic interactions (HI), which are necessary to capture physically realistic dynamics. The full HI calculation, performed via a Cholesky decomposition every time step, scales with the length of the polymer as O(N3). This limits the calculation to a few hundred simulated particles. A number of approximations in the literature can lower this scaling to O(N2 - N2.25), and explicit solvent methods scale as O(N); however both incur a significant constant per-time step computational cost. Despite this progress, there remains a need for new or alternative methods of calculating hydrodynamic interactions; large polymer chains or semidilute polymer solutions remain computationally expensive. In this paper, we introduce an alternative method for calculating approximate hydrodynamic interactions. Our method relies on an iterative scheme to establish self-consistency between a hydrodynamic matrix that is averaged over simulation and the hydrodynamic matrix used to run the simulation. Comparison to standard BD simulation and polymer theory results demonstrates that this method quantitatively captures both equilibrium and steady-state dynamics after only a few iterations. The use of an averaged hydrodynamic matrix allows the computationally expensive Brownian noise calculation to be performed infrequently, so that it is no longer the bottleneck of the simulation calculations. We also investigate limitations of this conformational averaging approach in ring polymers.

Controlled propulsion and separation of helical particles at the nanoscale.

Controlling the motion of nano and microscale objects in a fluid environment is a key factor in designing optimized tiny machines that perform mechanical tasks such as transport of drugs or genetic material in cells, fluid mixing to accelerate chemical reactions, and cargo transport in microfluidic chips. Directed motion is made possible by the coupled translational and rotational motion of asymmetric particles. A current challenge in achieving directed and controlled motion at the nanoscale lies in overcoming random Brownian motion due to thermal fluctuations in the fluid. We use a hybrid lattice-Boltzmann molecular dynamics method with full hydrodynamic interactions and thermal fluctuations to demonstrate that controlled propulsion of individual nanohelices in an aqueous environment is possible. We optimize the propulsion velocity and the efficiency of externally driven nanohelices. We quantify the importance of the thermal effects on the directed motion by calculating the Péclet number for various shapes, number of turns and pitch lengths of the helices. Consistent with the experimental microscale separation of chiral objects, our results indicate that in the presence of thermal fluctuations at Péclet numbers >10, chiral particles follow the direction of propagation according to its handedness and the direction of the applied torque making separation of chiral particles possible at the nanoscale. Our results provide criteria for the design and control of helical machines at the nanoscale.

Nanoparticle stochastic motion in the inertial regime and hydrodynamic interactions close to a cylindrical wall.

We have carried out direct numerical simulations (DNS) of the fluctuating Navier-Stokes equation together with the particle equations governing the motion of a nanosized particle or nanoparticle (NP) in a cylindrical tube. The effects of the confining boundary, its curvature, particle size, and particle density variations have all been investigated. To reveal how the nature of the temporal correlations (hydrodynamic memory) in the inertial regime is altered by the full hydrodynamic interaction due to the confining boundaries, we have employed the Arbitrary Lagrangian-Eulerian (ALE) method to determine the dynamical relaxation of a spherical NP located at various positions in the medium over a wide span of time scales compared to the fluid viscous relaxation time τv = a2/v, where a is the spherical particle radius and v is the kinematic viscosity. The results show that, as compared to the behavior of a particle in regions away from the confining boundary, the velocity autocorrelation function (VACF) for a particle in the lubrication layer initially decays exponentially with a Stokes drag enhanced by a factor that is proportional to the ratio of the particle radius to the gap thickness between the particle and the wall. Independent of the particle location, beyond time scales greater than a2/v, the decay is always algebraic followed by a second exponential decay (attributed to the wall curvature) that is associated with a second time scale D2/v, where D is the vessel diameter.

Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions

In this work we develop the Spectral Ewald Accelerated Stokesian Dynamics (SEASD), a novel computational method for dynamic simulations of polydisperse colloidal suspensions with full hydrodynamic interactions. SEASD is based on the framework of Stokesian Dynamics (SD) with extension to compressible solvents, and uses the Spectral Ewald (SE) method [Lindbo and Tornberg (2010) [29]] for the wave-space mobility computation. To meet the performance requirement of dynamic simulations, we use Graphic Processing Units (GPU) to evaluate the suspension mobility, and achieve an order of magnitude speedup compared to a CPU implementation. For further speedup, we develop a novel far-field block-diagonal preconditioner to reduce the far-field evaluations in the iterative solver, and SEASD-nf, a polydisperse extension of the mean-field Brownian approximation of Banchio and Brady (2003) [39]. We extensively discuss implementation and parameter selection strategies in SEASD, and demonstrate the spectral accuracy in the mobility evaluation and the overall O(Nlog⁡N) computation scaling. We present three computational examples to further validate SEASD and SEASD-nf in monodisperse and bidisperse suspensions: the short-time transport properties, the equilibrium osmotic pressure and viscoelastic moduli, and the steady shear Brownian rheology. Our validation results show that the agreement between SEASD and SEASD-nf is satisfactory over a wide range of parameters, and also provide significant insight into the dynamics of polydisperse colloidal suspensions.

Computation of shear viscosity of colloidal suspensions by SRD-MD

The behaviour of sheared colloidal suspensions with full hydrodynamic interactions (HIs) is numerically studied. To this end, we use the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) method. The shear viscosity of colloidal suspensions is computed for different volume fractions, both for dilute and concentrated cases. We verify that HIs help in the collisions and the streaming of colloidal particles, thereby increasing the overall shear viscosity of the suspension. Our results show a good agreement with known experimental, theoretical, and numerical studies. This work demonstrates the ability of SRD-MD to successfully simulate transport coefficients that require correct modelling of HIs.

Optimizing wave energy parks with over 1000 interacting point-absorbers using an approximate analytical method

Large arrays of wave energy converters of point-absorber type are studied using an approximate analytical model. The model is validated against a numerical method that takes into account full hydrodynamic interactions based on linear potential flow theory. The low computational cost of the analytical model enables parameter studies of parks in the MW range and includes up to over 1000 interacting devices. The model is actuated by irregular wave data obtained at the Swedish west coast. In particular, focus is on comparing park geometries and improving park configurations to minimize the power fluctuations.

Modeling the behavior of confined colloidal particles under shear flow.

We investigate the behavior of colloidal suspensions with different volume fractions confined between parallel walls under a range of steady shears. We model the particles using molecular dynamics (MD) with full hydrodynamic interactions implemented through the use of a lattice-Boltzmann (LB) fluid. A quasi-2d ordering occurs in systems characterized by a coexistence of coupled layers with different densities, order, and granular temperature. We present a phase diagram in terms of shear and volume fraction for each layer, and demonstrate that particle exchange between layers is required for entering the disordered phase.

Biopolymer Filtration in Corrugated Nanochannels

We examine pressure-driven nonequilibrium transport of linear, circular, and star polymers through a nanochannel containing a rectangular pit with full hydrodynamic interactions and thermal fluctuations. We demonstrate that with sufficiently small pressure differences, there is contour length-dependent entropic trapping of the polymer in the pit when the pit and the polymer sizes are compatible. This is due to competition between flow and chain relaxation in the pit, which leads to a nonmonotonic dependence of the polymer mobility on its size and should aid in the design of nanofiltration devices based on the polymer size and shape.

The medium amplitude oscillatory shear of semi-dilute colloidal dispersions. Part I: Linear response and normal stress differences

We study the medium amplitude oscillatory shear (MAOS) of a semi-dilute, hard-sphere colloidal dispersion. Through solution of the Smoluchowski equation governing the statistical distribution of suspended particles in the semi-dilute limit, we calculate the linear viscoelasticity and the normal stress differences that arise from oscillatory shear as an expansion in terms of small rates of deformation. The effects of hydrodynamic versus conservative interactions are studied via the excluded-annulus model for the hard-sphere interactions. This treats the hard-sphere interactions as a steric barrier that resides beyond the hydrodynamic radius of the particles and allows for continuous variation of the strength of hydrodynamic interactions. We see remarkable distinctions between suspensions that are freely draining and those for which hydrodynamic lubrication among the particles dominate their motion. In oscillatory shear flow of a freely draining suspension at high-frequency, the normal stress differences are generated by hard-sphere stresses. In contrast, for a hydrodynamically interacting suspension at high-frequency, the first normal stress difference derives from Brownian stresses while the second normal stress difference is dominated by hydrodynamic stresses. When the first normal stress difference is plotted parametrically against the oscillatory rate of strain, the resulting Lissajous-Bowditch curves for freely draining suspensions and those with full hydrodynamic interactions take on distinct and disparate shapes. Additionally, we use an asymptotic analysis to predict that the third harmonic of the suspension stress for hard spheres is dominated by the hydrodynamic lubrication in the limit of high frequency oscillation. Our calculations demonstrate that under MAOS, hydrodynamic interactions play a central and qualitative role in the stress response of a semi-dilute colloidal dispersion.

Shear-induced dynamics of polymeric globules at adsorbing homogeneous and inhomogeneous surfaces

The dynamics and adsorption behavior of a single collapsed homopolymer on a surface in shear flow is investigated by means of Brownian hydrodynamics simulations. We study different homogeneous and inhomogeneous surface models and determine dynamic state diagrams as a function of the cohesive strength, the adhesive strength, and the shear rate. We find distinct dynamical adsorbed states that are classified into rolling and slipping states, globular and coil-like states, as well as isotropic and prolate states. We identify two different cyclic processes based on trajectories of the polymer stretching and the polymer separation from the surface. For adsorption on an inhomogeneous surface consisting of discrete binding sites, we observe stick-roll motion for highly corrugated surface potentials. Although the resulting high surface friction leads to low drift velocities and reduced hydrodynamic lift forces on such inhomogeneous surfaces, a shear-induced adsorption is not found in the presence of full hydrodynamic interactions. A hydrodynamically stagnant surface model is introduced for which shear-induced adsorption is observed in the absence of hydrodynamic interactions.

Performance of large arrays of point absorbing direct-driven wave energy converters

Future commercial installation of wave energy plants using point absorber technology will require clusters of tens up to several hundred devices, in order to reach a viable electricity production. Interconnected devices also serve the purpose of power smoothing, which is especially important for devices using direct-driven power take off. The scope of this paper is to evaluate a method to optimize wave energy farms in terms of power production, economic viability, and resources. In particular, the paper deals with the power variation in a large array of point-absorbing direct-driven wave energy converters, and the smoothing effect due to the number of devices and their hydrodynamic interactions. A few array geometries are compared and 34 sea states measured at the Lysekil research site at the Swedish west coast are used in the simulations. Potential linear flow theory is used with full hydrodynamic interactions between the buoys. It is shown that the variance in power production depends crucially on the geometry of the array and the number of interacting devices, but not significantly on the energy period of the waves.