Restructuring a passive colloidal suspension using a rotationally driven particle.

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.

We show that discrete element simulations of colloidal gelation must account for hydrodynamic interactions between suspended particles through investigation of gelation in a dispersion of colloids interacting pair-wise via short-ranged attraction and long-ranged repulsion (SALR). These dynamic simulations juxtapose self-assembly with and without hydrodynamic interactions between the particles. The long-ranged repulsion impacts the relative rates of coagulation and compaction of colloidal aggregates pre-gel, and introduces a surprising sensitivity to the nature of hydrodynamic interactions between the suspended colloids. For such SALR dispersions, we observe a significant disparity between the percolation boundaries predicted by simulations including and neglecting long-ranged hydrodynamic interactions. Additionally, we find that the percolation boundaries predicted by simulations including hydrodynamic interactions agree well with those measured experimentally. Long-ranged repulsion promotes gelation via growth of anisotropic clusters regardless of the hydrodynamic model employed. However, differences between the models, which persist far from the percolation boundary, are apparent via measurements of the fractal dimension, local bond order parameters, and the collective relaxation dynamics. Notably, the growth of elongated clusters is augmented in simulations that incorporate long-ranged hydrodynamic interactions due to the anisotropic diffusion of elongated bodies at low Reynolds numbers, which favors percolation over a transition of anisotropic clusters to their more isotropic ground states. It is only in relatively dense suspensions that a combination of hydrodynamic screening and significantly faster aggregation combine to bring the two simulation methods into agreement. These results demonstrate the necessity of long-ranged hydrodynamic forces in discrete element simulations of heterogeneous gelation at the colloidal scale.

The hydrodynamic transport properties of hard-sphere dispersions are calculated for volume fractions (φ) spanning the dilute limit up to the fluid–solid transition at φ=0.49. Particle distributions are generated by a Monte Carlo technique and the hydrodynamic interactions are calculated by Stokesian dynamics simulation. The effects of changing the number of particles in the simulation cell are investigated, and the scaling laws for the finite-size effects are determined. The effects of using various levels of approximation in computing both the far- and near-field hydrodynamic interactions are also examined. The transport properties associated with porous media—permeabilities and hindered diffusion coefficients—are determined here. The corresponding properties of freely mobile suspensions are determined in a companion paper [Phys. Fluids 31, xxxx (1988)].

The velocity fluctuations present in macroscopically homogeneous suspensions of neutrally buoyant non-Brownian spheres undergoing simple shear flow, and their dependence on the microstructure developed by the suspensions, are investigated in the limit of vanishingly small Reynolds numbers using Stokesian dynamics simulations. We show that, in the dilute limit, the standard deviation of the velocity fluctuations (the so-called suspension temperature) is proportional to the volume fraction, in both the transverse and the flow directions, and that a theoretical prediction, which considers only the hydrodynamic interactions between isolated pairs of spheres, is in good agreement with the numerical results at low concentrations. We also simulate the velocity fluctuations that would result from a random hard-sphere distribution of spheres in simple shear flow, and thereby investigate the effects of the microstructure on the velocity fluctuations. Analogous results are discussed for the fluctuations in the angular velocity of the suspended spheres. In addition, we present the probability density functions for all the linear and angular velocity components, and for three different concentrations, showing a transition from a Gaussian to an exponential and finally to a stretched exponential functional form as the volume fraction is decreased. The simulations include a non-hydrodynamic repulsive force between the spheres which, although extremely short range, leads to the development of fore–aft asymmetric distributions for large enough volume fractions, if the range of that force is kept unchanged. On the other hand, we show that, although the pair distribution function recovers its fore–aft symmetry in dilute suspensions, it remains anisotropic and that this anisotropy can be accurately predicted theoretically from the two-sphere solution by assuming the complete absence of any permanent doublets of spheres. We also present a simple correction to the analysis of laser-Doppler velocimetry measurements, which substantially improves the interpretation of these measurements at low volume fractions even though it involves only the angular velocity of a single sphere in the vorticity direction. Finally, in an Appendix, we show that, in the dilute limit, the whole velocity autocorrelation function can be predicted using again only two-particle encounters.

Hydrodynamic interactions (HI) are important in a variety of systems such as colloidal suspensions and polymer solutions, both near and well beyond equilibrium. Detailed particulate simulations are increasingly an important tool in exploring the behaviour of such systems. An accurate method for coarse‐graining long‐range HI is desirable for designing efficient simulations, particularly when no obvious spatial symmetries can be exploited, as in the case of isolated flexible polymer molecules in solution. A recent model [Prabhakar et al. Phys. Rev. E, 76:011809 (2007)] proposed coarse‐graining HI in a dilute polymer solution by representing a macromolecule as a chain of axisymmetric ellipsoidal Gaussian density fields, whose instantaneous dimensions are derived from their end‐to‐end stretch and orientation by invoking the assumption of local equilibrium. In this “Gaussian Blob” (GB) model, an expression was derived for the tensor describing HI between any pair of blobs. By combining the resulting mobility matrix with entropic spring force laws also based on the local equilibrium assumption, the GB model provides an alternative to the conventional bead‐spring chain model with Rotne‐Prager‐Yamakawa HI. The advantage of the new model is that it has no free parameters, and all model parameters are uniquely related back to the polymer contour length, the Kuhn step length and the hydrodynamic diameter of the polymer contour. Preliminary simulations indicated that the GB model achieved a considerable reduction in the variation of predictions with respect to the number of blobs N chosen to represent the chain in comparison with the conventional bead spring model, irrespective of whether chains are stretched, or coiled near equilibrium. In this talk, I present more detailed results to confirm the practical viability of the coarse‐grained HI used in the GB model. Firstly, the universal viscoelastic features predicted by both the GB and conventional models are identical, in the linear response regime, in strong extensional flows, and during relaxation after being initially expanded. In addition, the much smaller variation with N observed with the GB model means that a single low choice of N∼5 can be used to perform reliable and computationally efficient simulations under a variety of conditions without the necessity for adjusting parameters. I also discuss applications of this model to model more complex structures and illustrate its use with simulations for linear and nonlinear rheological properties of rod‐coil block co‐polymers.

Hydrodynamic interactions have a major impact on the suspension properties, but they are absent in atomic and molecular fluids due to a lack of intervening medium at close range. To reproduce the correct hydrodynamic interactions, lubrication correction is essential to compensate the missing short-range hydrodynamics from the fluids. However, lubrication correction requires many simulations in particle-based simulations of colloidal suspensions. To address the problem, we employ an active learning strategy based on Gaussian process regression (GPR) for normal and tangential lubrication corrections to significantly reduce the number of necessary simulations and apply the correction to the coupled multiscale simulation of monodisperse hard-sphere colloidal suspensions. In particular, a single-particle dissipative particle dynamics (DPD) model with parameter correction is used to describe the solvent-solvent and colloid-solvent interactions, and a discrete element method (DEM) model to depict the colloid-colloid frictional contacts. The lubrication correction results demonstrate that only six and four independent simulations (observation points for GPR training) are required to achieve accurate normal and tangential lubrication corrections, respectively. To validate the machine learning of lubrication correction based on GPR, we investigate the self-diffusion coefficients of colloids, suspension rheology and microstructure using the coupled DPD-DEM model with GPR lubrication correction. Our simulation results show that the machine learning of lubrication correction based on GPR is effective and the lubrication corrected DPD-DEM model is indeed capable of accurately capturing hydrodynamic interactions and correctly reproducing dynamical and rheological properties of colloidal suspensions. Moreover, the machine learning of lubrication correction based on GPR is not limited to the coupled DPD-DEM simulation of colloidal suspensions presented here, but can be easily applied to other particle-based simulations of particulate suspensions.

The lattice Boltzmann method is applied to simulate the rheology of particle suspensions with low-to-moderate fluid inertia and a wide range of particle inertia. The viscous dissipation in a suspension of particles with a Maxwellian velocity distribution is shown to have a linear dependence on the Reynolds number similar to the Ergun correlation for the drag in a fixed bed of particles. Dynamic simulations of the flow of a suspension of elastic particles being sheared between two rough walls are used to determine the range of Reynolds and Stokes numbers for which a treatment of a homogeneous, sheared suspension based on kinetic theory and the simulated viscous dissipation can accurately describe the particle-phase kinetic energy and effective viscosity of the suspension. The dependence of the particle-phase slip velocity and the depletion of particles near the boundaries on the particle volume fraction and Stokes number is determined.

We develop a general framework for modeling the hydrodynamic self-propulsion (i.e., swimming) of bodies (e.g., microorganisms) at low Reynolds number via Stokesian Dynamics simulations. The swimming body is composed of many spherical particles constrained to form an assembly that deforms via relative motion of its constituent particles. The resistance tensor describing the hydrodynamic interactions among the individual particles maps directly onto that for the assembly. Specifying a particular swimming gait and imposing the condition that the swimming body is force- and torque-free determine the propulsive speed. The body’s translational and rotational velocities computed via this methodology are identical in form to that from the classical theory for the swimming of arbitrary bodies at low Reynolds number. We illustrate the generality of the method through simulations of a wide array of swimming bodies: pushers and pullers, spinners, the Taylor/Purcell swimming toroid, Taylor’s helical swimmer, Purcell’s three-link swimmer, and an amoeba-like body undergoing large-scale deformation. An open source code is a part of the supplementary material and can be used to simulate the swimming of a body with arbitrary geometry and swimming gait.

We consider tracer diffusion in colloidal suspensions under solid loading conditions, where hydrodynamic interactions play an important role. To this end, we carry out computer simulations based on the hybrid stochastic rotation dynamics-molecular dynamics (SRD-MD) technique. Many details of the simulation method are discussed in detail. In particular, our choices for the SRD-MD parameters and for the different scales are adapted to simulating colloidal suspensions under realistic conditions. Our simulation data are compared with published theoretical, experimental and numerical results and compared to Brownian dynamics simulation data. We demonstrate that our SRD-MD simulations reproduce many features of the hydrodynamics in colloidal fluids under finite loading. In particular, finite-size effects and the diffusive behavior of colloids for a range of volume fractions of the suspension show that hydrodynamic interactions are correctly included within the SRD-MD technique.

Electrorotation of colloidal suspensions

<div class="htmlview paragraph">Vehicle roll dynamics is strongly influenced by suspension properties such as roll center height, roll steer and roll camber. In this paper, the effects of suspension properties on vehicle roll response has been investigated using a multi-body vehicle dynamics program.</div> <div class="htmlview paragraph">A full vehicle model equipped with front MacPherson and rear multilink suspensions has been used for the study. Roll dynamics of the vehicle were evaluated by performing fixed timing fishhook maneuver in the simulation. Variations of vehicle roll response due to changes in the suspension properties were assessed by quantitatively analyzing the vehicle response through simulation.</div> <div class="htmlview paragraph">Critical suspension design parameters for vehicle roll dynamics were identified and adjusted to improve roll stability of the vehicle model with passive suspension. Design of Experiments has been used for identifying critical hardpoints affecting the suspension parameters and optimization techniques were employed for parameter optimization. This approach provides a viable alternative to costlier active control systems for economy class vehicles.</div>

We describe a practical approach for computing the mobility matrix of a system of colloidal particles near a hard wall. The approach can be carried out in principle to arbitrary accuracy and number of particles. We make use of this approach to perform Stokesian dynamics computer simulations of colloidal suspensions in both unbounded and bounded fluids. We study finite clusters of particles sedimenting parallel to a nearby hard wall under the influence of a uniform force. The convergence properties of the new scheme, the effect of the wall on the colloidal dynamics, and the additional effect of interparticle and wall–particle potentials are all examined.

An active suspension system attempts to overcome these compromises so as to provide the best performance for controlling the vehicle. A fully active suspension system aims to control the suspension over the full bandwidth, increase load carrying capacity, handling and ride quality. A model for vehicle’s dynamics while using an active suspension system has been developed. The equations are cast in both the state space form and transfer function forms. To compare the ideal system and a real system, a comparative analysis is also performed by incorporating various sensing and actuation constraints such as time delay and discrete sampling. Simple PID as well as feed-forward controllers is designed and the response is simulated for various disturbances such as road excitations and those arising due to cornering. Parameter studies are also performed to assess the response to various suspension properties. The comparison of the active suspension with respect to the passive suspension indicates significant improvement in performance characteristics such as riding comfort, tendency to rollover and road traction. The studies on the effect of sensing and actuation constraints provide valuable insights into the use of low-cost and/or robust control system elements. Full vehicle model, State space equation, Passive and active suspension system, PID controller, Road profile, MATLAB and SIMULINK

Hydrodynamic and electrokinetic effects on the dynamics of charged colloids andmacromolecules

Interaction between humic acid and montmorillonite in the presence of calcium ions II. Colloidal interactions: Charge state, dispersing and/or aggregation of particles in suspension