James W. Swan

Simulation of hydrodynamically interacting particles near a no-slip boundary

The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite—something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry.

Directed colloidal self-assembly in toggled magnetic fields

Suspensions of paramagnetic colloids are driven to phase separate and self-assemble by a toggled magnetic field. Initially, all suspensions form network structures that span the sample cell. When the magnetic field is toggled, this network structure coarsens diffusively for a time that scales exponentially with frequency. Beyond this break through time, suspensions cease diffusive coarsening and undergo an apparent instability. The magnetic field drives suspensions to condense into dispersed, domains of bodycentered tetragonal crystals. Within these domains the crystalline order depends on the pulse frequency. Because the scaling of the break through time with respect to frequency is exponential, the steady state limit corresponding to an infinite pulse frequency is kinetically arrested and the equilibrium state is unreachable. These experiments show that there is an out-of-equilibrium pathway that can be used to escape a kinetically arrested state as well as a diverging time scale for phase separation as the critical frequency for condensation is approached. Rather than fine tuning the strength of the interactions among particles, a simple annealing scheme - toggling of the magnetic field - is used to create a broad envelope for assembly of ordered particle structures.

Particle motion between parallel walls: Hydrodynamics and simulation

The low-Reynolds-number motion of a single spherical particle between parallel walls is determined from the exact reflection of the velocity field generated by multipoles of the force density on the particle’s surface. A grand mobility tensor is constructed and couples these force multipoles to moments of the velocity field in the fluid surrounding the particle. Every element of the grand mobility tensor is a finite, ordered sum of inverse powers of the distance between the walls. These new expressions are used in a set of Stokesian dynamics simulations to calculate the translational and rotational velocities of a particle settling between parallel walls and the Brownian drift force on a particle diffusing between the walls. The Einstein correction to the Newtonian viscosity of a dilute suspension that accounts for the change in stress distribution due to the presence of the channel walls is determined. It is proposed how the method and results can be extended to computations involving many particles and periodic simulations of suspensions in confined geometries.

Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

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.

Large amplitude oscillatory microrheology

We study the motion of a colloidal particle as it is driven by an oscillating external force of arbitrary amplitude and frequency through a colloidal dispersion. Large amplitude oscillatory flows (LAOFs) are examined predominantly from a phenomenological perspective in which experimental measurements inform constitutive models. Here, we investigate a LAOF from a microstructural perspective by connecting motion of the probe particle to the material response while making no assumptions a priori about how stress relaxes in the material. The suspension exerts nonconservative, hydrodynamic forces on the probe, while distortions in the particle configuration exert conservative forces: Brownian and interparticle forces, for example. The relative importance of each of these contributions to particle motion evolves with the degree of displacement from equilibrium. When the force on the probe is weak, the linear microviscoelasticity of the suspension is probed [see, e.g., Khair and Brady, J. Rheol. 49, 1449–1481 (2005)]. When oscillation rate is slow, the steady microrheology is probed [see, e.g., Squires and Brady, Phys. Fluids 17, 073101 (2005); Khair and Brady, J. Fluid Mech. 557, 73–117 (2006)]. This article develops a micromechanical model that recovers these limiting cases and then uses the same model to reveal the microrheology of colloidal dispersions deformed by a probe driven with arbitrary force amplitude and frequency. A chief result of this work is the discovery of a regime in which the resistance to motion of the probe particle is on average weaker than the resistance the probe experiences when deformed by high frequency oscillation. This hypoviscous effect arises when the reciprocating motion of the probe particle opens a channel free of other particles which is thus less resistive to probe motion. This effect is most apparent under the conditions of strong forces, rapid oscillation, and large extent of deformation.

Multi-scale kinetics of a field-directed colloidal phase transition

Polarizable colloids are expected to form crystalline equilibrium phases when exposed to a steady, uniform field. However, when colloids become localized this field-induced phase transition arrests and the suspension persists indefinitely as a kinetically trapped, percolated structure. We anneal such gels formed from magneto-rheological fluids by toggling the field strength at varied frequencies. This processing allows the arrested structure to relax periodically to equilibrium—colloid-rich, cylindrical columns. Two distinct growth regimes are observed: one in which particle domains ripen through diffusive relaxation of the gel, and the other where the system-spanning structure collapses and columnar domains coalesce apparently through field-driven interactions. There is a stark boundary as a function of magnetic field strength and toggle frequency distinguishing the two regimes. These results demonstrate how kinetic barriers to a colloidal phase transition are subverted through measured, periodic variation of driving forces. Such directed assembly may be harnessed to create unique materials from dispersions of colloids.

Active microrheology: Fixed-velocity versus fixed-force

In active microrheology, a probe particle is driven by an external force through a complex medium and its motion studied in order to infer properties of the embedding material. It is conducted in two limiting forms: either the probe is propelled by a fixed force, as with magnetic tweezers, or it is driven at a fixed velocity, as with optical tweezers. Recent work has shown that the mean probe motion can be interpreted as an effective material viscosity, but that this viscosity depends on whether the fixed-force or fixed-velocity mode is employed. We compute the effective viscosity probed by fixed-velocity active microrheology of a dilute colloidal dispersion. A comparison is made between this new result and the effective viscosity probed in the fixed-force mode. In the absence of hydrodynamic interactions, the particle-phase contributions to the effective viscosity for the two modes differ by exactly a factor of two. A simple scaling argument has been previously advanced to rationalize this difference: in...

Lipid Exchange Envelope Penetration (LEEP) of Nanoparticles for Plant Engineering: A Universal Localization Mechanism

Nanoparticles offer clear advantages for both passive and active penetration into biologically important membranes. However, the uptake and localization mechanism of nanoparticles within living plants, plant cells, and organelles has yet to be elucidated.1 Here, we examine the subcellular uptake and kinetic trapping of a wide range of nanoparticles for the first time, using the plant chloroplast as a model system, but validated in vivo in living plants. Confocal visible and near-infrared fluorescent microscopy and single particle tracking of gold-cysteine-AF405 (GNP-Cys-AF405), streptavidin-quantum dot (SA-QD), dextran and poly(acrylic acid) nanoceria, and various polymer-wrapped single-walled carbon nanotubes (SWCNTs), including lipid-PEG-SWCNT, chitosan-SWCNT and 30-base (dAdT) sequence of ssDNA (AT)15 wrapped SWCNTs (hereafter referred to as ss(AT)15-SWCNT), are used to demonstrate that particle size and the magnitude, but not the sign, of the zeta potential are key in determining whether a particle is spontaneously and kinetically trapped within the organelle, despite the negative zeta potential of the envelope. We develop a mathematical model of this lipid exchange envelope and penetration (LEEP) mechanism, which agrees well with observations of this size and zeta potential dependence. The theory predicts a critical particle size below which the mechanism fails at all zeta potentials, explaining why nanoparticles are critical for this process. LEEP constitutes a powerful particulate transport and localization mechanism for nanoparticles within the plant system.

On the hydrodynamics of ‘slip–stick’ spheres

The breakdown of the no-slip condition at fluid–solid interfaces generates a host of interesting fluid-dynamical phenomena. In this paper, we consider such a scenario by investigating the low-Reynolds-number hydrodynamics of a novel ‘slip–stick’ spherical particle whose surface is partitioned into slip and no-slip regions. In the limit where the slip length is small compared to the size of the particle, we first compute the translational velocity of such a particle due to the force density on its surface. Subsequently, we compute the rotational velocity and the response to an ambient straining field of a slip–stick particle. These three Faxen-type formulae are rich in detail about the dynamics of the particles: chiefly, we find that the translational velocity of a slip–stick sphere is coupled to all of the moments of the force density on its surface; furthermore, such a particle can migrate parallel to the velocity gradient in a shear flow. Perhaps most important is the coupling we predict between torque and translation (and force and rotation), which is uncharacteristic of spherical particles in unbounded Stokes flow and originates purely from the slip–stick asymmetry.

Dynamic, Directed Self-Assembly of Nanoparticles via Toggled Interactions

Crystals self-assembled from nanoparticles have useful properties such as optical activity and sensing capability. During fabrication, however, gelation and glassification often leave these materials arrested in defective or disordered metastable states. This is a key difficulty preventing adoption of self-assembled nanoparticle materials at scale. Processes which suppress kinetic arrest and defect formation while accelerating growth of ordered materials are essential for bottom-up approaches to creating nanomaterials. Dynamic, directed self-assembly processes in which the interactions between self-assembling components are actuated temporally offer one promising methodology for accelerating and controlling bottom-up growth of nanostructures. In this article, we show through simulation and theory how time-dependent, periodically toggled interparticle attractions can avoid kinetic barriers and yield well-ordered crystalline domains for a dispersion of nanoparticles interacting via a short-ranged, isotropic potential. The growth mechanism and terminal structure of the dispersion are controlled by parameters of the toggling protocol. This control allows for selection of processes that yield rapid self-assembled, low defect crystals. Although self-assembly via periodically toggled attractions is inherently unsteady and out-of-equilibrium, its outcome is predicted by a first-principles theory of nonequilibrium thermodynamics. The theory necessitates equality of the time average of pressure and chemical potential in coexisting phases of the dispersion. These quantities are evaluated using well known equations of state. The phase behavior predicted by this theory agrees well with measurements made in Brownian dynamics simulations of sedimentation equilibrium and homogeneous nucleation. The theory can easily be extended to model dynamic self-assembly directed by other toggled conservative force fields.