Hydrodynamics of Suspensions of Passive and Active Rigid Particles: A Rigid Multiblob Approach

We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a number of existing methods, we discretize rigid bodies using a collection of minimally-resolved spherical blobs constrained to move as a rigid body, to arrive at a potentially large linear system of equations for the unknown Lagrange multipliers and rigid-body motions. Here we develop a block-diagonal preconditioner for this linear system and show that a standard Krylov solver converges in a modest number of iterations that is essentially independent of the number of particles. For unbounded suspensions and suspensions sedimented against a single no-slip boundary, we rely on existing analytical expressions for the Rotne-Prager tensor combined with a fast multipole method or a direct summation on a Graphical Processing Unit to obtain an simple yet efficient and scalable implementation. For fully confined domains, such as periodic suspensions or suspensions confined in slit and square channels, we extend a recently-developed rigid-body immersed boundary method to suspensions of freely-moving passive or active rigid particles at zero Reynolds number. We demonstrate that the iterative solver for the coupled fluid and rigid body equations converges in a bounded number of iterations regardless of the system size. We optimize a number of parameters in the iterative solvers and apply our method to a variety of benchmark problems to carefully assess the accuracy of the rigid multiblob approach as a function of the resolution. We also model the dynamics of colloidal particles studied in recent experiments, such as passive boomerangs in a slit channel, as well as a pair of non-Brownian active nanorods sedimented against a wall.Comment: Under revision in CAMCOS, Nov 201

Bead Modeling of Transport Properties of Macromolecules in Free Solution and in a Gel

On the bead modeling methodology, or BMM, a macromolecule is modeled as a rigid, non-overlapping bead array with arbitrary radii. The BMM approach was pioneered by Kirkwood and coworkers (Kirkwood, J.G., Macromolecules, E.P. Auer (Ed.), Gordon and Breach, New York, 1967; Kirkwood, J.G., Riseman, J., J. Chem. Phys., 1948, 16, 565) and applied to such transport properties as diffusion, sedimentation, and viscosity. With the availability of computers, a number of investigators extended the work to account for the detailed shape of biomolecules in the 1970s. A principle objective of my research has been to apply the BMM approach to more complex transport phenomena such as transport in a gel, electrophoresis (free solution and in a gel), and also transport in more complex media (such as the viscosity of alkanes and benzene). Variables considered by the BMM include the number of beads (N), the radii of the beads, net charge and charge distribution, conformations, salt type, and salt concentration. The BMM has been extended to: (1) account for the existence of a gel; (2) characterize the charge and secondary structure of macromolecules; (3) account more accurately for hydrodynamic interaction (remove the orientationnal preaveraging approximation of hydrodynamic interaction); (4) study the effect of ion relaxation for particles in arbitrary size, shape, and charge; (5) consider the salt dependence of electrokinetic properties; (6) account for the formation of possible complex between guest ions and BGE ions. We also did diffusion constant measurement by NMR for amino acids and short peptides in 10%D2O-90% H2O at room temperature and applied to our modeling study by BMM

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.Comment: 27 pages, 10 figure

A fluctuating boundary integral method for Brownian suspensions

We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for generating Brownian displacements that arise in response to the thermal fluctuations in the fluid. Our approach relies on a first-kind boundary integral formulation of a mobility problem in which a random surface velocity is prescribed on the particle surface, with zero mean and covariance proportional to the Green's function for Stokes flow (Stokeslet). This approach yields an algorithm that scales linearly in the number of particles for both deterministic and stochastic dynamics, handles particles of complex shape, achieves high order of accuracy, and can be generalized to three dimensions and other boundary conditions. We show that Brownian displacements generated by our method obey the discrete fluctuation-dissipation balance relation (DFDB). Based on a recently-developed Positively Split Ewald method [A. M. Fiore, F. Balboa Usabiaga, A. Donev and J. W. Swan, J. Chem. Phys., 146, 124116, 2017], near-field contributions to the Brownian displacements are efficiently approximated by iterative methods in real space, while far-field contributions are rapidly generated by fast Fourier-space methods based on fluctuating hydrodynamics. FBIM provides the key ingredient for time integration of the overdamped Langevin equations for Brownian suspensions of rigid particles. We demonstrate that FBIM obeys DFDB by performing equilibrium BD simulations of suspensions of starfish-shaped bodies using a random finite difference temporal integrator.Comment: Submitted to J. Comp. Phy

Modeling and simulation of micro/nano-rod distribution in micro channel flows

The behavior of a typical nanorod particle in microscale flows was theoretically investigated, considering the effect of the wall on the rotational and translation motions of the non-spherical particle. Initially, a systematic method using Brownian dynamics simulation of the rotational motion of nanorod was performed to obtain the average orientation distribution of a nanorod in various range of Peclet number and position from the confining wall. Subsequently, the results of the angle distributions simulation were employed to generate a universal mathematical model for the particle orientation distribution, which our model of concentration distribution of high aspect ratio nanorods in the microchannel was later built on. We identified three different rod-wall interaction mechanisms in the entire rages of Pe. Then, the model was extended to study low and high aspect ratio ellipsoidal nanorod particle separation in a Field Flow Fractionation channel. The model can describe the aspect ratio dependent elution behavior. In addition, Brownian dynamics simulation of microchannel separation of differently sized DNA chains driven by electrophoretic properties of DNA in an electric field was studied. COMSOL Multiphysics®, a popular science and engineering simulation software based on the finite element method, was used to perform the bead-spring dynamic simulation of the semi-flexible chain. The simulation results for DNA migration in an array of entropic traps were validated with the previous findings --Abstract, page iv

Effect of Salt Concentration on the Electrophoretic Speed of a Polyelectrolyte through a Nanopore

In a previous paper [S. Ghosal, Phys. Rev. E 74, 041901 (2006)] a hydrodynamic model for determining the electrophoretic speed of a polyelectrolyte through an axially symmetric slowly varying nanopore was presented in the limit of a vanishingly small Debye length. Here the case of a finite Debye layer thickness is considered while restricting the pore geometry to that of a cylinder of length much larger than the diameter. Further, the possibility of a uniform surface charge on the walls of the nanopore is taken into account. It is thereby shown that the calculated transit times are consistent with recent measurements in silicon nanopores.Comment: 4 pages, 2 figure