Jason E. Butler

Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries.

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].

Flow-induced migration of polymers in dilute solution

We investigate the lateral migration of a confined polymer under pressure driven and uniform shear flows. We employ a hybrid algorithm which couples point particles to a fluctuating lattice-Boltzmann fluid. We observe migration in both uniform shear and pressure driven flows, supporting the idea that migration is driven by a combination of shear and hydrodynamic interactions with the wall, rather than by the shear gradient. Recent numerical and theoretical investigations have suggested that polymers migrate toward the centerline when hydrodynamic interactions are included, but our simulations show that in sufficiently narrow channels there is a reversal of direction and the polymers move toward the wall.

Improving the effectiveness of interfacial trapping in removing single-walled carbon nanotube bundles.

Single-walled carbon nanotube (SWNT) bundles are selectively removed from an aqueous dispersion containing individually suspended carbon nanotubes coated with gum Arabic via interfacial trapping. The suspensions are characterized with absorbance, fluorescence, and Raman spectroscopy as well as atomic force microscopy (AFM) and rheology. The resulting aqueous suspensions have better dispersion quality after interfacial trapping and can be further improved by altering the processing conditions. A two-step extraction process offers a simple and fast approach to preparing high-quality dispersions of individual SWNTs comparable to ultracentrifugation. Partitioning of SWNTs to the liquid-liquid interface is described by free energy changes. SWNT bundles prefer to reside at the interface over individually suspended SWNTs because of greater free energy changes.

Experimental investigation of the instability of a sedimenting suspension of fibres

Observations of the flow structures formed by rigid fibres of high aspect ratio sedimenting within a viscous fluid at a Reynolds number of approximately 10 −4 confirm the existence of an instability as reported in previous theories, experiments, and numerical simulations. Using data generated from particle image velocimetry measurements, we quantify the sedimentation structures over a wide range of parameters, which include the height of fluid, cross-section of the sedimentation cell, fibre dimensions, fluid properties, and volume fractions ranging from dilute to semi-dilute. Alternating structures of streamers and backflow regions which span the height of the sedimentation cell form at short times and transition from large wavelengths to smaller wavelength as the sedimentation proceeds. No simple dependence of the horizontal wavelength on the length scales and concentration was observed in the experiments, suggesting the need for additional analysis. We also report the mean velocities and velocity fluctuations; the strength of the velocity fluctuations strongly correlates with the size of the vertical component of the sedimentation structure. Measurements of the orientation distribution, using an efficient and newly employed technique, agree with previously published results. A movie is available with the online version of the paper.

Correlation between stresses and microstructure in concentrated suspensions of non-Brownian spheres subject to unsteady shear flows

Stresses within unsteady simple shear flows of suspensions of non-Brownian spheres constrained to move in the velocity-gradient plane are calculated using Stokesian dynamics simulations. The unsteady flows considered include shear reversal and oscillatory flows of varying strain amplitude. The evolution of the stresses in time are reported along with the corresponding microstructural development for all flow conditions. For shear reversal, the shear stress rapidly decreases to a minimum before gradually returning to the steady state value reached in the previous direction, whereas the normal stress briefly changes sign upon reversal of shear before returning to the steady state value. For oscillatory shear flow, the shear stress increases with total strain before attaining a steady state that depends upon the applied strain amplitude, indicating irreversible behavior even at small strain amplitudes. The shear stresses show a nonmonotonic dependence on the applied strain amplitude that agrees with experime...

Kinetic theory of a confined polymer driven by an external force and pressure-driven flow

Kinetic theory is used to investigate the mechanisms causing cross-stream migration of confined polymers and polyelectrolytes under the influence of external forces and flow fields. Numerical simulations and experiments have demonstrated that confined polymers migrate towards the center of the channel in response to both external forces and uniaxial flows. Yet, migration towards the walls has been observed with combinations of external force and flow. In this paper, the kinetic theory for an elastic dumbbell developed by Ma and Graham [Phys. Fluids 17, 083103 (2005)] has been extended to account for the effects of an external force. Further modifications account for counterion screening within a Debye-Huckel approximation. This enables qualitative comparison with experimental results [Zheng and Yeung, Anal. Chem. 75, 3675 (2003)] on DNA migration under combined electric and pressure-driven flow fields. The comparison supports the contention [Long et al., Phys. Rev. Lett. 76, 3858 (1996)] that the hydrodyn...

Simulations of concentrated suspensions of rigid fibers: Relationship between short-time diffusivities and the long-time rotational diffusion

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.

Comparison of the static and dynamic properties of a semiflexible polymer using lattice Boltzmann and Brownian-dynamics simulations.

The aim of this paper is to compare results from lattice Boltzmann and Brownian-dynamics simulations of linear chain molecules. We have systematically varied the parameters that may affect the accuracy of the lattice Boltzmann simulations including grid resolution, temperature, polymer mass, and fluid viscosity. The effects of the periodic boundary conditions are minimized by an analytic correction for the different long-range interactions in periodic and unbounded systems. Lattice Boltzmann results for the diffusion coefficient and Rouse mode relaxation times were found to be insensitive to temperature, which suggests that effects of hydrodynamic retardation are small. By increasing the resolution of the lattice Boltzmann grid with respect to the polymer size, convergent results for the diffusion coefficient and relaxation times were obtained; these results agree with Brownian dynamics to within 1%-2%.

Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Peclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech ., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech ., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev . E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

A cloud of rigid fibres sedimenting in a viscous fluid

Experiments and numerical simulations have been performed to investigate the deformation and break-up of a cloud of rigid fibres falling under gravity through a viscous fluid in the absence of inertia and interfacial tension. The cloud of fibres is observed to evolve into a torus that subsequently becomes unstable and breaks up into secondary droplets which themselves deform into tori in a repeating cascade. This behaviour is similar to that of clouds of spherical particles, though the evolution of the cloud of fibres occurs more rapidly. The simulations, which use two different levels of approximation of the far-field hydrodynamic interactions, capture the evolution of the cloud and demonstrate that the coupling between the self-motion and hydrodynamically induced fluctuations are responsible for the faster break-up time of the cloud. The dynamics of the cloud are controlled by a single parameter which is related to the self-motion of the anisotropic particles. The experiments confirm these findings.