J. Ravi Prakash

Implicit and explicit solvent models for the simulation of a single polymer chain in solution: Lattice Boltzmann versus Brownian dynamics

We present a comparative study of two computer simulation methods to obtain static and dynamic properties of dilute polymer solutions. The first approach is a recently established hybrid algorithm based on dissipative coupling between molecular dynamics and lattice Boltzmann (LB), while the second is standard Brownian dynamics (BD) with fluctuating hydrodynamic interactions. Applying these methods to the same physical system (a single polymer chain in a good solvent in thermal equilibrium) allows us to draw a detailed and quantitative comparison in terms of both accuracy and efficiency. It is found that the static conformations of the LB model are distorted when the box length L is too small compared to the chain size. Furthermore, some dynamic properties of the LB model are subject to an L(-1) finite-size effect, while the BD model directly reproduces the asymptotic L-->infinity behavior. Apart from these finite-size effects, it is also found that in order to obtain the correct dynamic properties for the LB simulations, it is crucial to properly thermalize all the kinetic modes. Only in this case, the results are in excellent agreement with each other, as expected. Moreover, Brownian dynamics is found to be much more efficient than lattice Boltzmann as long as the degree of polymerization is not excessively large.

Universal viscometric functions for dilute polymer solutions

The Gaussian approximation has been shown previously to be excellent for the treatment of hydrodynamic effects in dilute polymer solutions. However, the computational time required to find the viscometric functions in simple shear flow is prohibitively long for chains with a large number of beads. Here we introduce a new approximation which retains the accuracy of the Gaussian approximation but is significantly less computationally intensive. Thus the rheological behavior of long chains may be explored. Extrapolation of results obtained numerically for long chains to the infinite chain length limit is shown to lead to predictions independent of model parameters. As a result, within the context of the approximation introduced here, universal viscometric functions for dilute polymer solutions in simple shear flow under theta conditions are obtained.

Multiplicative separation of the influences of excluded volume, hydrodynamic interactions and finite extensibility on the rheological properties of dilute polymer solutions

Exact Brownian dynamics simulations of dumbbells and 20-bead chains, employing a novel semi-implicit, predictor-corrector algorithm, have been used to explore the qualitative features of the predictions of non-linear bead-spring chain models for dilute polymer solutions that incorporate the effects of excluded volume repulsions, hydrodynamics interactions and finite extensibility. It is observed that the combined influence of these three non-linear phenomena on most of the rheological properties of interest in shear and uniaxial extensional flows, can be expressed approximately as the product of independent contributions from each effect.

Fluid-structure interaction in deformable microchannels

A polydimethylsiloxane microfluidic device composed of a single microchannel with a thin flexible layer present over a short length along one side of the channel was fabricated and modelled in order to investigate the complex fluid-structure interaction that arises between a flowing fluid and a deformable wall. Experimental measurements of thin layer deformation and pressure drop are compared with predictions of two- and three-dimensional computational models that numerically solve the coupled set of equations governing both the elasticity of the thin layer and the fluid. It is shown that the two-dimensional model, which assumes the flexible thin layer comprises an infinitely wide elastic beam of finite thickness, reasonably approximates a three-dimensional model, and is in excellent agreement with experimental observations of the thin layer profile when the width of the thin layer is beyond a critical value, roughly twice the length of the thin layer.

Rouse chains with excluded volume interactions in steady simple shear flow

Viscometric functions for a dilute polymer solution, undergoing steady simple shear flow, are predicted using a modified version of the Rouse model. The presence of excluded volume interactions between different parts of a polymer chain, which is not taken into account in the original Rouse model, is incorporated into the present model with the help of a narrow Gaussian repulsive potential, which acts pairwise between the beads of the Rouse chain. Exact results are obtained numerically with the help of Brownian dynamics simulations, since the analytical tractability of the Rouse model is lost due to the modification. The presence of excluded volume effects is shown to cause the viscosity and the first normal stress difference to decrease with increasing shear rate—a feature not predicted by the Rouse model, though commonly observed experimentally. The exact simulation results are used to assess the quality of an approximate solution, obtained by assuming that the nonequilibrium distribution function is Ga...

Analysis of radial segregation of granular mixtures in a rotating drum

Abstract:This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected.

Effect of configuration-dependent intramolecular hydrodynamic interaction on elastocapillary thinning and breakup of filaments of dilute polymer solutions

We use a new constitutive model for the polymer stress in a dilute polymer solution to predict elastocapillary thinning and breakup of a thin filament of the solution. The constitutive model accounts for the effects of finite chain extensibility and configuration-dependent intramolecular hydrodynamic interaction, and is used in the simple stress balance equation proposed by Entov and Hinch [Entov, V. M., and E. J. Hinch, J. Non-Newtonian Fluid Mech. 72, 31–53 (1997)] for situations where inertial effects are negligible. In their seminal study, Entov and Hinch showed that during the period where the elastic polymer stresses are dominant, the filament radius decreases exponentially with time. We find that configuration-dependent hydrodynamic interactions cause the time constant in this exponential decay to depend on concentration, as observed in recent experiments. Moreover, the phenomenon of coil-stretch hysteresis permits a large polymer stress even though the transient Weissenberg number during elastocap...

Brownian dynamics simulation of polymer collapse in a poor solvent: influence of implicit hydrodynamic interactions

The effect of solvent on the collapse dynamics of homopolymers is investigated with Brownian dynamics simulations of a non-linear bead-spring chain model incorporating implicit hydrodynamic interactions. Our simulations suggest that the polymer collapse takes place via a three-stage mechanism, namely, formation of pearls, coarsening of pearls and the formation of a compact globule. The collapse pathways from a good solvent state to a poor solvent state are found to be independent of hydrodynamic interactions. On the other hand, hydrodynamic interaction is found to speed up the collapse rate. At a large quench depth (the depth of the Lennard-Jones potential), independent of the presence of hydrodynamic interaction, polymer molecules are found to be trapped in metastable states for long periods before acquiring their native globular state. The exponents characterizing the decay of various properties such as the radius of gyration are determined and compared with the values reported in the literature.

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Θ temperature: A Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.

Gaussian approximation for finitely extensible bead- spring chains with hydrodynamic interaction

The Gaussian Approximation, proposed originally by Ottinger [J. Chem. Phys., 90, 463–473 (1989)] to account for the influence of fluctuations in hydrodynamic interactions in Rouse chains, is adapted here to derive a new mean-field approximation for the FENE spring force. This FENE-PG force law approximately accounts for spring-force fluctuations, which are neglected in the widely used FENE-P approximation. The Gaussian Approximation for hydrodynamic interactions is combined with the FENE-P and FENE-PG spring force approximations to obtain approximate models for finitely extensible bead-spring chains with hydrodynamic interactions. The closed set of ordinary differential equations governing the evolution of the second moments of the configurational probability distribution in the approximate models is used to generate predictions of rheological properties in steady and unsteady shear and uniaxial extensional flows, which are found to be in good agreement with the exact results obtained with Brownian dynami...