Absence Of Hydrodynamic Interactions Research Articles

Effects of chain resolution on the configurational and rheological predictions of dilute polymer solutions in flow fields with hydrodynamic interactions

In a recent study, the resolution of a polymer chain model was shown to significantly affect rheological predictions from Brownian dynamics (BD) simulations [Kumar and Dalal, “Effects of chain resolution on the configurational and rheological predictions from Brownian dynamics simulations of an isolated polymer chain in flow,” J. Non-Newtonian Fluid Mech. 315, 105017 (2023)], even in the absence of hydrodynamic interactions (HI) and excluded volume. In this study, we investigate the effects of chain resolution in the presence of HI. Toward this, we perform BD simulations of a long polymer chain, with the discretization level varying from a single Kuhn step (bead–rod model) to several tens of Kuhn-steps (bead–spring model). The chain models were subjected to flow fields of uniaxial extension (purely stretching) and steady shear (equal rates of stretching and rotation). Broadly, our results indicate an amplification of the differences observed between the differently resolved bead–rod and bead–spring models, in the presence of HI. Interestingly, all rheological predictions qualitatively fall in two groups for extensional flow, with the predictions from the bead–spring model with HI being close to those of the bead–rod model without HI. This indicates significantly reduced sensitivity of coarser bead–spring models to HI, relative to the one resolved to a single Kuhn step. However, in shear flow, the bead–spring rheological predictions fall between those of the bead–rod model with and without HI, forming a third group. This is linked to the presence of stretched and coiled states in the ensemble for shear flow. HI effects are large for the coiled states and weak for the stretched states, thereby yielding predictions that are intermediate between those for no HI and dominant HI. Thus, quite surprisingly, the quality of predictions of the bead–spring models is strongly affected by the physics of the flow field, irrespective of the parameterization.

Brownian dynamics simulations of bottlebrush polymers in dilute solution under simple shear and uniaxial extensional flows.

We study the dynamics of bottlebrush polymer molecules in dilute solutions subjected to shear and uniaxial extensional flows using Brownian dynamics simulations with hydrodynamic interaction (HI). Bottlebrush polymers are modeled using a coarse-grained representation, consisting of a set of beads interacting pairwise via a purely repulsive potential and connected by finitely extensible nonlinear springs. We present the results for molecular stretching, stress, and solution viscosity during the startup of flow as well as under steady state as a function of side chain length while keeping the backbone length fixed. In extensional flow, the backbone fractional extension and the first normal stress difference decrease with an increase in side chain length at a fixed Weissenberg number (Wi). Using simulation results both in the presence of and in the absence of HI, we show that this is primarily a consequence of steric interaction resulting from the dense grafting of side chains. In shear flow, we observe a shear-thinning behavior in all cases, although it becomes less pronounced with increasing side chain length. Furthermore, nonmonotonicity in the backbone fractional extension is observed under shear, particularly at high Wi. We contextualize our simulation results for bottlebrush polymers with respect to existing studies in the literature for linear polymers and show that the unique dynamical features characterizing bottlebrush polymers arise on account of their additional molecular thickness due to the presence of densely grafted side chains.

Chain rotational dynamics in dilute polymer solutions and melts under shear flow

We present detailed scaling characteristics of the chain rotation dynamics in shear flow for melt and dilute linear polymer systems using extensive atomistic and coarse-grained Brownian dynamics (BD) molecular dynamics simulations, respectively. We find that the dilute systems with hydrodynamic interaction (HI) and excluded volume (EV) effects generally exhibit two distinct scaling behavior of the chain rotation time τrot between the intermediate and strong flow regimes, whereas the free-draining dilute polymer systems display a relatively simple single-scaling behavior for τrot with respect to the shear rate throughout the intermediate-to-strong flow regimes. This dynamic feature correlates with the scaling characteristics of average chain deformation and orientation of the system with respect to the flow strength. Notably, the combined HI and EV effects generally weaken the structural change of polymer chains in response to the applied flow and enhance the overall chain rotation dynamics by disturbing the chain stretch and alignment to the flow direction. Accordingly, due to the variation in the HI and EV effects (in association with chain deformation) with the flow strength, the dilute systems with HI and EV turn out to reveal relatively lower and higher scaling behaviors of τrot in the intermediate and strong flow regimes, respectively, in comparison to the corresponding free-draining systems. Despite the absence of HI and EV effects, the melt systems also exhibit two distinct scaling behaviors of τrot between the intermediate and strong flow regimes. This feature arises from the intermolecular interactions between chains, resulting in a significant influence of interchain entanglement and interchain dynamic collision on the chain rotation dynamics. It is further observed that the overall τrot scaling behavior for each system is predominantly determined by the corresponding scaling behavior of the kinematically stable (diffusive) angular regions near the flow direction, where the flow force is relatively weak. Additionally, polymer chains in kinematically unstable (convective) angular regions exhibit nearly affine chain rotation dynamics conforming to the imposed flow field, independent of the polymer concentration and chain length. This is considered to be a universal feature for general polymeric liquids in shear flow.

Rheology of non-Brownian particle suspensions in viscoelastic solutions. Part II: Effect of a shear thinning suspending fluid

The shear rheology of particle suspensions in shear-thinning polymeric fluids is studied experimentally using parallel plate measurements and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. Moreover, in highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself. Our dilute body-fitted simulations show that in the absence of hydrodynamic interactions, shear-thinning can arise from the particle-induced fluid stress (PIFS), which ceases to grow with increasing shear rate at low values of β (solvent viscosity ratio) and finite values of α (the Giesekus drag coefficient). In a Giesekus suspending fluid, the polymers surrounding the suspended particle are unable to stretch sufficiently at high Weissenberg numbers (Wi) and the reduced polymer stress results in a lower PIFS. When coupled with the shear-thinning stresslet, this effect creates an overall shear-thinning of the viscosity. We then explore the effects of particle-particle interactions on the suspension rheology using immersed boundary simulations. We show that multiparticle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. We also find that very low values of β and finite values of α have opposing effects on the per-particle viscosity that can lead to a nonmonotonic per-particle viscosity versus shear rate in a highly shear-thinning fluid. Overall, the addition of rigid particles to highly shear-thinning fluids, such as joint synovial fluid, leads to increased viscosity and also increased shear-thinning at high shear rates.

Effect of Charge Distribution on the Dynamics of Polyampholytic Disordered Proteins.

The stability and physiological function of many biomolecular coacervates depend on the structure and dynamics of intrinsically disordered proteins (IDPs) that typically contain a significant fraction of charged residues. Although the effect of relative arrangement of charged residues on IDP conformation is a well-studied problem, the associated changes in dynamics are far less understood. In this work, we systematically interrogate the effects of charge distribution on the chain-level and segmental dynamics of polyampholytic IDPs in dilute solutions. We study a coarse-grained model polyampholyte consisting of an equal fraction of two oppositely charged residues (glutamic acid and lysine) that undergoes a transition from an ideal chain-like conformation for uniformly charge-patterned sequences to a semi-compact conformation for highly charge-segregated sequences. Changes in the chain-level dynamics with increasing charge segregation correlate with changes in conformation. The chain-level and segmental dynamics conform to simple homopolymer models for uniformly charge-patterned sequences but deviate with increasing charge segregation, both in the presence and absence of hydrodynamic interactions. We discuss the significance of these findings, obtained for a model polyampholyte, in the context of a charge-rich intrinsically disordered region of the naturally occurring protein LAF-1. Our findings have important implications for understanding the effects of charge patterning on the dynamics of polyampholytic IDPs in dilute conditions using polymer scaling theories.

Modeling particle-particle binary coagulation rate constants for spherical aerosol particles at high volume fractions using Langevin Dynamics simulations

Effect of volume-fraction and particle-particle hydrodynamic interactions on the coagulation rate of particles are investigated. Particle coagulation is modeled using Langevin Dynamics (LD) based trajectory simulations of N mono-sized spherical particles in a periodic domain. The extended Kirkwood-Risemann approach (J. Fluid Mechanics 855, 535 (2018)) is invoked to compute particle-particle hydrodynamic interactions whose effect is parameterized as a function of the momentum Knudsen number (Kn). The results are summarized as a model for coagulation rate constant (βij) that depends on the diffusive Knudsen number (KnD) used in prior work to parameterize coagulation in the dilute regime (Aerosol Sci. Tech. 45, 1499 (2011)), Kn and particle volume-fraction ηv. In the absence of hydrodynamic interactions, it is observed that the coagulation rate constant in the continuum limit for mass transfer (KnD→0) is significantly enhanced by a factor of ∼80 at ηv∼0.3 due to particle crowding. While considering hydrodynamic interactions for ηv≥0.05, we use a screening distance around each particle that scales inversely with ηv beyond which the contribution of farther neighbors is neglected owing to the rapid decay of hydrodynamic interactions with distance. We also present new LD calculations of βij and elucidate the dependence of the same on Kn1 and the particle radii ratio θr for the coagulation of two particles in the dilute limit ηv→0. It is observed that the reduction of βij becomes significant as Kn1→0: at the lowest momentum Knudsen number considered (Kn1=0.1): βij is reduced by a factor of ∼10 for equally sized particles (θr=0.5). At high KnD,Kn1, the particle size disparity is not significant, and it is seen that βij matches hard sphere predictions, indicating the insignificant contributions by hydrodynamic interactions. A series of animations of 2-particle simulations are presented as part of the Supplemental Information to illustrate the role of hydrodynamic interactions in particle coagulation. Computational results are summarized as regressions for convenient incorporation into particle/droplet growth sectional models.

Resistance and mobility functions for the near-contact motion of permeable particles

A lubrication analysis is presented for the resistances between permeable spherical particles in near contact,$h_0/a\ll 1$, where$h_0$is the minimum separation between the particles, and$a=a_1 a_2/(a_1+a_2)$is the reduced radius. Darcy's law is used to describe the flow inside the permeable particles and no-slip boundary conditions are applied at the particle surfaces. The weak permeability regime$K=k/a^{2} \ll 1$is considered, where$k=\frac {1}{2}(k_1+k_2)$is the mean permeability. Particle permeability enters the lubrication resistances through two functions of$q=K^{-2/5}h_0/a$, one describing axisymmetric motions, the other transverse. These functions are obtained by solving an integral equation for the pressure in the near-contact region. The set of resistance functions thus obtained provide the complete set of near-contact resistance functions for permeable spheres and match asymptotically to the standard hard-sphere resistances that describe pairwise hydrodynamic interactions away from the near-contact region. The results show that permeability removes the contact singularity for non-shearing particle motions, allowing rolling without slip and finite separation velocities between touching particles. Axisymmetric and transverse mobility functions are presented that describe relative particle motion under the action of prescribed forces and in linear flows. At contact, the axisymmetric mobility under the action of oppositely directed forces is$U/U_0=d_0K^{2/5}$, where$U$is the relative velocity,$U_0$is the velocity in the absence of hydrodynamic interactions and$d_0=1.332$. Under the action of a constant tangential force, a particle in contact with a permeable half-space rolls without slipping with velocity$U/U_0=d_1(d_2+\log K^{-1})^{-1}$, where$d_1=3.125$and$d_2=6.666$; in shear flow, the same expression holds with$d_1=7.280$.

Predictions of polymer migration in a dilute solution between rotating eccentric cylinders

Our recent continuum theory for stress-gradient-induced migration of polymers in confined solutions, including the depletion from the solid boundaries [Hajizadeh, E., and R. G. Larson, Soft Matter, 13, 5942–5949 (2017)], is applied to a two-dimensional rotational shearing flow in the gap between eccentric cylinders. Analytical results for the steady-state distribution of polymer dumbbells in the limit of dilute polymer solution c/c∗≪1 (c∗ is the chain overlap concentration) and in the absence of hydrodynamic interactions are obtained. The effects of eccentricity e and of three perturbation variables, namely, Weissenberg number Wi, gradient number Gd(which defines the level of polymer chain confinement), and Péclet number Pe on the polymer concentration pattern, are investigated. The stress-gradient-induced migration results in polymer migration toward the inner cylinder, while wall-depletion-induced migration results in near-zero polymer concentration close to flow boundaries, which couples to a stress-gradient-induced migration effect. In the presence of wall-depletion, we obtain first order concentration variation proportional to Wi. However, in the absence of wall-depletion, there is no first order contribution and, therefore, the lowest-order concentration variation is proportional to Wi2. An upper limit of Wi=1.6 exists, beyond which the numerical solution demands an excessive under-relaxation to converge. In addition, for a high degree of polymer chain confinement, i.e., for Gd greater than 0.5, the continuum theory fails to be accurate and mesoscopic simulations that track individual polymer molecules are needed.

Viscometric functions and rheo-optical properties of dilute polymer solutions: Comparison of FENE-Fraenkel dumbbells with rodlike models

Rigid macromolecules or polymer chains with persistence length on the order of the contour length (or greater) have traditionally been modelled as rods or very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely extensible about a non-zero natural length with tunable harmonic stiffness, is one such model which has previously been shown to reproduce bead–rod behaviour in the absence of hydrodynamic interactions. The force law for the FENE-Fraenkel spring reduces to the Hookean or FENE spring force law for appropriately chosen values of the spring parameters. It is consequently possible to explore the crossover region between the limits of bead–spring and bead–rod behaviour by varying the parameters suitably. In this study, using a semi-implicit predictor–corrector Brownian dynamics algorithm, the FENE-Fraenkel spring is shown to imitate a rod with hydrodynamic interactions when spring stiffness, extensibility and simulation timestep are chosen carefully. By relaxing the spring stiffness and extensibility, the FENE-Fraenkel spring can also reproduce spring-like behaviour, such as a crossover from −1∕3 to −2∕3 power-law scaling in the viscosity with shear rate, and a change from positive to negative second normal stress difference. Furthermore, comparisons with experimental data on the viscosity and linear dichroism of high aspect ratio, rigid macromolecules shows that the extensibility and stiffness of the FENE-Fraenkel spring allows for equal or improved accuracy in modelling inflexible molecules compared to rodlike models.

The physics of active polymers and filaments

Active matter agents consume internal energy or extract energy from the environment for locomotion and force generation. Already, rather generic models, such as ensembles of active Brownian particles, exhibit phenomena, which are absent at equilibrium, particularly motility-induced phase separation and collective motion. Further intriguing nonequilibrium effects emerge in assemblies of bound active agents as in linear polymers or filaments. The interplay of activity and conformational degrees of freedom gives rise to novel structural and dynamical features of individual polymers, as well as in interacting ensembles. Such out-of-equilibrium polymers are an integral part of living matter, ranging from biological cells with filaments propelled by motor proteins in the cytoskeleton and RNA/DNA in the transcription process to long swarming bacteria and worms such as Proteus mirabilis and Caenorhabditis elegans, respectively. Even artificial active polymers have been synthesized. The emergent properties of active polymers or filaments depend on the coupling of the active process to their conformational degrees of freedom, aspects that are addressed in this article. The theoretical models for tangentially and isotropically self-propelled or active-bath-driven polymers are presented, both in the presence and absence of hydrodynamic interactions. The consequences for their conformational and dynamical properties are examined, with emphasis on the strong influence of the coupling between activity and hydrodynamic interactions. Particular features of emerging phenomena in semi-dilute systems, induced by steric and hydrodynamic interactions, are highlighted. Various important, yet theoretically unexplored, aspects are featured, and future challenges are discussed.

Role of Hydrodynamic Interactions in the Deformation of Star Polymers in Poiseuille Flow

Stretching polymer in fluid flow is a vital process for studying and utilizing the physical properties of these molecules, such as DNA linearization in nanofluidic channels. We studied the role of hydrodynamic interactions (HIs) in stretching a free star polymer in Poiseuille flow through a tube using mesoscale hydrodynamic simulations. As increasing the flow strength, star polymers migrate toward the centerline of tube due to HIs, whereas toward the tube wall in the absence of HIs. By analyzing the end monomer distribution and the perturbed flow around the star polymer, we found that the polymer acts like a shield against the flow, leading to additional hydrodynamic drag forces that compress the arm chains in the front of the star center toward the tube axis and lift the arm chains at the back toward the tube wall. The balanced hydrodynamic forces freeze the polymer into a trumpet structure, where the arm chains maintain a steady strongly stretched state at high flow strength. In contrast, the polymer displays remarkably large conformational change when switching off HIs. Our simulation results explained the coupling between HIs and the structure of star polymers in Poiseuille flow.

Trefoil Knot Hydrodynamic Delocalization on Sheared Ring Polymers.

The behavior of unknotted and trefoil-knotted ring polymers under shear flow is here examined by means of mesoscopic simulations. In contrast to most polymers, ring polymers in a hydrodynamic solvent at high shear rates do not get shortened in the vorticity direction. This is a consequence of the backflow produced by the interaction of the sheared solvent with the end-free polymer topology. The extended structures of the ring in the vorticity-flow plane, when they are aligned in a constant velocity plane, favor ring contour fluctuations. This variety of conformations largely suppresses the tank-treading type of rotation with extended conformations in favor of the tumbling type of rotations, where stretched and collapsed conformations alternate. The extension of trefoil knots is also enhanced, so that the knots become delocalized. We anticipate that these effects, which disappear in the absence of hydrodynamic interactions, will have a crucial impact on the rheological properties of concentrated ring solutions, and will also influence the behavior of more complicated systems such as mixtures of polymers with different topologies.

Impact of hydrodynamic interactions on protein folding rates depends on temperature.

We investigated the impact of hydrodynamic interactions (HI) on protein folding using a coarse-grained model. The extent of the impact of hydrodynamic interactions, whether it accelerates, retards, or has no effect on protein folding, has been controversial. Together with a theoretical framework of the energy landscape theory (ELT) for protein folding that describes the dynamics of the collective motion with a single reaction coordinate across a folding barrier, we compared the kinetic effects of HI on the folding rates of two protein models that use a chain of single beads with distinctive topologies: a 64-residue α/β chymotrypsin inhibitor 2 (CI2) protein, and a 57-residue β-barrel α-spectrin Src-homology 3 domain (SH3) protein. When comparing the protein folding kinetics simulated with Brownian dynamics in the presence of HI to that in the absence of HI, we find that the effect of HI on protein folding appears to have a "crossover" behavior about the folding temperature. This means that at a temperature greater than the folding temperature, the enhanced friction from the hydrodynamic solvents between the beads in an unfolded configuration results in lowered folding rate; conversely, at a temperature lower than the folding temperature, HI accelerates folding by the backflow of solvent toward the folded configuration of a protein. Additionally, the extent of acceleration depends on the topology of a protein: for a protein like CI2, where its folding nucleus is rather diffuse in a transition state, HI channels the formation of contacts by favoring a major folding pathway in a complex free energy landscape, thus accelerating folding. For a protein like SH3, where its folding nucleus is already specific and less diffuse, HI matters less at a temperature lower than the folding temperature. Our findings provide further theoretical insight to protein folding kinetic experiments and simulations.

Self-propulsion against a moving membrane: Enhanced accumulation and drag force.

Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity c. With respect to both the cases of passive colloids with c>0 and AP with c=0, the AP with finite c show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to cτ/ξ, where τ is the AP's reorientation time and ξ the width characterizing the surface's smoothness (ξ→0 for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.

How Hydrodynamic Interactions affect the Folding Rate of Proteins

Hydrodynamic interaction (HI) arises by the solvent flow generated by the movement of a particle that affects other particles. This long-range interaction is particularly important in the dynamics of proteins that are immersed in the crowded milieu of cells. Therefore, there is a need for a computationally and theoretical quantitative evaluation of its role in protein folding. Using coarse-grained molecular simulations and theoretical calculations according to the Energy Landscape Theory of protein folding, we assess the impact of hydrodynamic interaction in the folding of two model proteins, the 64-residue protein chymotrypsin inhibitor 2 (CI2), and the 57-residue alpha-spectrin Src-homology 3 (SH3) domain. In our study, we included hydrodynamic interaction into the equations of motion from Brownian dynamics by computing the diffusion correlation matrices between each residue. We investigated the folding kinetics as well as the thermodynamics of each protein in the presence and in the absence of hydrodynamic interaction. Our results suggest that the impact from hydrodynamic interaction is dependent on the topology of a protein, and temperature.

Local structure of percolating gels at very low volume fractions.

The formation of colloidal gels is strongly dependent on the volume fraction of the system and the strength of the interactions between the colloids. Here we explore very dilute solutions by the means of numerical simulations and show that, in the absence of hydrodynamic interactions and for sufficiently strong interactions, percolating colloidal gels can be realised at very low values of the volume fraction. Characterising the structure of the network of the arrested material we find that, when reducing the volume fraction, the gels are dominated by low-energy local structures, analogous to the isolated clusters of the interaction potential. Changing the strength of the interaction allows us to tune the compactness of the gel as characterised by the fractal dimension, with low interaction strength favouring more chain-like structures.

Force-induced diffusion in suspensions of hydrodynamically interacting colloids

We study the influence of hydrodynamic, thermodynamic and interparticle forces on the diffusive motion of a Brownian probe driven by a constant external force through a dilute colloidal dispersion. The influence of these microscopic forces on equilibrium self-diffusivity (passive microrheology) is well known: all three act to hinder the short- and long-time self-diffusion. Here, via pair-Smoluchowski theory, we explore their influence on self-diffusion in a flowing suspension, where particles and fluid have been set into motion by an externally forced probe (active microrheology), giving rise to non-equilibrium flow-induced diffusion. The probe’s motion entrains background particles as it travels through the bath, deforming the equilibrium suspension microstructure. The shape and extent of microstructural distortion is set by the relative strength of the external force $F^{\mathit{ext}}$ to the entropic restoring force $kT/a_{\mathit{th}}$ of the bath particles, defining a Péclet number $\mathit{Pe}\equiv F^{\mathit{ext}}/(2kT/a_{\mathit{th}})$; and also by the strength of hydrodynamic interactions, set by the range of interparticle repulsion ${\it\kappa}=(a_{\mathit{th}}-a)/a$, where $kT$ is the thermal energy and $a_{\mathit{th}}$ and $a$ are the thermodynamic and hydrodynamic sizes of the particles, respectively. We find that in the presence of flow, the same forces that hinder equilibrium diffusion now enhance it, with diffusive anisotropy set by the range of interparticle repulsion ${\it\kappa}$. A transition from hindered to enhanced diffusion occurs when diffusive and advective forces balance, $\mathit{Pe}\sim 1$, where the exact value is a sensitive function of the strength of hydrodynamics, ${\it\kappa}$. We find that the hindered to enhanced transition straddles two transport regimes: in hindered diffusion, stochastic forces in the presence of other bath particles produce deterministic displacements (Brownian drift) at the expense of a maximal random walk. In enhanced diffusion, driving the probe with a deterministic force through an initially random suspension leads to fluctuations in the duration of probe–bath particle entrainment, giving rise to enhanced, flow-induced diffusion. The force-induced diffusion is anisotropic for all $\mathit{Pe}$, scaling as $D\sim \mathit{Pe}^{2}$ in all directions for weak forcing, regardless of the strength of hydrodynamic interactions. When probe forcing is strong, $D\sim \mathit{Pe}$ in all directions in the absence of hydrodynamic interactions, but the picture changes qualitatively as hydrodynamic interactions grow strong. In this nonlinear regime, microstructural asymmetry weakens while the anisotropy of the force-induced diffusion tensor increases dramatically. This behaviour owes its origins to the approach toward Stokes flow reversibility, where diffusion along the direction of probe force scales advectively while transverse diffusion must vanish.

Stress-gradient-induced polymer migration: Perturbation theory and comparisons to stochastic simulations

While phenomenological expressions have been given in the past for polymer flux due to gradients in polymer stress or gradients in velocity gradient, we here provide a systematic perturbation theory for the coupled equations for polymer rheology, fluid dynamics, and polymer mass transport. Analytical results are obtained for the steady-state concentration of dilute dumbbells in the absence of hydrodynamic interactions, as a function of the Weissenberg number Wi, Peclet number Pe, and the “gradient number” Gd, where the latter is the ratio of polymer equilibrium size to the characteristic distance over which velocity gradients change. At lowest order in all three perturbation variables, the theory yields a Poisson's equation with the driving term given by 2c¯Dτ2 vj,k,j vj,j,k, where c¯ is the average concentration, D is the dumbbell diffusivity, τ is the relaxation time, and v is velocity with Einstein notation for the subscripts. We find using Brownian dynamics (BD) simulations in a simple Taylor vortex f...

Efficient simulation of semiflexible polymers

Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modeled with one bead-spring element per base pair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymer's fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of 5% of several key observables, the model allows for single Langevin time steps of ≈1.6, 8, 16, and 16 ps for a dsDNA model chain consisting of 64, 128, 256, and 512 base pairs (i.e., chains of 0.55, 1.11, 2.24, and 4.48 persistence lengths), respectively. Correspondingly, in 1 h, a standard desktop computer can simulate 0.23, 0.56, 0.56, and 0.26 ms of these dsDNA chains, respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretized) wormlike chain (WLC) model. Importantly, we demonstrate that at the same level of discretization, i.e., when each discretization element is one base pair long, our algorithm gains about five to six orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one on one to a discretized version of the extensible WLC model, implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behavior of a dsDNA segment in a shear flow.

Particle segregation in falling polydisperse suspension droplets

The problem of a suspension droplet falling under gravity was examined for polydisperse droplets composed of a mixture of particles with different densities and sizes. The study was conducted using both simulations based on oseenlet particle interactions and laboratory experiments. The hydrodynamic interactions of the particles within the suspension droplet allow a polydisperse collection of particles to fall as a coherent droplet, even for cases where the difference in particle terminal velocity would cause them to separate quickly from each other in the absence of hydrodynamic interactions. However, a gradual segregation phenomenon is observed in which particles with lower terminal velocity preferentially leave the suspension droplet by entering into the droplet tail, whereas particles with higher terminal velocity remain for longer periods of time within the droplet. When computations and experiments are performed for bidisperse mixtures, a point is eventually reached where all of the lighter/smaller particles are ejected into the droplet tail and the droplet continues to fall with only the heavier/larger particles.