Polymers in shear flow are ubiquitous and we study their motion in a viscoelastic fluid under shear. Employing dumbbells as representative, we find that the center of mass motion follows: $\langle x^2_c(t) \rangle \sim \dotγ^2 t^{α+2}, ~0< α<1$, generalizing the earlier result: $\langle x^2_c(t) \rangle \sim \dotγ^2t^3 ~(α= 1)$. Motion of the relative coordinate, on the other hand, is quite intriguing in that $\langle x^2_r(t) \rangle \sim t^β$ with $β= 2(1-α)$ for small $α$. This implies nonexistence of the steady state. We remedy this pathology by introducing a nonlinear spring with FENE-LJ interaction and study tumbling dynamics of the dumbbell. The overall effect of viscoelasticity is to slow down the dynamics in the experimentally observed ranges of the Weissenberg number. We numerically obtain the characteristic time of tumbling and show that small changes in $α$ result in large changes in tumbling times.
A polymer placed in chaotic flow with large mean shear tumbles, making a-periodic flips. We describe the statistics of angular orientation, as well as of tumbling time (separating two subsequent flips) of polymers in this flow. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction. The tails of this angular PDF are algebraic. The PDF of the tumbling time, $τ$, has a maximum at the value estimated as inverse Lyapunov exponent of the flow. This PDF shows an exponential tail for large $τ$ and a small-$τ$ tail determined by the simultan…
We study the dynamics of a polymer that is pulled by a constant force through a viscoelastic medium. This is a model for a polymer being pulled through a cell by an external force, or for an active biopolymer moving due to a self generated force. Using a Rouse model with a memory dependent drag force, we find that the center of mass of the polymer follows a subballistic motion. We determine the time evolution of the length and the shape of the polymer. Through an analysis of the velocity of the monomers, we investigate how the tension propagates through the polymer. We discuss how polymers can…
We present exact spatio-temporal correlation functions of a Rouse polymer chain submerged in a fluid having planar mixed flow, in the steady state. Using these correlators, determination of the time scale distribution functions associated with the first-passage tumbling events is difficult in general; it was done recently in Phys. Rev. Lett.,101, 188301 (2008), for the special case of "simple shear" flow. We show here that the method used in latter paper fails for the general mixed flow problem. We also give many new estimates of the exponent $θ$ associated with the exponential tail of the ang…
We numerically investigate viscoelastic phase separation in polymer solutions under shear using a time-dependent Ginzburg-Landau model. The gross variables in our model are the polymer volume fraction and a conformation tensor. The latter represents chain deformations and relaxes slowly on the rheological time giving rise to a large viscoelastic stress. The polymer and the solvent obey two-fluid dynamics in which the viscoelastic stress acts asymmetrically on the polymer and, as a result, the stress and the diffusion are dynamically coupled. Below the coexistence curve, interfaces appear with …
The non-equilibrium structural and dynamical properties of a semiflexible polymer confined in a cylindrical microchannel and exposed to a Poiseuille flow is studied by mesoscale hydrodynamic simulations. For a polymer with a length half of its persistence length, large variations in orientation and conformations are found as a function of radial distance and flow strength. In particular, the polymer exhibits U-shaped conformations near the channel center. Hydrodynamic interactions lead to strong cross-streamline migration. Outward migration is governed by the polymer orientation and the corres…
We show using Brownian dynamics simulations and theory how the shear relaxation modulus G(t) of dilute solutions of relatively stiff semiflexible polymers differs qualitatively from that of rigid rods. For chains shorter than their persistence length, G(t) exhibits three time regimes: At very early times, when the longitudinal deformation is affine, G(t) \sim t^{-3/4}. Over a broad intermediate regime, during which the chain length relaxes, G(t) \sim t^{-5/4}. At long times, $G(t) mimics that of rigid rods. A model of the polymer as an effectively extensible rod with a frequency dependent elas…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the existence of a finite stress relaxation time. This present work is motivated by renewed interest in instabilities in polymer flow. The majority of currently used numerical methods discretize a constitutive equation on a grid with finite difference or similar methods. We present work in progress in which we simulate viscoelastic flow with dissipative particl…
The non-equilibrium structural and dynamical properties of flexible polymers confined in a square microchannel and exposed to a Poiseuille flow are investigated by mesoscale simulations. The chain length and the flow strength are systematically varied. Two transport regimes are identified, corresponding to weak and strong confinement. For strong confinement, the transport properties are independent of polymer length. The analysis of the long-time tumbling dynamics of short polymers yields non-periodic motion with a sublinear dependence on the flow strength. We find distinct differences for con…
Surface tension-driven flow techniques have recently emerged as an efficient means of shedding light into the rheology of thin polymer films. Motivated by experimental and theoretical approaches in films bearing a varying surface topography, we present results on the capillary relaxation of a square pattern at the free surface of a viscoelastic polymer film, using molecular dynamics simulations of a coarse-grained polymer model. Height profiles are monitored as a function of time after heating the system above its glass-transition temperature and their time dependence is fitted to the theory o…
We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times $τ$ of the polymer decays exponentially as $\sim \exp(-ατ/τ_0)$ (where $τ_0$ is the longest relaxation time). We show that for a Rouse chain, this nontrivial constant $α$ can be calculated in the limit of large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of $α\simeq 0.324$. We also derive exactly the distribution functions for the length and th…
The non-equilibrium structural and dynamical properties of semiflexible polymers confined to two dimensions are investigated by molecular dynamics simulations. Three different scenarios are considered: The force-extension relation of tethered polymers, the relaxation of an initially stretched semiflexible polymer, and semiflexible polymers under shear flow. We find quantitative agreement with theoretical predictions for the force-extension relation and the time dependence of the entropically contracting polymer. The semiflexible polymers under shear flow exhibit significant conformational chan…
Using molecular simulations, we study the properties of a polymer brush in contact with an explicit solvent under Couette and Poiseuille flow. The solvent is comprised of chemically identical chains. We present evidence that individual, unentangled chains in the dense brush exhibit cyclic, tumbling motion and non-Gaussian fluctuations of the molecular orientations similar to the behaviour of isolated tethered chains in shear flow. The collective molecular motion gives rise to an inversion of hydrodynamic flow direction in the vicinity of the brush-coated surface. Utilising Couette and Poiseuil…
We study the dynamics of an ideal polymer chain in a crowded, viscoelastic medium and in the presence of active forces. The motion of the centre of mass and of individual monomers is calculated. On time scales that are comparable to the persistence time of the active forces, monomers can move superdiffusively while on larger time scales subdiffusive behaviour occurs. The difference between this subdiffusion and that in absence of active forces is quantified. We show that the polymer swells in response to active processes and determine how this swelling depends on the viscoelastic properties of…
We use non-equilibrium atomistic molecular dynamics simulations of unentangled melts of linear and star polymers ($\mathrm{C_{25}H_{52}}$) to study the steady-state viscoelastic response under confinement within nanoscale hematite $\left ( \mathrm{α-Fe_2O_3} \right )$ channels. We report (i) the negative (positive) first (second) normal stress difference and (ii) the presence of viscoelastic tension at low shear rates. We link these effects to bond alignment such that chains near the surface can carry the elastic force exerted on the walls, which decays as the chains become more aligned in the…
Needs to impart appropriate elasticity and high toughness to viscoelastic polymer materials are ubiquitous in industries such as concerning automobiles and medical devices. One of the major problems to overcome for toughening is catastrophic failure linked to a velocity jump, i.e., a sharp transition in the velocity of crack propagation occurred in a narrow range of the applied load. However, its physical origin has remained an enigma despite previous studies over 35 years. Here, we propose an exactly solvable model that exhibits the velocity jump incorporating linear viscoelasticity with a cu…
Quantitatively understanding of the dynamics of an active Brownian particle (ABP) interacting with a viscoelastic polymer environment is a scientific challenge. It is intimately related to several interdisciplinary topics such as the microrheology of active colloids in a polymer matrix and the athermal dynamics of the in vivo chromosome or cytoskeletal networks. Based on Langevin dynamics simulation and analytic theory, here we explore such a viscoelastic active system in depth using a star polymer of functionality $f$ with the center cross-linker particle being ABP. We observe that the ABP cr…
