We use Brownian dynamics (BD) simulations and single molecule experiments to investigate the influence of topological constraints and hydrodynamic interactions on the dynamics and rheology of solutions of ring-linear polymer blends at the overlap concentration. We find agreement between simulation and experiment in that rings in solution blends exhibit large conformational fluctuations, including extension overshoots in the startup of flow and tumbling and tank-treading at steady state. Ring polymer fluctuations increase with blend fraction of linear polymers and are peaked at a ring Weissenberg number $\textrm{Wi}_R \approx 1.5$. On the contrary, linear and ring polymers in pure solutions show a peak in fluctuations at the critical coil-stretch Weissenberg number $\textrm{Wi} = 0.5$. BD simulations show that extension overshoots on startup of flow are due to flow-induced intermolecular ring-linear polymer hooks, whereas fluctuations at steady state are dominated by intermolecular hydrodynamic interactions (HI). This is supported by simulations of bidisperse linear polymer solution blends, which show similar trends in conformational dynamics between rings and linear polymers with a matched contour length. Compared to BD simulations, single molecule experiments show quantitatively larger fluctuations, which could arise because experiments are performed on higher molecular weight polymers with stronger topological constraints. To this end, we have advanced the understanding of the effects of topological interactions and intermolecular HI on the dynamics of semidilute ring-linear polymer blend solutions.
The interplay between concentration, flow, hydrodynamic interactions (HI), and topological interactions governing semidilute polymer dynamics in strong flows are challenging to characterize. Brownian dynamics (BD) simulations are particularly valuable as a way to direct visualize how molecular interactions arise in these systems; however, BD simulations are often computationally limited by the need to calculate the correlated Brownian noise via decomposition of the diffusion tensor. Previously we have introduced an iterative conformational averaging (CA) method for BD simulations which bypasse…
The extensional rheology of polymeric liquids has been extensively examined through experiments and theoretical predictions. However, a systematic study of the extensional rheology of polymer solutions in the semidilute regime, in terms of examining the effects of concentration and molecular weight, has not been carried out so far. Prior studies of the shear rheology of semidilute polymer solutions have demonstrated that their behaviour is distinctively different from that observed in the dilute and concentrated regimes. This difference in behaviour is anticipated to be even more pronounced in…
The dynamics of individual DNA molecules in semidilute solutions undergoing planar extensional flow is simulated using a multi-particle Brownian dynamics algorithm, which incorporates hydrodynamic and excluded volume interactions in the context of a coarse-grained bead-spring chain model for DNA. The successive fine-graining protocol [1, 2], in which simulation data acquired for bead-spring chains with increasing values of the number of beads $N_b$, is extrapolated to the number of Kuhn steps $N_\text{K}$ in DNA (while keeping key physical parameters invariant), is used to obtain parameter-fre…
The rheology of semidilute bacterial suspensions is studied with the tools of kinetic theory, considering binary interactions, going beyond the ideal gas approximation. Two models for the interactions are considered, which encompass both the steric and short range interactions. In these, swimmers can either align polarly regardless of the state previous to the collision or they can align axially, being possible the end up antiparallel if the relative angle between directors is large. In both cases, it is found that an ordered phase develops when increasing the density, where the shear stress o…
Ring polymers exhibit unique flow properties due to their closed chain topology. Despite recent progress, we have not yet achieved a full understanding of the nonequilibrium flow behavior of rings in nondilute solutions where intermolecular interactions greatly influence chain dynamics. In this work, we directly observe the dynamics of DNA rings in semidilute ring-linear polymer blends using single molecule techniques. We systematically investigate ring polymer relaxation dynamics from high extension and transient and steady-state stretching dynamics in planar extensional flow for a series of …
Extensional rheometry of mobile fluids. Part II: Comparison between the uniaxial, planar and biaxial extensional rheology of dilute polymer solutions using numerically-optimized stagnation point microfluidic devices
We investigate the steady-state extensional rheology of a dilute suspension of spherical particles in a dilute polymer solution. For a particle-free polymeric fluid, in addition to the solvent viscosity, the extensional viscosity due to the polymers, $μ^\text{poly}$, contributes to the total non-dimensionalized extensional viscosity $1+μ^\text{poly}$. When a small volume fraction, $ϕ$, of spheres is added to a polymeric fluid, the stress is altered by the Einstein viscosity of 2.5$ϕ$ and two additional stress contributions: the interaction stresslet and the particle-induced polymer stress (PIP…
Extensional rheometry and Brownian Dynamics simulations of flexible polymer solutions confirm predictions based on blob concepts that coil--stretch hysteresis in extensional flows increases with concentration, reaching a maximum at the critical overlap concentration $c^\ast$ before progressively vanishing in the semidilute regime. These observations demonstrate that chain stretching strengthens intermolecular hydrodynamic screening in dilute solutions, but weakens it in semidilute solutions. Flow can thus strongly modify the concentration dependence of viscoelastic properties of polymer soluti…
We study granular suspensions under a variety of extensional deformations and simple shear using numerical simulations. The viscosity and Trouton's ratio (the ratio of extensional to shear viscosity) are computed as functions of solids volume fraction $ϕ$ close to the limit of zero inertia. Suspensions of frictionless particles follow a Newtonian Trouton's ratio for $ϕ$ all the way up to $ϕ_0$, a universal jamming point that is independent of deformation type. In contrast, frictional particles lead to a deformation-type-dependent jamming fraction $ϕ_m$, which is largest for shear flows. Trouto…
Exact analytical solutions for start-up and cessation flows are obtained for the affine linear Phan-Thien--Tanner fluid model. They include the results for start-up and cessation of steady shear flows, of steady uniaxial and biaxial extensional flows, and of steady planar extensional flows. The solutions obtained show that at start-up of steady shear flows, the stresses go through quasi-periodic exponentially damped oscillations while approaching their steady-flow values (so that stress overshoots are present); at start-up of steady extensional flows, the stresses grow monotonically, while at …
The linear and nonlinear rheological behavior of two rod-like particle suspensions as a function of concentration is studied using small amplitude oscillatory shear, steady shear and capillary breakup extensional rheometry. The rod-like suspensions are composed of fd virus and its mutant fdY21M, which are perfectly monodisperse, with a length on the order of 900 nm. The particles are semi flexible yet differ in their persistence length. The effect of stiffness on the rheological behavior in both, shear and extensional flow, is investigated experimentally. The linear viscoelastic shear data is …
The Granular Integration Through Transients (GITT) formalism gives a theoretical description of the rheology of moderately dense granular flows and suspensions. In this work, we extend the GITT equations beyond the case of simple shear flows studied before. Applying this to the particular example of extensional flows, we show that the predicted behavior is somewhat different from that of the more frequently studied simple shear case, as illustrated by the possibility of non monotonous evolution of the effective friction coefficient $μ$ with the inertial number $\mathcal{I}$. By the reduction o…
Swallowing disorders deteriorate significantly the quality of life and can be lifethreatening. Texture modification using shear thinning food thickeners have proven effective in the management of dysphagia. Some studies have recently considered the positive role of cohesiveness, but there is still an insufficient understanding of the effect of the rheological properties of the liquid bolus on the dynamics of bolus transport, particularly when elasticity and extensional properties are combined with a shear thinning behaviour. This study combines steady shear, SAOS and capillary breakage extensi…
Extensive molecular simulations are applied to characterize the equilibrium dynamics, entanglement topology, and nonlinear extensional rheology of symmetric ring-linear polymer blends with systematically varied ring fraction $ϕ_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10 well-entangled systems with $ϕ_R$ varying from neat linear to neat ring melts. Primitive path analysis are used to visualize and quantify the structure of the composite ring-linear entanglement network. We directly measure the quantity of ring-linear threading and linear-linear entanglement as a fun…
The COMOFLO dynamic Monte Carlo algorithm is extended to enable the simulation of steady-state extensional rheology of dense melts for the first time ever. This significant advancement provides the ability to accurately capture the extensional viscosity of entangled polymer melts from low deformation rates, throughout the strain hardening regime, and into the region of viscosity thinning To do so, the purely extensional flow field associated with a four roll mill experiment is implemented in three dimensions. Periodic boundary conditions exist in all directions to enable a uniform deformation …
Rheological properties of a material often require to be probed under extensional deformation. Examples include fibrous materials such as spider-silk, high-molecular weight polymer melts, and the contractile response of living cells. Such materials have strong molecular-level anisotropies which are either inherent or are induced by an imposed extension. However, unlike shear rheology, which is well-established, techniques to perform extensional rheology are currently under development and setups are often custom-designed for the problem under study. In this article, we present a versatile devi…
The dynamics of an adhesive two-dimensional vesicle doublet under various flow conditions is investigated numerically using a high-order, adaptive-in-time boundary integral method. In a quiescent flow, two nearby vesicles move slowly towards each other under the adhesive potential, pushing out fluid between them to form a vesicle doublet at equilibrium. A lubrication analysis on such draining of a thin film gives the dependencies of draining time on adhesion strength and separation distance that are in good agreement with numerical results. In a planar extensional flow we find a stable vesicle…
We present a numerical study of the rheology of a two-fluid emulsion in dilute and semidilute conditions. The analysis is performed for different capillary numbers, volume fraction and viscosity ratio under the assumption of negligible inertia and zero buoyancy force. The effective viscosity of the system increases for low values of the volume fraction and decreases for higher values, with a maximum for about 20 % concentration of the disperse phase. When the dispersed fluid has lower viscosity, the normalised effective viscosity becomes smaller than 1 for high enough volume fractions. To sing…
Linking molecular timescales to linear viscoelastic response in dilute and semidilute unentangled wormlike micelle solutions
IITB-Monash Research Academy（IITB-蒙纳士研究学院）；Department of Chemical Engineering, Indian Institute of Technology Bombay（印度理工学院孟买分校化学工程系）；Department of Chemical and Biological Engineering, Monash University（蒙纳士大学化学与生物工程系）；School of Chemistry, Monash University（蒙纳士大学化学学院）
Biconcave-discoid (empirical shape of a red blood cell) capsule finds numerous applications in the field of bio-fluid dynamics and rheology, apart from understanding the behavior of red blood cells (RBC) in blood flow. A detailed analysis is, therefore, carried out to understand the effects of the uniaxial extensional flow and electric field on the deformation of a RBC and biconcave-discoid polymeric capsule in the axisymmetric regime. The transient deformation is computed numerically using axisymmetric boundary integral method for Stokes flow considering the Skalak membrane constitutive law a…
We study the linear instability with respect to necking of a filament of polymeric fluid undergoing uniaxial extension. Contrary to the widely discussed Considere criterion, we find the onset of instability to relate closely to the onset of downward curvature in the time (and so strain) evolution of the zz component of the molecular strain, for extension along the z axis. In establishing this result numerically across five of the most widely used models of polymer rheology, and by analytical calculation, we argue it to apply generically. Particularly emphasized is the importance of polymer cha…
Suspensions of motile cells are model systems for understanding the unique mechanical properties of living materials which often consist of ensembles of self-propelled particles. We present here a quantitative comparison of theory against experiment for the rheology of such suspensions. The influence of motility on viscosities of cell suspensions is studied using a novel acoustically-driven microfluidic capillary-breakup extensional rheometer. Motility increases the extensional viscosity of suspensions of algal pullers, but decreases it in the case of bacterial or sperm pushers. A recent model…
We examine the dynamics of silica particles grafted with high molecular weight polystyrene suspended in semidilute solutions of chemically similar linear polymer using x-ray photon correlation spectroscopy. The particle dynamics decouple from the bulk viscosity despite their large hydrodynamic size and instead experience an effective viscosity that depends on the molecular weight of the free polymer chains. Unlike for hard sphere nanoparticles in semidilute polymer solutions, the diffusivities of the polymer-grafted nanoparticles do not collapse onto a master curve as a function of normalized …
A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as finitely elongated nonlinear elastic dumbbells, where effective charges (interacting through a simple Coulomb force) are added to the beads in order to model the repulsion between the charged sections of polyelectrolyte chains. It is shown that the relative strength of this repulsion is regulated by the electric-to-elastic energy ratio, $E$, which is one of the key parameters of the model. In particular, $E$ accounts for the intrinsic rigidit…
We investigate the rheological characteristics of human blood plasma in shear and elongational flows. While we can confirm a Newtonian behavior in shear flow within experimental resolution, we find a viscoelastic behavior of blood plasma in the pure extensional flow of a capillary break-up rheometer. The influence of the viscoelasticity of blood plasma on capillary blood flow is tested in a microfluidic device with a contraction-expansion geometry. Differential pressure measurements revealed that the plasma has a pronounced flow resistance compared to that of pure water. Supplementary measurem…
Suspensions of copper nanowires are emerging as new electronic inks for next-generation flexible electronics. Using a novel surface acoustic wave driven extensional flow technique we are able to perform currently lacking analysis of these suspensions and their complex buffer. We observe extensional viscosities from 3 mPa$\cdot$s (1 mPa$\cdot$s shear viscosity) to 37.2 Pa$\cdot$s via changes in the suspension concentration, thus capturing low viscosities that have been historically very challenging to measure. These changes equate to an increase in the relative extensional viscosity of nearly 1…
Compound particles are a class of composite systems in which solid particles encapsulated in a fluid droplet are suspended in another fluid. They are encountered in various natural and biological processes, for e.g., nucleated cells, hydrogels, microcapsules etc. In this work, we analyze the flow in and around a concentric compound particle and investigate the deformation and reorientation dynamics of the confining drop and its stability against breakup in imposed linear flows. We obtain analytical expressions for the flow fields upto O(Ca) (capillary number) and the deformed shape of the conf…
The dynamic properties of a model transient network have been studied by dynamic light scattering. The network is formed by microemulsion droplets linked by telechelic polymers (modified hydrophilic polymers with two grafted hydrophobic stickers). We compare the properties of two networks that are similar but for the residence time of the hydrophobic stickers in the droplets. The results are interpreted according to the so-called two-fluids model, which was initially developed for semidilute polymer solutions and which we extend here to any Maxwellian viscoelastic medium characterized by its e…
For optimal application, pressure-sensitive adhesives must have rheological properties in between those of a viscoplastic solid and those of a viscoelastic liquid. Such adhesives can be produced by emulsion polymerisation, resulting in latex particles which are dispersed in water and contain long-chain acrylic polymers. When the emulsion is dried, the latex particles coalesce and an adhesive film is formed. The rheological properties of the dried samples are believed to be dominated by the interface regions between the original latex particles, but the relation between rheology and latex parti…
We present a reformulation of the 'reactive rod model' (RRM) of Dutta and Graham [Dutta, Sarit and Graham, Michael D., JNNFM 251 (2018)], a constitutive model for describing the behavior of dilute wormlike micelle solutions. The RRM treats wormlike micelle solutions as dilute suspensions of rigid Brownian rods undergoing reversible scission and growth in flow. Evolution equations for micelle orientation and stress contribution are coupled to a kinetic reaction equation for a collective micelle length, producing dynamic variations in the length and rotational diffusivity of the rods. This model…
We employ a first principles, force-level approach to self-consistently construct the anharmonic tube confinement field for entangled fluids of rigid needles and for primitive-path (PP) level chains in two limiting situations where chain stretching is assumed to either completely relax or remain unrelaxed. The influence of shear and extensional deformation and polymer orientation is determined in a nonlinear elastic limit where dissipative relaxation processes are intentionally neglected. For needles and PP-level chains, a Gaussian analysis of transverse polymer dynamical fluctuations predicts…
We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines micro-scale data from non-equilibrium molecular dynamics (NEMD) with macro-scale continuum equations to achieve a data-driven prediction of complex flows. At the continuum level, the method is model-free, since the Cauchy stress tensor is determined locally in space and time from NEMD data. The modelling effort is thus limited to the identification of suitable inte…
Bioprinting of living cells can cause major shape deformations, which may severely affect cell survival and functionality. While the shear stresses occurring during cell flow through the printer nozzle have been quantified to some extent, the extensional stresses occurring as cells leave the nozzle into the free printing strand have been mostly ignored. Here we use Lattice-Boltzmann simulations together with a finite-element based cell model to study cell deformation at the nozzle exit. Our simulation results are in good qualitative agreement with experimental microscopy images. We show that f…
We analyze the capillarity-driven thinning dynamics of entangled polymer solutions described by the Doi-Edwards-Marrucci-Grizzuti (DEMG) model and the Rolie-Poly (RP) model. Both models capture polymer reptation, finite rates of chain retraction and finite extensibility of single polymer molecules, while differing slightly in their final form regarding to the convective constraint release. We calculate numerically the filament thinning profiles predicted by the two models with realistic entanglement densities, assuming cylindrical filament shapes and no fluid inertia. Both results reveal an ea…
