The dynamic behavior of semi-dilute polymer solutions is governed by an interplay between solvent quality, concentration, molecular weight, and flow type. Semi-dilute solutions are characterized by large fluctuations in concentration, wherein polymer coils interpenetrate but may not be topologically entangled at equilibrium. In non-equilibrium flows, it is generally thought that polymer chains can self-entangle in semi-dilute solutions, thereby leading to entanglements in solutions that are nominally unentangled at equilibrium. Despite recent progress, we still lack a complete molecular-level understanding of these dynamics. In this work, we use single molecule techniques to study the dynamics of semi-dilute solutions of DNA in planar extensional flow, including polymer relaxation from high stretch, transient stretching dynamics in step-strain experiments, and steady-state stretching in flow. Our results are consistent with a power-law scaling of the longest polymer relaxation time in semi-dilute solutions, revealing an effective excluded volume exponent $ν$ = 0.56. We further studied the non-equilibrium stretching dynamics in extensional flow, with results showing a decrease in transient polymer stretch at moderate Weissenberg number and a milder coil-to-stretch transition in semi-dilute solutions compared to dilute solutions. Interestingly, a unique set of molecular conformations during the transient stretching process for single polymers in semi-dilute solutions is observed, which suggests transient stretching pathways for polymer chains in semi-dilute solutions are qualitatively different than dilute solutions due to intermolecular interactions. Taken together, this work provides a molecular framework for understanding the non-equilibrium stretching dynamics of semi-dilute solutions in strong flows.
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…
Enhancement of coil--stretch hysteresis by self-concentration in extensional flows, and its implications for capillary thinning of liquid bridges of dilute polymer solutions
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 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
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…
The viscosity of dilute and semidilute unentangled DNA solutions, in steady simple shear flow, has been measured across a range of temperatures and concentrations. For polystyrene solutions, measurements of viscosity have been carried out in the semidilute unentangled regime, while results of prior experimental measurements in the dilute regime have been used for the purpose of data analysis, and for comparison with the behaviour of DNA solutions. Interpretation of the shear rate dependence of viscosity in terms of suitably defined non-dimensional variables, is shown to lead to master plots, i…
Cellulose nanocrystals (CNC) can be considered as model colloidal rods and have practical applications in the formation of soft materials with tailored anisotropy. Here, we employ two contrasting microfluidic devices to quantitatively elucidate the role of shearing and extensional flows on the alignment of a dilute CNC dispersion. Characterization of the flow field by micro-particle image velocimetry is coupled to flow-induced birefringence analysis to quantify the deformation rate--alignment relationship. The deformation rate required for CNC alignment is 4$\times$ smaller in extension than i…
The swelling of the viscosity radius, $α_η$, and the universal viscosity ratio, $U_{ηR}$, have been determined experimentally for linear DNA molecules in dilute solutions with excess salt, and numerically by Brownian dynamics simulations, as a function of the solvent quality. In the latter instance, asymptotic parameter free predictions have been obtained by extrapolating simulation data for finite chains to the long chain limit. Experiments and simulations show a universal crossover for $α_η$ and $U_{ηR}$ from $θ$ to good solvents in line with earlier observations on synthetic polymer-solvent…
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…
Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previo…
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 …
Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of producing polymers of different topologies, the dynamics of topological polymer blends remains poorly understood. We address this void by using both passive and active microrheology to characterize the linear and nonlinear rheological properties of blends of relaxed circular and supercoiled DNA. We characterize the dynamics as we vary the concentration from belo…
We develop an analytical theory that accounts for the image and surface charge interactions between a charged dielectric membrane and a DNA molecule translocating through the membrane. Translocation events through neutral carbon-based membranes are driven by a competition between the repulsive DNA-image-charge interactions and the attractive coupling between the DNA segments on the trans and the cis sides of the membrane. The latter effect is induced by the reduction of the coupling by the dielectric membrane. In strong salt solutions where the repulsive image-charge effects dominate the attra…
We derive scaling relations for the extension statistics and the confinement free energy for a semi-flexible polymer confined to a channel with a rectangular cross-section. Our motivation are recent numerical results [Gupta {\em et al.}, JCP {\bf 140} (2014) 214901] indicating that extensional fluctuations are quite different in rectangular channels compared to square channels. Our results are of direct relevance for interpreting current experiments on DNA molecules confined to nano-channels, as many experiments are performed for rectangular channels with large aspect ratios while theoretical …
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…
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…
'Soft' patchy surfactant micelles have become an additional building tool in self-assembling systems. The triblock copolymer, Pluronic F108, forms spherical micelles in aqueous solutions upon heating leading to a simple phase diagram with a micellar crystalline solid at higher temperatures and concentrations. Here we report the strong influence of end-functionalising the chain ends either with an azide or azide-DNA complex on the systems' phase behaviour. We find that the azide(N3)- functionalisation renders the chain ends weakly hydrophobic at lower temperatures, causing them to self-assemble…
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…
We develop a correlation-corrected transport theory in order to predict ionic and polymer transport properties of membrane nanopores in physical conditions where mean-field electrostatics breaks down. The experimentally observed low KCl conductivity of open alpha-Hemolysin pores is quantitatively explained by the presence of surface polarization effects. Upon the penetration of a DNA molecule into the pore, these polarization forces combined with the electroneutrality of DNA sets a lower boundary for the ionic current, explaining the weak salt dependence of blocked pore conductivities at dilut…
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…
To characterize the thermodynamical equilibrium of DNA chains interacting with a solution of non-specific binding proteins, a Flory-Huggins free energy model was implemented. We explored the dependence on DNA and protein concentrations of the DNA collapse. For physiologically relevant values of the DNA-protein affinity, this collapse gives rise to a biphasic regime with a dense and a dilute phase; the corresponding phase diagram was computed. Using an approach based on Hamiltonian paths, we show that the dense phase has either a molten globule or a crystalline structure, depending on the DNA b…
New materials made through controlled assembly of dispersed cellulose nanofibrils (CNF) has the potential to develop into biobased competitors to some of the highest performing materials today. The performance of these new cellulose materials depends on how easily CNF alignment can be controlled with hydrodynamic forces, which are always in competition with a different process driving the system towards isotropy, called rotary diffusion. In this work, we present a flow-stop experiment using polarized optical microscopy (POM) to study the rotary diffusion of CNF dispersions in process relevant …
Tunability of Dissipative Particle Dynamics simulations for Excluded Volume and Hydrodynamic Interactions in polymer solutions and Rheological predictions
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the dynamics of semiflexible polymers under the influence of an imposed flow in a structured two-dimensional lattice serving as an idealization of a porous medium. This problem has received much attention in the limit of reptation and for long-chain polymer molecules such as DNA that are transported through micropost arrays for electrophoretic chromatographic sepa…
