The intrinsic viscosity of a dilute dispersion of rigid rods is studied using a recently developed direct numerical simulation (DNS) method for particle dispersions. A reentrant transition from shear-thinning to the 2nd Newtonian regime is successfully reproduced in the present DNS results around a Peclet number ${\rm Pe}=150$, which is in good agreement with our theoretical prediction of ${\rm Pe}=143$, at which the dynamical crossover from Brownian to non-Brownian behavior takes place in the rotational motion of the rotating rod. The viscosity undershoot is observed in our simulations before reaching the 2nd Newtonian regime. The physical mechanisms behind these behaviors are analyzed in detail.
Complex fluids containing low concentrations of slender colloidal rods can display a high viscosity, while little flow is needed to thin the fluid. This feature makes slender rods essential constituents in industrial applications and biology. Though this behaviour strongly depends on the rod-length, so far no direct relation could be identified. We employ a library of filamentous viruses to study the effect of rod size and flexibility on the zero-shear viscosity and shear-thinning behaviour. Rheology and small angle neutron scattering data are compared to a revised version of the standard theo…
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 p…
Flow-history-dependent orientational relaxation in dilute polydisperse colloidal rod suspensions
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；University of the Basque Country UPV/EHU（巴斯克地区大学）；University of Cambridge（剑桥大学）
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…
We discuss unusual aspects of symmetry that can happen due to entropic effects in the context of multi-scalar field theories at finite temperature. We present their consequences, in special, for the case of nonrelativistic models of hard core spheres. We show that for nonrelativistic models phenomena like inverse symmetry breaking and symmetry non-restoration cannot take place, but a reentrant phase at high temperatures is shown to be possible for some region of parameters. We then develop a model of interest in studies of Bose-Einstein condensation in dilute atomic gases and discuss about its…
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 calculate tractable microscopic expressions for the low-shear normal-stress coefficients of colloidal dispersions. Although restricted to the low rate regime, the presented formulas are valid for all volume fractions below the glass transition and for any interaction potential. Numerical results are presented for a system of colloids interacting via a hard-core attractive Yukawa potential, for which we explore the interplay between attraction strength and volume fraction. We show that the normal-stress coefficients exhibit nontrivial features close to the critical point and at high volume f…
We quantified the Manning free (uncondensed) counterions fraction $θ$ for dilute solutions of rod-like polyions - 150bp DNA fragments, in very low salt $<0.05$mM. Conductivity measurements of aqueous DNA solutions in the concentration range $0.015\leq c \leq 8$~mM (bp) were complemented by fluorescence correlation spectroscopy (FCS) measurements of the DNA polyion diffusion coefficient $D_p(c)$. We observed a crossover in the normalized conductivity $σ(c)/c$ which nearly halved across $c=0.05-1$ mM range, while $D_p(c)$ remained rather constant, as we established by FCS. Analyzing these data w…
As a stiff polymer tumbles in shear flow, it experiences compressive viscous forces that can cause it to buckle and undergo a sequence of morphological transitions with increasing flow strength. We use numerical simulations to uncover the effects of these transitions on the steady shear rheology of a dilute suspension of stiff polymers. Our results agree with classic scalings for Brownian rods in relatively weak flows but depart from them above the buckling threshold. Signatures of elastoviscous buckling include enhanced shear thinning and an increase in the magnitude of normal stress differen…
The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and dilute, salt-free solutions. The classical Poisson-Boltzmann solution of the cell model correctly predicts a strong decrease in the osmotic coefficient, but upon closer look systematically overestimates its value. The contribution of ion-ion-correlations are quantitatively studied by MD simulations and the recently proposed DHHC theory. However, our comparis…
It is well known that suspensions of particles in a viscous fluid can affect the rheology significantly, producing a pronounced non-Newtonian response even in dilute suspension. However, it is unclear a priori which particle shapes lead to this behaviour. We present two simple symmetry conditions on the shape which are sufficient for a dilute suspension to be Newtonian for all strain sizes and one sufficient for Newtonian behavior for small strains. We also construct a class of shapes out of thin, rigid rods not found by the symmetry argument which share this property for small strains.
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited surface waves displays discontinuous and hysteretic features. This subcritical behaviour is attributed to the shear-thinning properties of our colloidal suspensions thanks to a phenomenological model based on rheological data under large amplitude oscillatory shear. Birefringence measurements provide direct evidence that Faraday waves induce local nematic or…
We analyse the time dependent non-linear rheology of a dilute bacterial suspension (e.g. E. coli) for a pair of impulsively started linear flows - simple shear and uniaxial extension. The rheology is governed by the bacterium orientation distribution which satisfies a kinetic equation that includes rotation by the imposed flow, and relaxation to isotropy via rotary diffusion and tumbling. The relevant dimensionless parameters are the Peclet number $Pe\equiv \dotγτ$, which dictates the importance of flow-induced orientation anisotropy, and $τD_r$, which quantifies the relative importance of the…
Suspensions of non-Brownian rods: droplet pinch-off, onset of heterogeneity and effective extensional viscosity
PMMH, CNRS, ESPCI Paris, Sorbonne Université, Université Paris-Cité（PMHH，法国国家科学研究中心，巴黎高等物理化工学院，索邦大学，巴黎 Cité 大学）；Department of Mechanical Engineering, University of California, Santa Barbara（加州大学圣塔芭芭拉分校机械工程系）；Institute of Physics, University of Amsterdam（阿姆斯特丹大学物理研究所）；Department of Mechanical Engineering, University of Maryland（马里兰大学机械工程系）；Department of Chemical and Biomolecular Engineering, University of Maryland（马里兰大学化学与生物分子工程系）
Bounded potentials are good models to represent the effective two-body interaction in some colloidal systems, such as dilute solutions of polymer chains in good solvents. The simplest bounded potential is that of penetrable spheres, which takes a positive finite value if the two spheres are overlapped, being 0 otherwise. Even in the one-dimensional case, the penetrable-rod model is far from trivial, since interactions are not restricted to nearest neighbors and so its exact solution is not known. In this paper we first derive the exact correlation functions of penetrable-rod fluids to second o…
We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of swimming direction for a finite fraction of swimmers from do…
Sol-gel transition in heteroassociative RNA-protein solutions: A quantitative comparison of coarse-grained simulations and the Semenov-Rubinstein theory
We study a generic model of self-assembling chains which can branch and form networks with branching points (junctions) of arbitrary functionality. The physical realizations include physical gels, wormlike micells, dipolar fluids and microemulsions. The model maps the partition function of a solution of branched, self-assembling, mutually avoiding clusters onto that of a Heisenberg magnet in the mathematical limit of zero spin components. The model is solved in the mean field approximation. It is found that despite the absence of any specific interaction between the chains, the entropy of the …
