R. G. Larson

A Purely Elastic Instability in Taylor-Couette Flow

A non-inertial (zero Taylor number) viscoelastic instability is discovered for Taylor–Couette flow of dilute polymer solutions. A linear stability analysis of the inertialess flow of an Oldroyd-B fluid (using both approximate Galerkin analysis and numerical solution of the relevant small-gap eigenvalue problem) show the growth of an overstable (oscillating) mode when the Deborah number exceeds f ( S ) e −½ , where e is the ratio of the gap to the inner cylinder radius, and f ( S ) is a function of the ratio of solvent to polymer contributions to the solution viscosity. Experiments with a solution of 1000 p.p.m. high-molecular-weight polyisobutylene in a viscous solvent show an onset of secondary toroidal cells when the Deborah number De reaches 20, for e of 0.14, and a Taylor number of 10 −6 , in excellent agreement with the theoretical value of 21. The critical De was observed to increase as e decreases, in agreement with the theory. At long times after onset of the instability, the cells become small in wavelength compared to those that occur in the inertial instability, again in agreement with our linear analysis. For this fluid, a similar instability occurs in cone-and-plate flow, as reported earlier. The driving force for these instabilities is the interaction between a velocity fluctuation and the first normal stress difference in the base state. Instabilities of the kind that we report here are likely to occur in many rotational shearing flows of viscoelastic fluids.

Monte Carlo simulation of model amphiphile‐oil–water systems

A square‐lattice model of amphiphile‐oil–water systems is developed in which oil and water molecules occupy single sites and amphiphiles occupy chains of sites. Energies and free energies estimated by Monte Carlo sampling of configuration space show that when the head, or water‐loving portion, of the amphiphile has no tendency to hydrate or surround itself with water, as opposed to surrounding itself with other heads, the capability of even long amphiphiles to solubilize repellant oil and water into a single phase is weak. Although the Monte Carlo free energies deviate markedly from those given by quasichemical theory, the deviation of the phase behavior is modest. Computer drawings of typical equilibrium configurations show highly irregular interfaces, apparently caused by capillary waves which are pronounced in two dimensions.

Self‐assembly of surfactant liquid crystalline phases by Monte Carlo simulation

Three‐dimensional microstructures of surfactant–water–oil systems self‐assemble in a Monte Carlo lattice model, as shown here. The microstructures that form depend on the volume ratios of oil, water, and surfactant, and on the length of the surfactant, and on the ratio R of the length of the oil‐loving to the water‐loving portion. For R=1 we find lamellar phases when the surfactant is mixed with equal amounts of oil and water. The lamellar spacing increases as the surfactant concentration is lowered. In the presence of water only, as the surfactant concentration is lowered the microstructure evolves from lamellar to broken lamellar to cylinders to spheroids. This progression is found to be independent of lattice size for lattices as large as 40×40×40. For R=3, the progression seems to be replaced by a progression from lamellae to regular bicontinuous structures to cylinders, although we are not yet confident that this latter progression is independent of lattice size effects. The Monte Carlo technique can be used to study a wide variety of interesting phenomena, from micelle size and shape transitions to packing transitions and phase behavior to interfacial properties in the presence of surfactant.

Brownian dynamics simulations of a DNA molecule in an extensional flow field

The unraveling dynamics of long, isolated, molecules of DNA subjected to an extensional flow in a crossed-slot device [, “Single polymer dynamics in an elongational flow,” Science 276, 2016–2021 (1997); “Response of Flexible Polymers to a Sudden Elongational Flow,” Science 281, 1335–1340 (1998)] are predicted by Brownian dynamics simulations using measured elastic and viscous properties of the DNA as the only inputs. Quantitative agreement is obtained both in the percentages of various unraveling states, such as “folds,” “kinks,” “dumbbells,” half-dumbbells,” and “coils,” and in the ensemble-averaged stretch and rate of stretch. Under fast flows (De≳10), unraveling is initially nearly affine, but for fractional stretch greater than ≈1/3, stretching is delayed to an extent that varies widely from molecule to molecule by flow-induced folded states, which are far-from-equilibrium kinetic hindrances not predicted by dumbbell models. From the computer simulations, the source of the high molecule-to-molecule he...

Monte Carlo simulation of microstructural transitions in surfactant systems

In a lattice model of mixtures of idealized surfactant, oil, and water molecules, the microseparation of hydrophobic components (oil and surfactant tails) from hydrophilic ones (water and surfactant heads) is simulated by a Monte Carlo technique. In water, symmetric surfactants, i.e., with heads as long as the tails, achieve lamellar or hexagonal‐cylindrical order as the temperature is reduced; the lamellae and cylinders form at surfactant concentrations that are similar to the concentrations at which symmetric block copolymers mixed with homopolymers have been found to form these structures. The lamellae containing tails can have many holes; as the temperature is reduced the holes attain hexagonal order within each layer. At low concentrations in water, symmetric surfactants form spherical micelles; the size distribution of these is computed, as well as the critical micelle concentration. When the surfactant tail is larger than the head, the micelles are cigar shaped or cylindrical. Cylindrical micelles ...

Mesoscopic domain theory for textured liquid crystalline polymers

Here we present a mesoscopic theory of the low‐flow‐rate rheological properties of textured or polydomain samples of liquid crystalline polymers. In this theory, the Leslie–Ericksen equations are assumed to apply to each domain; these equations are averaged over a spatial region, large compared to a single domain, yet small compared to bulk dimensions. Along with these averaged equations, phenomenological expressions are postulated that allow us to obtain a relatively simple set of coupled equations for the domain size and the mesoscopic orientation and stress tensors. The values of the Leslie–Ericksen viscosities that appear in the equations are obtained from the Doi theory for nematic polymers. We apply the theory to several shear flows, namely recoverable shear after cessation of steady shearing, and step reversal and step increase of shear rate. In each case promising agreement is found between the predictions of the mesoscopic theory and measurements on lyotropic liquid crystalline polymers.

Flow-induced mixing, demixing, and phase transitions in polymeric fluids

In polymer solutions or blends, flow can strongly influence the degree of mixing of the components. In a shearing flow, droplets in a dispersion can be broken down to sizes comparable to the dimensions of the polymer molecules themselves, thereby inducing molecular-scale mixing. Demixing can also occur when the two components of the mixture differ greatly in viscoelastic properties. Shear or extensional flow can induce polymer migration in nonhomogeneous flows or in flows with curved streamlines, and can render turbid solutions or blends that are otherwise transparent. Flow can also induce polymer gelation, and can induce ordering transitions in liquid crystals or block copolymers. Here, we review these phenomena, discuss proposed mechanisms, and assess the degree to which recent theories can account for the observations. Because the phenomena are complex, multiple experimental probes and theoretical methods are required to study them. Successful theories must incorporate polymer/polymer or polymer/solvent thermodynamics, critical phenomena, and phase transitions, as well as polymer theology and the kinetics of diffusion or crystallization. The experimental techniques used to study these phenomena are equally wide ranging, and include turbidity measurements, light, x-ray, and neutron scattering, fluorescence quenching, microscopy, and theology.

Monte Carlo lattice simulation of amphiphilic systems in two and three dimensions

Microstructures such as 2D micelles (in two dimensions) and lamellar arrays, cylinders, and spheres (in three dimensions) are allowed to self‐assemble via Monte Carlo simulation of an idealized lattice model for amphiphile–oil–water systems. Energies, free energies, equilibrium phase diagrams, and solution microstructures are estimated by Monte Carlo sampling of configuration space. In two dimensions (2D) at a temperature at which oil units have only a 3% solubility in the water phase, amphiphile at 20% concentration solubilizes any ratio of oil and water into a single phase and at lower concentrations produces phases with ultralow interfacial tension between them. As expected, in 3D solubilization is weaker and interfacial tensions higher than in 2D at comparable temperatures. Nevertheless, 3D systems containing the longest amphiphile (four head and four tail units) shows ordered solution structures, such as micelles at modest amphiphile concentration and periodic lamellar and cylindrical structures at h...

A transition occurring in ideal elastic liquids during shear flow

Abstract Dilute solutions of high molecular weight polyisobutylene dissolved in kerosene and low molecular weight polybutene have previously been reported to behave as ideal elastic liquids (“Boger fluids”). We report here rheological properties for similar solutions, having, however, higher molecular weights for the polyisobutylene. At low shear rates, these solutions exhibit the expected Boger-type rheological behavior, and approximately obey the Oldroyd-B constitutive equation. However, above a critical shear rate that depends upon molecular weight, prolonged shearing in a cone-and-plate or parallel-plate rheometer induces a time-dependent increase in the solution viscosity and elasticity. We find that the dependence of this transition on the Weissenberg number and the gap width or cone angle is consistent with a viscoelastic instability predicted by Phan-Thien for Oldroyd-B fluids. This instability appears to be of some generality for Boger fluids, since we have also observed it in a new monodisperse Boger fluid (polystyrene in low molecular weight polystyrene and dioctyl phthalate). Furthermore, this transition may have previously been observed (though not identified) by Jackson et al., using the Boger fluid polyacrylamide in maltose.

The rheology of layered liquids: lamellar block copolymers and smectic liquid crystals

The frequency-dependence of the viscoelastic shear modulus at low frequencies in a lamellar polystyrene-polyisoprene block copolymer is qualitatively identical to that measured in small-molecule smectics, namely, the rod-like 4-cyano-4′-octylbiphenyl and the flexible n-nonyl-1-O-β-D-glucopyranoside. All three materials were studied after quenching from the isotropic state, and during and after alignment by large-amplitude oscillatory shearing. The kinetics of aligning, as measured by changes in moduli during shearing, are similar, despite great differences in molecular characteristics. These moduli and the aligning process are evidently controlled by smectic fluctuations and defects, the dynamics of which have universal features.