Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that, at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: Its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: Velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signaling the reduction of Lagrangian chaos.     

Hydrodynamics of dilute rouse polymer solutions under flow

Using Langevin method the hydrodynamics of dilute polymer solutions under flow is described by deriving an effective hydrodynamic equation for these solutions. The systematics of the present treatment is demonstrated by considering Rouse chains as a simple example.     

Hydrodynamic interactions of dilute polymer solutions in elongational flow

Dumbbell models are only crude representations of actual polymer molecules, but their simplicity allows for explicit calculations which in many instances have shed light on the connection between molecular properties and rheological behavior. On the other hand, hydrodynamic interactions are known to strongly influence the dynamic response of polymer solutions and this makes the representation of the hydrodynamic drag an important aspect in the calculations. In the present work, the effects of the state of flow are incorporated explicitly in the frictional properties of the FENE model of a dilute polymer solution. Results for the steady elongational viscosity and the mean square end-to-end distance arc presented.     

Frictional properties of dilute polymer solutions IV. Intrinsic viscosity

In the framework of our generalization of the Debye-Bueche theory for the frictional properties of dilute polymer solutions we study the intrinsic viscosity. A careful definition of the intrinsic viscosity for polymers with spherically symmetric density distribution is given. The equations are solved explicity for uniform spheres and spherical shells. For the general case a perturbation method is applied and a variational principle of minimum energy dissipation is formulated which is suitable for numerical work.     

Frictional properties of dilute polymer solutions: III. Translational-friction coefficient

In the framework of our generalization of the Debye-Bueche theory for the frictional properties of dilute polymer solutions we study the translational-friction coefficient of polymers with spherically symmetric segment distribution. A variational principle of minimum energy dissipation is formulated which is suitable for numerical work.     

Calculation of the intrinsic viscosity for dilute polymer solutions undergoing shear flow

Starting from a set of coupled Langevin equations describing the dynamics of flexible (Gaussian) polymer chains in the presence of hydrodynamic interactions and undergoing a weak shear flow, the stress tensor is determined using Kramers formula. With the aid of renormalization group techniques the steady state intrinsic viscosity is extracted toO() (4–d,d being the spatial dimensionality) and to lowest nontrivial order in the flow strength. Within the preaveraging approximation we find a numerically small effect of shear thinning.     

Pattern formation in Taylor-Couette flow of dilute polymer solutions: dynamical simulations and mechanism

We report spatiotemporal pattern formation in Taylor-Couette flow (i.e., flow between rotating cylinders) of viscoelastic dilute polymer solutions obtained for the first time from first-principles dynamical simulations. Solution structures with varying spatial and temporal symmetries, such as rotating standing waves, flames, disordered oscillations, and solitary vortex solutions which include diwhirls (stationary and axisymmetric) and oscillatory strips (axisymmetric or nonaxisymmetric), are observed, depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process are also discussed.     

Dielectric studies in dilute solutions

Dielectric studies in dilute solutions of cyclohexane and benzene have been carried out in the temperature range 294–318°K. The observed data have been utilized to evaluate the relaxation times and thermodynamic parameters of these molecules. The high values ofα for 2-acetyl pyridine indicate the occurrence of more than one relaxation time. In the remaining systems, the observed lowα values indicate their rigid behaviour. The variation in the dielectric relaxation time is mostly correlated with the change in the heterocyclic configuration of the system.     

Irreversible adsorption of colloid particles on heterogeneous surfaces

Irreversible adsorption of polystyrene latex particles of micrometer size range at heterogeneous surfaces was studied experimentally. Model substrate surfaces of controlled site coverage (heterogeneity degree) used in these studies were produced by preadsorption of positively charged latex particles on mica sheets. Deposition kinetics of latex was studied as a function of the site coverage, particle to site size ratio λ and ionic strength of the colloid suspension. Particle distributions over surfaces and coverage were quantitatively evaluated by the direct microscope observation techniques using the diffusion cell. In this way, pair correlation function for various coverage degree and particle size ratio was evaluated. It also was determined the dependence of the jamming coverage of colloid particles on site coverage and ionic strength of the suspension. It was demonstrated that the decrease in the ionic strength of the suspension resulted in a significant decrease in the jamming coverage. This was attributed to the effect of the electrostatic field generated by the interface whose range was increased for low ionic strength. These experimental data revealed, in accordance with theoretical predictions derived from numerical simulations, that the multiple site coordination exerted a pronounced effect on the jamming coverage and the structure of adsorbed layers. It also was shown that this effect can be regulated by changes in the ionic strength of particle suspensions. This could allow one to produce particle clusters at the surface of targeted composition.     

Rheological observation of glassy dynamics of dilute polymer solutions near the coil-stretch transition in elongational flows

It has long been conjectured that the macroscopic dynamics of dilute polymer solutions may exhibit a glasslike slowdown caused by ergodicity breaking, in the vicinity of the coil-stretch transition in elongational flows. We report experimental observations using a filament stretching rheometer that confirm the existence of such glassy states. It is observed that different time-dependent elongational strain-rate profiles lead to a pronounced history dependence and aging effects within a narrow range of strain rates. The results have a direct bearing on the analysis and design of processes employing dilute polymer solutions, such as ink-jet printing, surface coating, and turbulent-drag reduction.     

Critical behavior of dilute electrolyte solutions

A theory of the critical behavior of a dilute ionic solution is constructed. An expression for the susceptibility in a wide temperature range is obtained. It is shown that ionic solutions belong to the universality class of the Ising model. The Ginzburg parameter of the ionic solutions decreases with the increase of the solvent concentration. In the general case, the critical exponent of susceptibility nonmonotonically depends on the temperature in the crossover region from the Ising-like to the mean-field behavior. In the vicinity of the transition point, the Debye-Hückel screening radius is proportional to the correlation length. As T→T _c, the screening radius tends to infinity and the screening disappears. The voltage between the two phases of the ionic solution is proportional to the order parameter and changes as |T/T _c?1|^β in the vicinity of the phase transition point.     

Irreversibility and polymer adsorption

Physisorption or chemisorption from dilute polymer solutions often entails irreversible polymer-surface bonding. We present a theory of the resultant nonequilibrium layers. While the density profile and loop distribution are the same as for equilibrium layers, the final layer comprises a tightly bound inner part plus an outer part whose chains make only fN surface contacts where N is chain length. The contact fractions f follow a broad distribution, P(f) approximately f(-4/5), in rather close agreement with strong physisorption experiments [H. M. Schneider, Langmuir 12, 994 (1996)]].     

Mesomorphic polymer solutions

Summary A mean-field theory for the nematic-isotropic phase transition in semi-rigid polymer solutions is proposed. Phase diagrams are calculated. New effects due to chain flexibility are found for the transition temperature and the nematic order parameter of the polymer. An abrupt increase of chain extension in the nematic phase is demonstrated. Paper presented at the ?Meeting on Lyotropics and Related Fields?, held in Rende, Cosenza, September 13–18, 1982.     

Counterion phase transitions in dilute polyelectrolyte solutions

In dilute solutions of rodlike polyelectrolytes some counterions are distributed far from polyions while others are located in their vicinity in the regions of cylindrical symmetry of the electrostatic potential. For these cylindrical regions around rodlike polyelectrolytes we find an exact solution of the nonlinear Poisson-Boltzmann equation for the case of nonzero net charge in these regions. This exact solution implies three qualitatively different phases of counterion distribution around the polyions with second order phase transitions between these phases.     

Chirooptical effects in dilute solutions of gelators

The chirooptical properties of a number of compounds in a variety of achiral solvents are studied. The results are interpreted within the framework of the standard model of chiral molecules. It is demonstrated that, with increasing concentration, chiral aggregates emerge, up to the formation of a macrophase (strings), which radically changes the chirooptical characteristics of the solution.