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We arrange the loopwise perturbation theory for the critical viscosity exponent x(eta), which happens to be very small, as a power series in x(eta) itself, and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by x(eta)=(8/15pi(2))(1+8/3pi(2)) approximately 0.0685.
This study presents a solvable model in renormalization group analysis for the effective eddy viscosity. It is found fruitful to take a simple hypothesis that large-scale eddies are statistically independent of those of smaller scales. A limiting operation of renormalization group analysis yields an inhomogeneous ordinary differential equation for the invariant effective eddy viscosity. The closed-form solution of the equation facilitates derivations of an expression of the Kolmogorov constant C(K) and of the Smagorinsky model for large-eddy simulation of turbulent flow. The Smagorinsky constant C(S) is proportional to C(3/4)(K). In particular, we shall illustrate that the value of C(K) ranges from 1.35 to 2.06, which is in close agreement with the generally accepted experimental values (1.2 approximately 2.2).
We report a study of viscosity by the method of Helfand moment in systems with periodic boundary conditions. We propose a new definition of Helfand moment which takes into account the minimum image convention used in molecular dynamics with periodic boundary conditions. Our Helfand-moment method is equivalent to the method based on the Green-Kubo formula and is not affected by ambiguities due to the periodic boundary conditions. Moreover, in hard-ball systems, our method is equivalent to that developed by Alder, Gass, and Wainwright [J. Chem. Phys. 53, 3813 (1970)]. We apply and verify our method in a fluid composed of N> or =2 hard disks in elastic collisions. We show that the viscosity coefficients already take values in good agreement with Enskog's theory for N=2 hard disks in a hexagonal geometry.
In the selective withdrawal experiment, fluid is withdrawn through a tube with its tip suspended above a two-fluid interface. At sufficiently high flow rates, the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a spout. Previous experiments address the scalings and similarity profiles characterizing steady states of the system near the transition for one combination of fluids. In the present study, we show that these scalings and similarity profiles extend to systems with different viscosity ratios. Surprisingly, we find no dependence of the scalings and similarity profiles on the lower fluid viscosity. We use the results of a low-Reynolds-number flow dimensional analysis to show that for different fluid combinations the curves denoting the transition straw height as a function of flow rate can be collapsed. Finally, these results are used to argue that in the low-Reynolds-number regime, the capillary length sets the scale for the final curvature of the interface before the transition.
We demonstrate, by using suitable shell models, that drag reduction in homogeneous turbulence is usefully discussed in terms of a scale-dependent effective viscosity. The essence of the phenomenon of drag reduction found in models that couple the velocity field to the polymers can be recaptured by an "equivalent" equation of motion for the velocity field alone, with a judiciously chosen scale-dependent effective viscosity that succinctly summarizes the important aspects of the interaction between the velocity and the polymer fields. Finally, we clarify the differences between drag reduction in homogeneous and in wall bounded flows.
A self-consistent mode-coupling calculation of the critical viscosity exponent z(eta) for classical fluids is performed by including the memory effect and the vertex corrections. The incorporation of the memory effect is through a self-consistency procedure that evaluates the order parameter and shear momentum relaxation rates at nonzero frequencies, thereby taking their frequency dependence into account. This approach offers considerable simplification and efficiency in the calculation. The vertex corrections are also demonstrated to have significant effects on the numerical value for the critical viscosity exponent, in contrast to some previous theoretical work which indicated that the vertex corrections tend to cancel out from the final result. By carrying out all of the integrations analytically, we have succeeded in tracing the origin of this discrepancy to an error in earlier work. We provide a thorough treatment of the two-term epsilon expansion, as well as a complete three-dimensional analysis of the fluctuating order-parameter and transverse hydrodynamic modes. The study of the interactions of these modes is carried out to high order so as to arrive at z(eta) = 0.0679+/-0.0007 for comparison with the experimentally observed value, 0.0690+/-0.0006 .
We present molecular dynamics simulation results for the viscosity and mutual diffusion constant of a strongly asymmetric binary ionic mixture. We compare the results with available theoretical models previously tested for much smaller asymmetries. For the case of viscosity we propose a predictive framework based on the linear mixing rule, while for mutual diffusion we discuss some consistency problems of widely used Boltzmann-equation-based models.
The different finger morphologies that arise at the interface separating two immiscible fluids in a rotating Hele-Shaw cell are studied numerically. The whole range of viscosity contrast is analyzed and a variety of fingering patterns systematically introduced, including the case in which the inner fluid is less viscous than the outer one. Our numerical results demonstrate that both the magnitude and the sign of the viscosity contrast strongly affect the shape of the emerging fingers, and also their length distribution. We have also found that the occurrence and location of pinch-off singularities are remarkably modified when the inner fluid is less viscous: instead of generating an isolated detaching drop, a full finger is disconnected from the interface. Finally, we have verified that the finger competition phenomena revealed by our simulations are correctly predicted by a weakly nonlinear analysis of the pattern development, showing that such important finger competition dynamics is already set at relatively early stages of interfacial evolution.
We propose a relation which predicts the low-frequency thermal conductivity of a one-dimensional (1D) system from the thermal conductivity and bulk viscosity at higher frequency. Our theory is based on the assumption that "ballistic" transport by sound waves dominates the heat transport. For a system with equal heat capacities (c(p) = c(v)) this relation is particularly simple. We test the prediction by simulating a chain of particles with quartic interparticle potentials under zero pressure conditions. As the frequency omega --> 0 the theory predicts that the energy current power spectrum diverges as omega(-1/2), not seen in previous simulations. Because we simulate very long chains to long times we do observe the crossover into this regime. The bulk viscosity of a 1D chain has been determined via simulation. It is found to be finite for our system, in contrast to the thermal conductivity which is infinite.
We deduce the thermophysical properties of near-critical xenon from measurements of the frequencies and half-widths of the acoustic resonances of xenon maintained at its critical density in centimeter-sized cavities. In the reduced temperature range 1 x 10-3<(T-Tc)/Tc<7 x 10 (-6), we measured the resonance frequency and quality factor (Q) for each of six modes spanning a factor of 27 in frequency. As Tc was approached, the frequencies decreased by a factor of 2.2 and the Q's decreased by as much as a factor of 140. Remarkably, these results are predicted (within +/-2% of the frequency and within a factor of 1.4 of Q) by a model for the resonator and a model for the frequency-dependent bulk viscosity zeta(omega) that uses no empirically determined parameters. The resonator model is based on a theory of acoustics in near-critical fluids developed by Gillis, Shinder, and Moldover [Phys. Rev. E 70, 021201 (2004)]. In addition to describing the present low-frequency data (from 120 Hz to 7.5 kHz), the model for zeta(omega) is consistent with ultrasonic (0.4--7 MHz) velocity and attenuation data from the literature. However, the model predicts a peak in the temperature dependence of the dissipation in the boundary layer that we did not detect. This suggests that the model overestimates the effect of the bulk viscosity on the thermal boundary layer. In this work, the acoustic cavities were heated from below to stir the xenon, thereby reducing the density stratification resulting from Earth's gravity. The stirring reduced the apparent equilibration time from several hours to a few minutes, and it reduced the effective temperature resolution from 60 mK to approximately 2 mK, which corresponds to (T-Tc)/Tc approximately =7 x 10(-6).
The five nematiclike viscosity coefficients corresponding to the Smectic-C* (SmC*) phase are calculated by a combination of the existing statistical-mechanical approach and NMR theory, based on a rotational diffusion model for two ferroelectric smectogens. The order parameter S2, the smectic tilt angle Theta, and the rotational diffusion coefficient D(perpendicular), corresponding to molecular tumbling in the SmC* phase, for the ferroelectric smectogens 4-[4'-(1-methylheptyloxy)]biphenyl'-(10-undecenyloxy)benzoate and (S)-[4-(2-methylbutyl)phenyl]-4'-n-octylbiphenylcarboxylate have been obtained by means of 2H NMR spectroscopy and these data have been used to calculate viscosity quantities. For practical purposes a specific form of the functional dependence of S4 on S2 is used. As the main result, our calculations also predict a laminar flow regime in a high shear flow for these liquid crystal compounds.
The increase in viscosity that is observed in attractive colloidal systems by varying the temperature or the volume fraction can be related to the formation of structures due to particle aggregation. In particular we have studied the nontrivial dependence of the viscosity from the temperature and the volume fraction in the copolymer-micellar system L64. The comparison of the experimental data with the results of numerical simulations in a simple model for gelation phenomena suggests that this intriguing behavior can be explained in terms of cluster formation and that this picture can be quite generally extended to other attractive colloidal systems.
The pretransitional equilibrium properties of isotropic liquids in the proximity of the isotropic-nematic phase transition are well known and successfully modeled. Much less is known about the dynamic behavior, and in particular about the pretransitional viscosity. In this work we combine two techniques [dynamic light scattering (DLS) and electric birefringence spectroscopy (EBS)] offering complementary insights into both static and dynamic pretransitional behavior of the homologous nCB family (n-alkyl cyanobiphenyl). EBS explores the single molecule flipping dynamics retarded by a paranematic potential barrier and enables extracting the associated transport coefficient, which is found to be of Arrhenius type in the whole temperature range explored. DLS reflects the collective dynamics of correlated domains and depends on the viscous damping of the orientational order. Such a viscosity displays Arrhenius behavior only sufficiently far from the transition temperature, with deviations growing as a power law of the appropriate reduced temperature with exponents around 0.1.
We report three-dimensional parallel Lagrangian particle simulations using the lattice Boltzmann method, conducted at a low Reynolds number. Using modified Lees-Edwards boundary conditions and directly calculated viscous dissipation, we show that it is possible to recover excellent agreement with the Einstein viscosity formula in the low concentration limit and to predict viscosity corrections for larger concentrations.
In order to understand the long known anomalies in the composition dependence of diffusion and viscosity of binary mixtures, we introduce here two new models and carry out extensive molecular dynamics simulations. In these models, the two molecular species (A and B) have the same diameter and mass. In model I the interspecies interaction is more attractive than that between the pure components, while the reverse is true for model II. Simulations and mode coupling theory calculations reveal that the models can capture a wide variety of behavior observed in experiments, including the reentrant viscosity dependence of relaxation time.
Using the anti-de Sitter/conformal field theory correspondence, we relate the shear viscosity eta of the finite-temperature N = 4 supersymmetric Yang-Mills theory in the large N, strong-coupling regime with the absorption cross section of low-energy gravitons by a near-extremal black three-brane. We show that in the limit of zero frequency this cross section coincides with the area of the horizon. From this result we find eta = pi / 8N(2)T3. We conjecture that for finite 't Hooft coupling g(2)(YM)N the shear viscosity is eta = f(g(2)(YM)N)N2T3, where f(x) is a monotonic function that decreases from O(x(-2)ln(-1)(1/x)) at small x to pi/8 when x-->infinity.
Measurements of the viscosity in quiescent magnetized pure-electron plasmas are up to 10(8) times larger than predicted by classical collisional theory. This strong viscosity is due to long-range " E x B drift collisions" between electrons separated by up to a Debye length. Recent theories of long-range collisions show order-of-magnitude agreement with the measurements, but do not give the observed dependence on the plasma column length. A simple empirical scaling law fits the length and magnetic field dependence surprisingly well.
Motivated by turbulent drag reduction by minute concentrations of polymers we study the effects of minor viscosity contrasts on the stability of hydrodynamic flows. The key player is a localized region where fluctuations are produced by interactions with the mean flow (the "critical layer"). We show that a layer of weakly space-dependent viscosity placed near the critical layer has a very large stabilizing effect on hydrodynamic fluctuations, retarding significantly the onset of turbulence. The effect is not due to a modified dissipation (as is assumed in theories of drag reduction) but is due to reduced energy intake from the mean flow to the fluctuations. Similar physics may act in turbulent drag reduction.