Low Viscosity Regime Research Articles

DIFFERENTIALLY ROTATING WHITE DWARFS. I. REGIMES OF INTERNAL ROTATION

ABSTRACT Most viable models of Type Ia supernovae (SNe Ia) require the thermonuclear explosion of a carbon/oxygen white dwarf that has evolved in a binary system. Rotation could be an important aspect of any model for SNe Ia, whether single or double degenerate, with the white dwarf mass at, below, or above the Chandrasekhar limit. Differential rotation is specifically invoked in attempts to account for the apparent excess mass in the super-Chandrasekhar events. Some earlier work has suggested that only uniform rotation is consistent with the expected mechanisms of angular momentum transport in white dwarfs, while others have found pronounced differential rotation. We show that if the baroclinic instability is active in degenerate matter and the effects of magnetic fields are neglected, both nearly uniform rotation and strongly differential rotation are possible. We classify rotation regimes in terms of the Richardson number, Ri. At small values of Ri 0.1, we find both the low-viscosity Zahn regime with a nonmonotonic angular velocity profile and a new differential rotation regime for which the viscosity is high and scales linearly with the shear, σ. Employment of Kelvin–Helmholtz viscosity alone yields differential rotation. Large values of Ri ≫ 1 produce a regime of nearly uniform rotation for which the baroclinic viscosity is of intermediate value and scales as . We discuss the gap in understanding of the behavior at intermediate values of Ri and how observations may constrain the rotation regimes attained by nature.

Effect of plasma motion on tearing modes in cylindrical plasmas

The effect of equilibrium plasma motion on the resistive m/n = 2/1 tearing mode (TM) in low β plasmas is investigated in cylindrical geometry (with m and n being poloidal and toroidal mode numbers). Without equilibrium plasma motion but with viscosity, the TM stability is mainly determined by the Reynolds number S and reaches maximum near S = 104, which is consistent with previous findings. The poloidal plasma rotation has stabilizing effect on TM; however, the rotation shear has destabilization effect in the low viscosity regime. The axial plasma motion has strong stabilizing effect on TM in the low viscosity regime for Prandtl number Pr < 1, while its shear has slight stabilizing effect with the decrease of growth rate less than 15%. When the axial velocity becomes large enough, the mode frequency tends to be independent of the Prandtl number. In the presence of parallel plasma motion, the growth rate is determined by the axial component at low parallel velocity, while determined by poloidal component at large parallel velocity. The parallel plasma motion drives the TM rotating in the opposite direction. It is shown that the equilibrium motion reduces the growth rate of TM by changing the phase difference and coupling coefficient between potential perturbation and magnetic flux perturbation (deviating from π/2), which results in a lower mode frequency. Compared to the role of velocity shear, the magnitude of plasma velocity itself at the m/n = 2/1 rational surface is dominant in determining the TM characteristics.

S-shaped flow curves of shear thickening suspensions: direct observation of frictional rheology.

We study the rheological behavior of concentrated granular suspensions of simple spherical particles. Under controlled stress, the system exhibits an S-shaped flow curve (stress vs shear rate) with a negative slope in between the low-viscosity Newtonian regime and the shear thickened regime. Under controlled shear rate, a discontinuous transition between the two states is observed. Stress visualization experiments with a fluorescent probe suggest that friction is at the origin of shear thickening. Stress visualization shows that the stress in the system remains homogeneous (no shear banding) if a stress is imposed that is intermediate between the high- and low-stress branches. The S-shaped shear thickening is then due to the discontinuous formation of a frictional force network between particles upon increasing the stress.

Penetration of resonant magnetic perturbations in a rotating tokamak plasma with neoclassical poloidal viscosity

The penetration of time-dependant resonant magnetic perturbations (RMPs) is numerically studied by means of reduced magnetohydrodynamic simulations, taking into account the neoclassical poloidal viscosity (NPV) damping. It is found that with the increase of the RMP growth rate, the scalings of penetration threshold on resistivity as well as viscosity are significantly weakened in both viscoresistive and resistive-inertial regimes. In the high neoclassical viscosity regime, the scalings on neoclassical viscosity νnc are numerically obtained in the cases of different RMP growth rate and viscosity ν. In the low neoclassical viscosity regime, νnc almost has no effect on penetration threshold, which is unlike ν. Moreover, the synergistic effect of both νnc and ν on the threshold is discussed as well. Finally, the role of the NPV in the torque balance is analysed. It is shown that the NPV tends to restore the velocity profile in the vicinity of the rational surface.

Dynamical approach to weakly dissipative granular collisions.

Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually (but admittedly not always), constant coefficients of restitution are introduced phenomenologically to account for energy dissipation when grains collide. The collisions are assumed to be instantaneous and to conserve momentum. Here, we introduce the dissipation through a viscous (velocity-dependent) term in the equations of motion for two colliding grains. Using a first-order approximation, we solve the equations of motion in the low viscosity regime. This approach allows us to calculate the collision time, the final velocity of each grain, and a coefficient of restitution that depends on the relative velocity of the grains. We compare our analytic results with those obtained by numerical integration of the equations of motion and with exact ones obtained by other methods for some geometries.

Electron spin-lattice relaxation mechanisms of nitroxyl radicals in ionic liquids and conventional organic liquids: temperature dependence of a thermally activated process.

During the past two decades, several studies have established a significant role played by a thermally activated process in the electron spin relaxation of nitroxyl free radicals in liquid solutions. Its role has been used to explain the spin relaxation behavior of these radicals in a wide range of viscosities and microwave frequencies. However, no temperature dependence of this process has been reported. In this work, our main aim was to investigate the temperature dependence of this process in neat solvents. Electron spin-lattice relaxation times of 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) and 4-hydroxy-TEMPO (TEMPOL), in X-band microwave frequency, were measured by the pulse saturation recovery technique in three room-temperature ionic liquids ([bmim][BF4], [emim][BF4], and [bmim][PF6]), di-isononyl phthalate, and sec-butyl benzene. The ionic liquids provided a wide range of viscosity in a modest range of temperature. An auxiliary aim was to examine whether the dynamics of a probe molecule dissolved in ionic liquids was different from that in conventional molecular liquids, as claimed in several reports on fluorescence dynamics in ionic liquids. This was the reason for the inclusion of di-isononyl phthalate, whose viscosities are similar to that of the ionic liquids in similar temperatures, and sec-butyl benzene. Rotational correlation times of the nitroxyl radicals were determined from the hyperfine dependence of the electron paramagnetic resonance (EPR) line widths. Observation of highly well-resolved proton hyperfine lines, riding over the nitrogen hyperfine lines, in the low viscosity regime in all the solvents, gave more accurate values of the rotational correlation times than the values generally measured in the absence of these hyperfine lines and reported in the literature. The measured rotational correlation times obeyed a modified Stokes-Einstein-Debye relation of temperature dependence in all solvents. By separating the contributions of g-anisotropy, A-anisotropy and spin-rotation interactions from the observed electron spin-lattice relaxation rates, the contribution of the thermally activated process was obtained and compared with its expression for the temperature dependence. Consistent values of various fitted parameters, used in the expression of the thermal process, have been found, and the applicability of the expression of the thermally activated process to describe the temperature dependence in liquid solutions has been vindicated. Moderate solvent dependence of the thermally activated process has also been observed. The rotational correlation times and the spin-lattice relaxation processes of nitroxyls in ionic liquids and in conventional organic liquids are shown to be explicable on a similar footing, requiring no special treatment for ionic liquids.

Speed of Conformational Change: Comparing Explicit and Implicit Solvent Molecular Dynamics Simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

Opto-mechano-fluidic viscometer

The recent development of opto-mechano-fluidic resonators has provided—by harnessing photon radiation pressure—a microfluidics platform for the optical sensing of fluid density and bulk modulus. Here, we show that fluid viscosity can also be determined through optomechanical measurement of the vibrational noise spectrum of the resonator mechanical modes. A linear relationship between the spectral linewidth and root-viscosity is predicted and experimentally verified in the low viscosity regime. Our result is a step towards multi-frequency measurement of viscoelasticity of arbitrary fluids, without sample contamination, using highly sensitive optomechanics techniques.

A phase field description of self-propulsion of twin sessile drops induced by surface tension gradients

We describe the self-propulsion of two sessile drops induced by surface tension gradients at the droplet interfaces using a three-dimensional phase field model. We study the problem for the low viscosity regime when the width of the connecting neck between the interacting drops increases linearly with increasing t1/2 and the merger is dominated by capillary forces. We investigate the dependence of the displacement achieved by self-propulsion on viscous shearing as well as the internal flow structure during the coalescence process.

A new and easy surface functionalization technnology for monitoring wettability in heterogeneous nano- and microfluidic devices

We have developed a new and easy surface functionalization technology for monitoring wettability in heterogeneous nano- and microfluidic devices. This technology is based on mussel inspired, dopamine chemistry and it permits to end-graft hydrophilic polymer brushes onto virtually any surface in a low-viscosity regime. We have successfully modified a variety of different solid surfaces, such as Si, SiO2, Ag, Cu, SU8 and PDMS. The modified surfaces were characterized by water contact angle measurements, atomic force microscopy, cyclic voltammetry and by electrokinetic measurements. The adsorption of proteins on the unmodified and modified surfaces was probed with fluorescently labeled albumin. We clearly demonstrated that the studied surfaces became non-fouling when modified with a hydrophilic, polyacrylamide brush, while they remained protein adsorbing when unmodified and/or modified with the dopamine film only. We believe that this universal surface modification approach will be extremely useful in nano- and micro-fluidic devices build from a variety of different materials.

ACCRETION OF JUPITER-MASS PLANETS IN THE LIMIT OF VANISHING VISCOSITY

In the core-accretion model the nominal runaway gas-accretion phase brings most planets to multiple Jupiter masses. However, known giant planets are predominantly Jupiter-mass bodies. Obtaining longer timescales for gas accretion may require using realistic equations of states, or accounting for the dynamics of the circumplanetary disk (CPD) in low-viscosity regime, or both. Here we explore the second way using global, three-dimensional isothermal hydrodynamical simulations with 8 levels of nested grids around the planet. In our simulations the vertical inflow from the circumstellar disk (CSD) to the CPD determines the shape of the CPD and its accretion rate. Even without prescribed viscosity Jupiter's mass-doubling time is $\sim 10^4$ years, assuming the planet at 5.2 AU and a Minimum Mass Solar Nebula. However, we show that this high accretion rate is due to resolution-dependent numerical viscosity. Furthermore, we consider the scenario of a layered CSD, viscous only in its surface layer, and an inviscid CPD. We identify two planet-accretion mechanisms that are independent of the viscosity in the CPD: (i) the polar inflow -- defined as a part of the vertical inflow with a centrifugal radius smaller than 2 Jupiter-radii and (ii) the torque exerted by the star on the CPD. In the limit of zero effective viscosity, these two mechanisms would produce an accretion rate 40 times smaller than in the simulation.

Viscosity-dependent structural fluctuation of the M80-containing Ω-loop of horse ferrocytochrome c

To determine the effect of solvent viscosity on low-frequency local motions that control the slow changes in structural dynamics of proteins, we have studied the effects of solvent viscosity on the structural fluctuation of presumably the M80-containing Ω-loop by measuring the rate of thermally-driven CO-dissociation from a natively-folded carbonmonoxycytochrome c (NCO-state) in the 0.65–92.5cP range of viscosity at pH 7.0. At low viscosities (⩽8cP), the rate coefficient, kdiss for dissociation of CO from the NCO-state varies inversely with the viscosity, but saturates at high viscosities, suggesting that CO-dissociation reaction involves sequential stages that depend differently on solvent friction, i.e., solvent coupled and nonsolvent-coupled stages of the process. In the low viscosity regime (0.65⩽ηs⩽8.0cP), the rate-viscosity data were fitted to modified Kramers model, kdiss=[A′/(σ+ηs)n]exp(−ΔG/RT), which produced internal friction, σ=1.35cP (±0.88), which suggests that the speed of CO-dissociation from NCO at ηs⩽8.0cP is controlled by internal friction.

Evolution of primordial magnetic fields from phase transitions

We consider the evolution of primordial magnetic fields generated during cosmological, electroweak or QCD, phase transitions. We assume that the magnetic field generation can be described as an injection of magnetic energy to cosmological plasma at a given scale determined by the moment of magnetic field generation. A high Reynolds number ensures strong coupling between magnetic field and fluid motions. The subsequent evolution of the magnetic field is governed by decaying hydromagnetic turbulence. Both our numerical simulations and a phenomenological description allow us to recover "universal" laws for the decay of magnetic energy and the growth of magnetic correlation length in the turbulent (low viscosity) regime. In particular, we show that during the radiation dominated epoch, energy and correlation length of non-helical magnetic fields scale as conformal time to the powers -1/2 and +1/2, respectively. For helical magnetic fields, energy and correlation length scale as conformal time to the powers -1/3 and +2/3, respectively. The universal decay law of the magnetic field implies that the strength of magnetic field generated during the QCD phase transition could reach $\sim 10^{-9}$\,G with the present day correlation length $\sim 50$ kpc. The fields generated at the electroweak phase transition could be as strong as $\sim 10^{-10}$ G with correlation lengths reaching $\sim 0.3$\,kpc. These values of the magnetic fields are consistent with the lower bounds of the extragalactic magnetic fields.

Note: Precision viscosity measurement using suspended microchannel resonators

We report the characterization of a suspended microchannel resonator (SMR) for viscosity measurements in a low viscosity regime (<10 mPa s) using two measurement schemes. First, the quality factor (Q-factor) of the SMR was characterized with glycerol-water mixtures. The measured Q-factor at 20 °C exhibits a bilinear behavior with the sensitivity of 1281 (mPa s)(-1) for a lower (1-4 mPa s) and 355 (mPa s)(-1) for a higher viscosity range (4-8 mPa s), respectively. The second scheme is the vibration amplitude monitoring of the SMR running in a closed loop feedback. When compared in terms of the measurement time, the amplitude-based measurement takes only 0.1 ~ 1 ms while the Q-factor-based measurement takes ~30 s. However, the viscosity resolution of the Q-factor-based measurement is at least three times better than the amplitude-based measurement. By comparing the Q-factors of heavy water and 9.65 wt.% glycerol-water mixture that have very similar viscosities but different densities, we confirmed that the SMR can measure the dynamic viscosity without the density correction. The obtained results demonstrate that the SMR can measure the fluid viscosity with high precision and even real-time monitoring of the viscosity change is possible with the amplitude-based measurement scheme.

Fluorescence Anisotropy of Molecular Rotors

We present polarization-resolved fluorescence measurements of fluorescent molecular rotors 9-(2-carboxy-2-cyanovinyl)julolidine (CCVJ), 9-(2,2-dicyanovinyl)julolidine (DCVJ), and a meso-substituted boron dipyrromethene (BODIPY-C(12)). The photophysical properties of these molecules are highly dependent on the viscosity of the surrounding solvent. The relationship between their quantum yields and the viscosity of the surrounding medium is given by an equation first described and presented by Förster and Hoffmann and can be used to determine the microviscosity of the environment around a fluorophore. Herein we evaluate the applicability of molecular rotors as probes of apparent viscosity on a microscopic scale based on their viscosity dependent fluorescence depolarization. We develop a theoretical framework, combining the Förster-Hoffmann equation with the Perrin equation and compare the dynamic ranges and usable working regimes for these dyes in terms of utilising fluorescence anisotropy as a measure of viscosity. We present polarization-resolved fluorescence spectra and steady-state fluorescence anisotropy imaging data for measurements of intracellular viscosity. We find that the dynamic range for fluorescence anisotropy for CCVJ and DCVJ is significantly lower than that of BODIPY-C(12) in the viscosity range 0.6<η<600 cP. Moreover, using steady-state anisotropy measurements to probe microviscosity in the low (<3 cP) viscosity regime, the molecular rotors can offer a better dynamic range in anisotropy compared with a rigid dye as a probe of microviscosity, and a higher total working dynamic range in terms of viscosity.

Semi-Lagrangian multistep exponential integrators for index 2 differential–algebraic systems

Implicit-explicit (IMEX) multistep methods are very useful for the time discretization of convection diffusion PDE problems such as the Burgers equations and the incompressible Navier–Stokes equations. In the latter as well as in PDE models of plasma physics and of electromechanical systems, semi-discretization in space gives rise to differential–algebraic (DAE) system of equations often of index higher than 1. In this paper we propose a new class of exponential integrators for index 2 DAEs arising from the semi-discretization of PDEs with a dominating and typically nonlinear convection term. This class of problems includes the incompressible Navier–Stokes equations. The integration methods are based on the backward differentiation formulae (BDF) and they can be applied without modifications in the semi-Lagrangian integration of convection diffusion problems. The approach gives improved performance at low viscosity regimes.

Non-Newtonian viscous shear thinning in ionic liquids

We have studied the shear thinning of several protic and aprotic ionic liquids (ILs) by stress-controlled rheometry, which indicated that some ILs exist as liquid phase aggregates that can be disrupted or broken at high shear rates. Increasing the temperature shifted the onset of shear thinning to higher frequency and indicated that a smaller or less cohesive aggregate was formed. However, upon application of a sufficiently high temperature, the sample resumed the characteristics of a Newtonian fluid. (HOEt)2NH.AcOH was selected as an example of a protic ionic liquid (PIL) to probe concentration effects on liquid ordering. At water concentrations lower than one equivalent per PIL component pair, the viscosity rapidly decreased, although the onset frequency of shear thinning remained constant. The shear thinning and low viscosity regime remained until approximately 3–4 equivalents of water were added and the PIL behaved as a Newtonian fluid. The effect of water on the shear thinning of (HOEt)2NH.AcOH indicated that small dilution volumes did not alter the aggregate structure, but instead reduced the number of aggregates. Both the temperature and additive water strongly suggested that the IL aggregates were due to intermolecular hydrogen bond networks.

Modelling texture perception by soft epithelial surfaces

This paper introduces a mechanistic approach to relate the sensations of touch by epithelial surfaces of for example skin, eye or mouth to the material properties of the substrate. The approach is to model the hydrodynamic and frictional forces exerted by the substrate onto the surfaces, which are deformable and compliant to these forces. Subsequently these forces are related to the neurological responses of the mechanoreceptors buried in these surfaces. The potential of the approach is illustrated for textural perception of food materials in the mouth. It leads to several concepts for textural perception in the mouth, some of which have been demonstrated previously and some of which are new. As a first example, the branching into high and low viscosity regimes for thickness perception found experimentally can be linked directly to the detection limit of the neural receptors. As a second example, by taking into account the intrinsic roughness and deformability of the papilla surface, estimates are obtained for the cross-over between the hydrodynamic friction regime, where the papilla tips are lubricated by a thin liquid film (smooth mouthfeel), and the boundary friction regime, where the papilla tips are in direct contact with the opposing surface of the palate (rough mouthfeel). This has implications for the role of viscosity on smoothness and astringency sensations. As a final example, the model suggests that the sensation of hard particles (grittiness) can be suppressed by increasing the viscosity of the medium, which is in agreement with experimental findings from sensory studies.

The construction of exact Taylor states. II: The influence of an inner core

The geodynamo mechanism, responsible for sustaining Earth’s magnetic field, is believed to be strongly influenced by the solid inner core through its influence on the structure of convection within the tangent cylinder. In the rapidly rotating low-viscosity regime of the geodynamo equations relevant to the Earth’s core, the magnetic field must satisfy a continuum of conditions known as Taylor’s constraint. Magnetic fields that satisfy this constraint, termed Taylor states, have the property that their axial magnetic torque vanishes when averaged over any geostrophic contour, cylinders of fluid coaxial with the rotational axis. In recent theoretical developments, we proved that when adopting a truncated spherical harmonic expansion, the continuous constraint in space reduced to a finite spectral set of conditions. Furthermore, an expedient choice of regular radial basis presents an under-determined problem when constructing Taylor states in a full-sphere showing the ubiquity of such solutions. A spherical-shell geometry, with a conducting inner core, complicates the formulation of Taylor’s constraint due to the partitioning of the geostrophic contours into three distinct regions, ostensibly trebling the stringency of the constraint. This raises questions as to the admissible structures of such Taylor states, and their relation to those in a full-sphere. In this paper, we address these issues in two stages. First, we present a mathematical characterisation of the structure of Taylor’s constraint in a spherical-shell. We then enumerate the effective number of conditions that must be satisfied by any magnetic field that is everywhere C ∞ inside the core, and show that, assuming an equal truncation in radial and solid angle representation, the number of conditions is approximately 5/3 times that for a full-sphere Taylor state. Second, we investigate the influence of the inner core on the structure of admissible Taylor states by constructing a low-degree family of optimally smooth observationally consistent examples in both a spherical-shell and a full-sphere. We show that the introduction of an inner core into a full-sphere increases the minimum magnetic field complexity, simply by virtue of the increased potency of Taylor’s constraint, a trait more pronounced in our quasi-axisymmetric models. We speculate that axisymmetric dynamo-generated exact Taylor states, particularly those generated in a spherical-shell, in general have small radial length scales that may be difficult to resolve.

Computing the viscosity of supercooled liquids

We describe an atomistic method for computing the viscosity of highly viscous liquids based on activated state kinetics. A basin-filling algorithm allowing the system to climb out of deep energy minima through a series of activation and relaxation is proposed and first benchmarked on the problem of adatom diffusion on a metal surface. It is then used to generate transition state pathway trajectories in the potential energy landscape of a binary Lennard-Jones system. Analysis of a sampled trajectory shows the system moves from one deep minimum to another by a process that involves high activation energy and the crossing of many local minima and saddle points. To use the trajectory data to compute the viscosity we derive a Markov Network model within the Green-Kubo formalism and show that it is capable of producing the temperature dependence in the low-viscosity regime described by molecular dynamics simulation, and in the high-viscosity regime (10(2)-10(12) Pa s) shown by experiments on fragile glass-forming liquids. We also derive a mean-field-like description involving a coarse-grained temperature-dependent activation barrier, and show it can account qualitatively for the fragile behavior. From the standpoint of molecular studies of transport phenomena this work provides access to long relaxation time processes beyond the reach of current molecular dynamics capabilities. In a companion paper we report a similar study of silica, a representative strong liquid. A comparison of the two systems gives insight into the fundamental difference between strong and fragile temperature variations.